Bridge V+ BIDDING

by Timothy R. Scanlan

© copyright 2020-2023 by Timothy R. Scanlan

INTRODUCTION

This handbook describes the method of bidding used by Bridge V+. It won't teach you how to bid if you know nothing at all about Contract Bridge: however, it will prepare you to know what to expect, and what not to expect from Bridge V+ bidding, and how you should bid in a way that the program will know what you mean. The handbook assumes that you already know the absolute basics about card play in Whist-type games, that is you know what tricks are, that the ace is the highest card in a suit, and such like.

If you are an experienced player, you should be able to read through the text, take note of certain points as you go along, and then only on rare occasions refer back to the handbook. You will most likely only study a few of the sections in detail.

Bridge V+ uses a few bidding conventions as standard, and gives you the possibility of choosing some others via Game Preferences. The handbook covers all these conventions and variants. However, if you use a convention that Bridge V+ has not been programmed for, the result may be disappointing. Unlike a human, Bridge V+ cannot consider an unexpected bid, and use its knowledge of Bridge to figure out something reasonable. This is because Bridge V+ has no knowledge of Bridge. It can follow an immense complexity of rules, beyond anything that any human would attempt, but if something falls outside the rules, the result is unpredictable.

If you are an inexperienced player, perhaps even a rank beginner, Bridge V+ proposes several methods to help you to learn, and to improve. First, the application guide (click on the teacher-owl in the top left-hand corner of the screen) will give you the very basics of Bridge. Following that, you can use this handbook to discover the system of bidding used by Bridge V+.

Initially, you might just want to read fairly rapidly through the handbook, without trying to assimilate all the material, just to get familiar with the basics. Then, it’s probably best just to start playing the app! You can refer to the handbook whenever you want to, and in addition you have several other features in the program to help you. And you will never find a partner or Bridge teacher as patient as Bridge V+!

The Hint button (“?”) will tell you what bid or what play Bridge V+ would make in your place. Using this might get you out of a spot, and allow you to get on with the hand. Sometimes the suggestion might make sense to you on reflection; even if it doesn't, you can make the bid, then click on the bid in the record of bidding to see what the Info feature says about it. Bridge V+ will tell you what your partner should understand by your bidding up to that point (including the information given by the bid itself). This will include suits held, their probable lengths, evaluation points, and sometimes aces and kings. If you still don’t understand the bid, check the handbook. If you still don’t understand, ask a friend who plays well (but don't do this too often!).

When your partner (Bridge V+) makes its bid, you can check what the program would have understood in your place, by tapping on partner's bid. For this, the program never uses its knowledge of the actual cards in the hand (to which it of course has access in computer memory), but only what the bidding rules would have implied. You can use this Info feature on any of the bids in the bidding record, including passes.

As you play through the game, you can use the Review button (a solid left-pointing triangle) to see the bids made so far. If you wish, you can even see how many cards have been played in a particular suit, or whether a particular card is still in play. You shouldn’t use this feature too much, because in a real game of Bridge with humans you won’t be able to do it! You can also use the Review button to go back to a previous point in the bidding or the play, where you think you may have made an error, or when you are just interested to see what would happen if you do something differently.

At the end of the play, Bridge V+ will show the “Hand Over” screen, giving the result of the game, and what result Bridge V+ would have had in your place. Don’t be upset if Bridge V+ often does better than you: if you’re a beginner that will probably happen quite a lot. However, you can take advantage of this situation to learn. You can use the Review button to see how Bridge V+ would have bid and played the hand. Tap on the bid or card from which you want to start, then use the Autoplay button (the Infinity sign) to watch Bridge V+ bid and then play the cards in all the hands. If this goes too fast, go back to some point in the play, and use the Hint “?” button to step slowly through the play.

All the examples used in the handbook are actual deals taken from Bridge V+. I have taken great care in choosing the examples, and in analysing the bidding sequences, but I am not a professional Bridge expert, and I expect that I've made some mistakes here and there. I shall welcome any remarks and commentaries that will allow me to make this handbook (and the Bridge engine) better, and shall keep it up to date as Bridge V+ evolves.

It is quite possible, also, that as I make changes to the program, the program will not behave the same in one or more examples. I hope this does not happen, but please tell me if it does, and I'll change the example, or correct the program, or both!

I shall also welcome suggestions for additions to the program. We do occasionally get users asking for their favourite bidding convention or variant (or even a variant of a variant!), but it is very difficult to know just how popular each convention is, and so far I have preferred to err on the side of keeping things simple so as not to confuse inexperienced users, while improving as much as possible the quality of bidding and play within the adopted constraints.

I welcome problem reports, especially when the program does something particularly silly. For the moment, it is still fairly easy for me to find occasions where the program does not make the best bid, or the best play, so having too many reports would be unmanageable, but I always try to correct glaring errors as quickly as possible. Please, if you do report a problem, make sure that you give the Deal No and the dealer, the bidding conventions that you have set, and any bids that you made, so that I can reproduce the situation.

I have chosen to describe the bidding assuming the Conventions set by Bridge V+ in Tournaments mode, and have reserved a section later in the handbook to examine some cases where different variants are chosen. I found that if there are too many digressions during the main text to consider what would happen if you were not using one or another convention, the explanation can become confusing and difficult to follow.

In Tournaments mode, the East/West partnership always bids using the default convention settings described in "Bidding Conventions". North/South conventions are set to the last settings by the user in Rubber Bridge or Chicago Bridge modes. During Tournaments mode also, almost all of the Help features are turned off.

The organization of the Handbook reflects closely the organization of the code in the Bridge V+ bidding engine. In a way, the Handbook provides the user with the technical specifications that have guided the implementation of the program. The biggest difference is that you, the user, will be able to apply the general rules described in the Handbook, while if I have forgotten something, or programmed something badly, the program may well do something stupid! Please accept my apologies in advance, for any such occurrence.

Tim Scanlan, June 29th, 2020

Updated: November 2023

EVALUATING THE HAND

Before making any bid, you need to evaluate your hand. Bridge V+ uses various methods for this, depending on exact circumstances, and these will all be presented in this section. The points-count system, invented in the early days of Contract Bridge, is the most important.

High-Card Points (HCP)

High-card points reflect the relative trick-taking potential of high cards in the hand: the picture-cards are valued as follows: Ace = 4; King = 3; Queen = 2; Jack = 1. (In this handbook, the term "honours" is used to refer to the picture-cards, plus the 10-spot).

Distribution Points

Short suits have value in suit contracts, since trumps can be used to take tricks in the suit once all the cards initially held in the suit have been played. The values assigned to short suits are as follows:

Ø Void (no card in a suit) = 3 points

Ø Singleton (one card) = 2 points

Ø Doubleton (two cards) = 1 point

In addition, to better appreciate the value of long suits, an extra point is added for each card from the sixth in a given suit. Thus a 6-3-2-2 hand is favoured over 5-4-2-2, and so on.

Singleton honours are very tricky to evaluate, and different authorities recommend slightly different methods. Bridge V+ counts 4 points (HCP + distribution) for a singleton King. Singleton Queens or Jacks are allotted only their distributional value of 2 points.

An extra point is counted for some particularly strong two-suit combinations with good honours in both suits (at least QJ, or K): this applies to holdings of 5-5, 6-4, 6-5 or 6-6. The six-card suits still each receive an extra point for length as stated above.

Other points may be added during the bidding to express particularly favourable holdings in relation to partner or opponents. Throughout this handbook, the "number of points in a hand" will mean the sum of the high-card points plus the various distribution points. When bidding notrump, only high-card points are important.

Support Points

When considering a hand in terms of a trump suit bid by partner, you need to be able to quantify the value of the hand as a potential dummy (hence the alternative term "dummy points"). Extra strength in the trump suit (the suit bid by partner) will increase the chances that other suits can be ruffed (when a trump is used to take a trick in a suit where the player no longer holds any cards). If you hold at least 4 cards in the trump suit, you can re-evaluate short suits as follows:

Ø Void (no cards in the suit): 5 points

Ø Singleton (one card): 3 points

Ø Doubleton (two cards): 1 points (unchanged)

In some circumstances, it is necessary to deduct points. For instance, in later stages of the bidding, it is possible to support partner's trump suit while holding less than 3 cards, either because partner has shown a six-card suit, or because no other bid is available. In this case, you should deduct the distributional value of the trump suit before determining the level of support, since obviously shortness in trumps is a disadvantage, not an advantage.

Points for Game and Slam

A Game bid is one of the following: 3NT, 4♥, 4♠, 5♣, and 5♦. A bid at level 6 (taking 12 tricks) is a Small Slam, and a Grand Slam (level 7) requires all 13 tricks. Hearts and spades are called major suits, clubs and diamonds are minor suits.

The two most important points numbers in Contract Bridge are the points needed for game, and the points needed for slam. Especially in the later stages of bidding, these numbers will largely determine whether you should make a bid or not.

Game in notrump requires 25 HCP in the combined hands of declarer and dummy. Game in a major suit contract requires 26 points, and game in a minor suit requires 28 points. Notrump slams need 33 HCP, while slams in a suit contract need 32 points.

These values are true most of the time. With a favourable distribution of the cards, game or slam can be made with less points; if the cards are placed unfavourably you might need extra points. Also, a good player against weaker opponents will often make a contract that would normally go down, and so he or she might be ready to bid to game or slam with relatively weaker hands. You can decide for yourself how you should play against Bridge V+.

In this handbook, you will often see rules expressed in the form "with x to y points, do such and such". This is how most Bridge books represent things, and indeed it makes sense to commit a certain number of frequent situations to memory, but you don't need to remember all the rules as long as you bear in mind the key numbers introduced above: essentially 25 HCP, 26 points, 28 points, 32 points, and 33 HCP. After the rebid (the second bid of the player who opens the bidding), almost all of the point range rules can be deduced in reverse from these five numbers:

Ø if the partnership is sure to have 25 HCP, you have enough for 3NT. Otherwise, with 23 HCP you can bid 2NT to invite partner to bid game.

Ø if the partnership has at least 26 points you can bid game in a major, and with 28 points you can bid minor game; if the partnership has around 24 points you can make an encouraging bid in a major suit.

Ø if the partnership has at least 32 points, you can try for slam in a suit; with 33 HCP slam in notrump is reasonable.

Partnership points are calculated by adding together the points in your own hand, and the points indicated by partner's bidding. As the bidding goes on, you can refine the range of points in partner's hand: this range is given when you use the "Info" feature (by tapping on the bid in the Bidding display, or on the "Bid Info" button on the Review screen).

[A few decades ago, many Bridge books defined biddable suits, imposing a minimum honours holding in addition to the various minimum lengths defined above. This concept has not proven useful in Bridge V+, and has not been included in the code. However, should you be used to this idea, there would be no problem in using your preferred variant; just remember that V+ does not].

Playing Tricks

Bridge V+ uses a different method for evaluating the hand when considering whether to overcall an opponent’s bid, or when deciding whether or not to make a sacrifice bid (a bid at a level where the contract will most probably go down, made in order to stop the opponents making their own contract). Bridge V+ also considers playing tricks in other competitive or borderline situations as supplementary data to the number of points held.

The count of playing tricks is obtained by considering the hand as declarer, with a favourable trump suit, and an assumed liberty in deciding in which direction to play the suit. Playing tricks are of two kinds: high-card tricks, and length tricks.

Suppose, for instance, that you hold the honours combination A,Q,10 in a suit: the Ace is worth a trick, but what of the Queen and ten? If your left-hand opponent holds both missing honours, no tricks will be made in the suit other than the ace. On the other hand, if your right-hand opponent holds both King and Jack, and assuming that the hand can be played in such a way as to successively finesse the Queen and the 10-spot, both cards are good and the combination will take all three tricks. With the King and Jack split between the opponents, one finesse will fail, and only two tricks can be made. This split can occur in two ways, and so considering the four possible distributions for the missing honours, we conclude that, on average, the combination A,Q,10 can be expected to take two tricks.

Applying equivalent calculations to other combinations, Bridge V+ will use the following values in counting high-card tricks:

A K Q 3 K Q J 2

A K J 2 ½ K Q 10 1 ½

A K x 2 K Q x 1 ½

A Q J 2 ½ K J 10 1 ½

A Q 10 2 K J x 1

A Q x 1 ½ K x x ½

A J 10 1 ½ Q J 10 1

A x x 1 Q J x ½

Q 10 9 ½

Now consider length-tricks (tricks available in long suits once the opponents have been forced to play all of their cards in the suit). Taking account of the normally expected distributions of thirteen cards in the four hands, we can suppose that the fourth card held in a suit will be worth a trick roughly half of the time, and that any cards from the fifth onwards are almost certainly good tricks. Thus we can count one ½-trick for the fourth card, and one trick for each card beyond the fourth. Whenever the fourth card in the suit is in sequence with the next higher card, it can be counted for a whole trick; it is really a high-card trick. (Thus A,Q,10,8 is worth 2½ tricks - 2 high-card tricks and one ½ trick for 4 cards in the suit, while A,Q,10,9 is worth 3 tricks).

Quick-Tricks

Defensive tricks, or "quick-tricks", are tricks which can be considered almost certain in defense against a contract played by one of the opponents. Quick-tricks are essentially high card tricks which can be taken before declarer takes control of the suit by ruffing (playing a trump card). Quick-tricks are most important when deciding whether to double a contract. The following table covers possible quick-trick combinations:

AK = 2 quick-tricks

AQ = 1½ quick-tricks

A = 1 quick-trick

KQ = 1 quick-trick

Kx = ½ quick-trick

BIDDING CONVENTIONS

Bridge V+ uses a mostly natural bidding system, where a bid in a suit means some kind of strength in that suit. A certain number of variants on the basic system, each with its own particular merits and disadvantages, have been introduced to the Bridge-playing community over time. Bridge V+ uses a few conventions that are so well known as to be effectively standard, like the Stayman and Blackwood conventions, and control bids when going for slam.

We shall briefly introduce all the conventions below, and then describe them more fully in later sections of the handbook, as appropriate. Conventions not used by Bridge V+ in Tournaments mode are dealt with in Appendix I, to avoid creating confusion for users not yet very familiar with these variants.

Five card majors

If you use this convention, you must have at least 5 cards in hearts or spades in order to open the bidding in that suit. This rule facilitates the discovery of a contract in the major suit (at the possible expense of not finding a contract in a minor suit). Given the considerable scoring advantage of major suits, this trade-off makes a lot of sense, and this convention is widely used.

Strong 2 Clubs

Any hand with 24 points (or 23 HCP), or more is opened 2♣. The idea is to move rapidly towards a slam when holding a very strong hand. Partner's conventional reply of 2♦ shows a relatively weak hand, and usually dashes any hopes for a slam, but the partnership will normally get to a game contract. Any reply other than 2♦ will probably initiate a search for slam. Having chosen Strong 2 Clubs, you must decide whether other 2-bids (2♦, 2♥ and 2♠) are strong or weak (see Weak 2-bids below).

Strong 2 Diamonds

This convention determines the meaning of all the 2-bids, and implicitly requires the use of Weak 2-bids for 2♥ and 2♠ (see Weak 2-bids). The Benjamin 2♦ opening replaces the Strong 2♣ bid described above for a very strong suit, or notrump, hand, and the weak response is 2♥. 2♣ is then used as a limited 2-bid, showing a strong suit of at least 6 cards and a hand with 20-23 points.

Weak 2-Bids

A weak 2-opener shows a hand that is marginally too weak to open (usually 11-13 points), with six cards or more in the opened suit. When you choose Strong 2-Diamonds, 2♥ and 2♠ will implicitly show weak hands. If you select Strong 2-Clubs, 2♦ is also a weak 2-bid. If you do not choose this convention having set Strong 2-Clubs, 2-bids other than 2♣ show 20-23 points and a very strong suit. Weak 2-bids do not apply unless either Strong 2-Clubs, or Strong 2-Diamonds are used.

Short Club

If you are using five-card majors and you do not have 5 cards in a major suit, you should open the longer of the two minors, or if the minors have the same length you should open the higher-ranking suit, that is diamonds. This is the “Better Minor” convention. In this case, an opening bid of 1 in a minor will always show at least 3 cards in the bid suit. If,however, you set the Short Club convention and open 1♦ you show at least 4 cards in diamonds. Then, you may be forced to bid 1♣ to show opening points even when you have only two clubs, hence the term "Short Club": this situation occurs when you have 4 cards in each major, and 3 cards in diamonds, and so an opening bid of 1♣ says effectively nothing about the club suit.

Jacoby transfers

Jacoby transfers are used after an opening of 1NT to arrange for the strong hand to be hidden as declarer's hand. (Note that Bridge V+ does not use transfers after 2NT). Thus, for instance, with a long heart suit you would reply 2♦ after 1NT, asking partner to bid the next suit up, that is 2♥. More details will be given in the section covering Jacoby transfers. Jacoby transfers include a special case, often called the Texas Convention, where bids of 4♦ and 4♥, are used after a 1NT opener with 6 cards in a major suit, requiring partner to bid 4♥ or 4♠ respectively.

2NT = 11-12 points

Standard American bidding (which does not use 5-card majors) uses a 2NT reply to show 13-15 HCP. Nowadays people generally prefer 2NT to show 11-12 HCP and 3NT to show 13-15 HCP. In Bridge V+, when this convention is set it also implies that a 3-level support reply (1♣ — 3♣) is a limit raise showing 11,12 support points, whereas in Standard American this bid shows 13-16 points.

Gerber Convention

The Gerber Convention (4♣) is a convenient way of asking partner to show the number of aces in his hand after a notrump opening bid, when a notrump reply always gives a count of high-card points. It means that responder has a good suit of at least six cards (the opener must have at least a doubleton to have opened notrump), and enough points for slam. It will be described in the section on bidding after notrump openings.

2/1 forcing to game

The two-over-one convention is designed to provide a precise way of bidding when holding 12 points opposite an opening bid of 1 of a major. If you hold 3 cards in support of the major, or a hand that you would open, you bid two of your longest suit, rather than three of the major. This allows more choice in choosing the game bid: your partner must bid, and continue to game. With 5-11 points (less than 12), you bid 1NT. This bid is forcing for one round. With less than 5 points, you will pass.

Weak Jump Overcalls

Weak jump overcalls follow the modern tendency to use pre-emptive bids as much as possible. If this convention is not set, jump overcalls are strong, showing at least 7 playing-tricks and a very strong suit. It is, of course, fairly rare to have such good hands, so the logic of weak jump overcalls is to jump instead with weaker hands in order to hinder the opponents' bidding, and to bid all other overcalls at the minimum level, using later bids to decide on the final contract. The details will be explained in the section on Overcalls.

1NT opening ranges

Bridge V+ allows all the possible ranges for an opening bid of 1NT. In all cases, a 1NT opening bid shows a regular hand (suit distribution 5-3-3-2, 4-4-3-2 or 4-3-3-3), with no 5-card major. A 1NT opening can thus be "weak" (12-14 or 13-15 HCP), or "strong" (15-17 or 16-18 HCP). Weak 1NT bids are slightly pre-emptive. Strong 1NT openings often lead to a game contract, since the partner needs only about 9 HCP (for a range of 16-18), or 10 HCP (opposite 15-17) for the partnership to get to game.

THE OPENING BID

OPENING 1 OF A SUIT

Bridge V+ follows the five-card major system in Tournaments mode (the "Five-card majors" convention is set in Bidding Conventions). If you want to know how to bid without five-card majors, (Standard American, or "Length before strength"), you can refer to the description in Appendix I: "Other Convention settings".

Bridge V+ will open any hand with at least 13 points. Thus Bridge V+ will open 1♣ with the following hand, which is the South hand in Deal Number 323:

♠ A 10 8

♥ 8 4

♦ J 5 3

♣ A Q J 7 2

[I have not been able to find a rule that would exclude certain hands with just 13 points. Bridge experts in the past have suggested requiring at least a 5-card suit, or minimum defensive values in terms of quick tricks. I have found no rule of this kind which gives a demonstrable advantage over a large number of deals, but am of course open to suggestions].

Bridge V+ uses a number generator to choose a new deal when you hit “Next hand”. Each generated deal is associated with a number, and can thus be reproduced, and replayed or studied. To choose a particular deal, tap the Menu button (≡), then tap “Select hand”. You then have various possibilities for setting the context of the deal, including "Dealer", and "Deal No". To see hand number 323 with South as Dealer, tap Dealer, and choose South, then tap Deal No and enter 323. Then, tap "Deal". You can check what Bridge V+ would bid by successively tapping the Hint button ("?") for each player, or by tapping Autoplay (∞).

One of a suit is by far the most frequent opening bid. It can be used on hands varying from 13 to 23 points. With five-card majors set in Bidding conventions, you should only open a major suit when it contains at least 5 cards. If you don't have 5 cards in a major suit, the rules depend on the setting of the "Short Club" convention.

When you don't set this convention, you are using the "Better Minor" system. Since both alternatives are fairly simple, and because to best understand Short Club, you need to understand Better Minor, we shall deal with both here, rather than deferring the description to "Other Convention Settings". Bridge V+ in E/W in Tournament mode uses Short Club. We shall start with Better Minor:

Better Minor

Ø With minor suits of different lengths, open the longer suit.

Ø Otherwise, open 1♦, unless the hand is absolutely flat (4-3-3-3), when 1♣ is preferable.

Take a look at South's hand in Deal 343:

♠ K 8 7 6

♥ A K 5 4

♦ Q 7 3

♣ 4 2

Since neither major has 5 cards, you should open 1♦.

Short Club

Ø Open 1♦ only when there are 4 cards in the diamond suit.

Ø Otherwise, open 1♣, even when (like in deal 343 above) there are only 2 cards in the suit.

To a certain extent, Short Club would be better named "Four cards in diamonds guaranteed", but that's a bit long. The point of Short Club is to give priority to finding a 4-4 fit in diamonds, rather than being sure that a minor suit has at least 3 cards. As a result, a club bid effectively promises nothing about the length of the suit, which you will show, if necessary, on the rebid.

Returning to deal 343, shown above, since there are only 3 cards in the diamond suit, this hand must be opened 1♣.

[NOTE: if you're wondering whether to use Better Minor or Short Club, here's my take: it absolutely doesn't matter! Which you choose will have no statistical effect on your results; indeed, only a handful of hands in thousands will show any effect at all, and there will be about as much positive for one system, as negative. However, if you find yourself playing with people you don't know already, you will have to decide. My advice is to play what your new partner prefers!]

OPENING NOTRUMP

1NT is a very strict and precise opening bid. It guarantees a regular distribution of the cards, with no suit having less than two cards or more than five, and a narrow points range. In Bidding Conventions you can specify a 3-point range for the opening bid of one notrump. There are 4 possible high-card point (HCP) ranges: 12-14; 13-15; 15-17 and 16-18. Bridge V+ uses 15-17 HCP in Tournaments mode.

If you have a 5-card suit, it must be a minor. With five cards in a major suit, you will always open the major suit first, and show the regular distribution if possible at a later stage of the bidding. The strength of the doubleton is immaterial.

You will see a number of examples of notrump openings in the chapter on Bidding after notrump openings. Here is a typical example to illustrate the 15-17 HCP range used by Bridge V+ in Tournaments mode. East has 15 HCP, and a perfectly regular hand:

♠ A J 9 5

♥ A 9 4

♦ 8 6 2

♣ A Q 6

Examples of 1NT bids with other ranges will be given in "Other Convention Settings".

To open 2NT the same distributional requirements apply; only the number of points changes. If the Strong 2-Clubs convention, or Strong 2-Diamonds, is chosen in Bidding Conventions, the 2NT bid is worth 20-22 HCP, stronger hands being first opened 2♣ or 2♦. If neither Strong 2-Clubs, nor Strong 2-Diamonds is used, you need 22-24 HCP to open 2NT.

An opening bid of 3NT requires 25-27 HCP. This is a very limiting opening, and allows little room for exploration. It is also very rare.

OPENING 2 OF A SUIT

If you have a hand that you would like to open, but that does not satisfy the criteria for opening one of a suit, or notrump, you must consider whether you can open with 2 of a suit. Typically, you will either have a strong hand, a very strong hand, or a hand that is not quite strong enough to open 1 of a suit.

Strong 2-Diamonds

Bridge V+ uses an ingenious system of 2-bids devised by Albert Benjamin: an opening bid of 2♦ shows a very strong hand and 2♣ shows quite a strong hand, while 2♥ or 2♠ both show hands with a good suit, not quite strong enough to open at the 1-level. To use this system, you must set the Strong 2-Diamonds convention, and Weak 2-bids. These settings are the defaults for Bridge V+ playing in Tournaments mode.

The other types of 2-bids available are Demand 2-bids, Strong 2-Clubs, and Limited 2-Bids. These will all be described in "Other Convention Settings".

Using the Benjamin system, you will open 2♦ with a very strong hand usually worth about 8 playing tricks or more (at least 24 points and a long, very strong suit), or a regular hand with 23-24 HCP (and hence too strong to open 2NT).

Deal 145 shows a strong-suit hand:

♠ A K Q 10 5 4

♥ —

♦ A K 7

♣ A Q 8 4

This is the South hand in Deal 145. Bridge V+ opens 2♦, and partner replies 2♥. This reply shows weakness (indeed North has just 1 point!), and the final contract is 4♠, which makes.

2-Clubs (Benjamin)

An opening bid of 2♣ shows a strong suit (at least 6 cards with 3 honours), and 20-23 points. This is sometimes called a "Limited 2-bid". In deal 89, West bids 2-Clubs (Benjamin):

West East

♠ A K J 5 ♠ 8 3

♥ A K J 9 7 3 ♥ Q 8 5 2

♦ 8 6 ♦ 2

♣ 9 ♣ A K J 6 4 3

West shows the strength of the hand with the 2♣ opening. This also implies a good suit, but West still has to show that suit. East is obliged to bid 2♦ (called a "relay"), so that opener can then bid 2♥, 2♠, 3♣ or 3♦, to show the long suit. Here, West rebids 2♠ of course

Weak 2-Bids

The remaining 2-bids are 2♥ or 2♠: these are used to show a hand that has a good long suit (6 cards with at least Q,J,10), but which is too weak to justify an opening of 1 of a suit. The hand should have about 11-13 points.

Weak 2-bids are partly pre-emptive, because they make it difficult for the opponents to describe their own hands when they have more points than the opening partnership. Sometimes a weak 2-opener will allow the partnership to get to a major game contract that they might have missed if not using the Weak 2-Bids convention.

Bridge V+ Deal number 311, nicely illustrates a weak 2-bid. West has the following hand:

♠ A 10 6

♥ K J 10 9 7 5

♦ 9 5

♣ 8 5

If Weak 2-Bids are selected, Bridge V+ will open this hand with 2♥. Partner then jumps to game.

Part of the logic of using 2 bids to show weak hands rather than strong ones, is that if you open one of a suit instead of a strong 2-bid, it is practically always possible to show the strong hand later in the bidding. Unless partner has almost nothing, the extra strength in the opening hand should give the partnership time to find the appropriate contract.

PRE-EMPTIVE OPENINGS

You should use a pre-emptive bid when holding a very long suit (at least 7 cards) and 4 to 8 high-card points. (With more than 8 HCP the hand is certainly strong enough to be opened at the 1-level). You pre-empt by bidding the suit at the 3-level, a bid that can severely hinder the opponents bidding (they may even have enough for slam). Bridge V+ will mostly avoid pre-empts when vulnerable, and weak pre-emptive interventions at the 4-level: they can be very expensive when doubled for penalties.

Responses to pre-emptive bids are simple: you will bid only with a very strong hand, containing aces and kings. If the opening suit is major, you need something like 18 points, and at least 3½ quick-tricks. If the opened suit is a minor, it's best to bid 3NT, and for this you need at least 4 quick-tricks. Deal 474 gives an example:

South North

♠ 7 ♠ A J 10 2

♥ 10 8 5 2 ♥ K 4

♦ K Q 8 7 5 4 2 ♦ A J

♣ 6 ♣ A 10 8 7 4

South pre-empts with 3♦, and North replies 3NT, and makes the contract.

BIDDING AFTER AN OPENING OF 1 OF A SUIT

REPLY TO 1 OF A SUIT

When your partner opened one of a suit, the bids available to you as responder depend on the strength of your hand, and on the type of hand. Three types of response will be considered, roughly in order of preference:

Ø change of suit

Ø support of partner's suit

Ø notrump

Change of Suit

If you set “2/1 forcing to game” in Bidding Conventions, you will slightly change the meaning of certain 2-level bids made after an opening bid of 1 of a major. Details of these changes are given below in the section headed “2/1 forcing to game”.

You can make two types of suit-change; the simple raise, where you bid at the first level available above the opening bid; and the jump-shift, where you bid at one level higher than the simple raise. The jump-shift is a particularly strong bid showing slam potential. The simple raise will be considered first:

You can bid a new suit at the 1-level with a minimum of 5 HCP (or 8 points including at least 3 HCP). The suit must contain at least 4 cards.

A new suit at the 2-level requires greater strength:

· a 4-card suit if the hand contains at least 10 HCP.

· a 5-card suit containing an honour may be bid with 9 HCP.

· a 6-card suit containing 2 honours needs only 6 HCP.

Take a look at North's hand in Deal 11:

♠ A 9

♥ J 10

♦ K 7 5 4 2

♣ Q 6 4 3

South has opened 1♥. North has enough points to bid at the 2-level, and the diamonds are longer than the clubs, so the reply is 2♦.

The normal maximum for a simple raise is 15 HCP. With 16 HCP and more, you should use a jump-shift. You can also jump-shift when holding 17 points in support of partner (naturally including support points). After the jump-shift, you will return to your partner's suit. Finally, you can use a jump-shift with an exceptionally strong hand (usually containing a very long suit) worth some eight tricks and at least 10 HCP.

Support of Partner's Suit

Bridge V+ uses limit raises in response to 1 of a suit if Bidding convention 2NT = 11-12 is set; that is, the level of support bears a natural relationship to the number of points held. The jump-raise is not forcing.

If the 5-card majors convention has not been selected, you should have 4 cards in order to support partner's suit; using 5-card majors, however, you can support a major suit with only 3 cards. You need 4 cards to support diamonds, and 5 cards to support clubs if using the Short Club convention (which is the case for Bridge V+ in Tournaments mode). Using Better Minor, you always need 5 cards to support a minor, because partner may have opened with only 3 cards. Also, in this latter case, no extra support points may be counted, until partner shows length in the minor suit by rebidding it. Given adequate length, the values of the possible support bids are as follows:

· 2-level 6-10 points

· 3-level 11-12 points

· 4-level 13-16 points

When holding more than 16 points in support of partner, you should first make a jump-shift in a side-suit, or failing that, a simple raise in a new suit. There is one qualification to be made concerning the above point-ranges: to support a minor at the 3-level, you should have at least 9 HCP. This gives partner the option of bidding 3 NT rather than continuing on to the generally more difficult minor game contract.

Here is North's hand in Deal 12:

♠ K

♥ A10 5

♦ A J 10 3

♣ A 10 9 6 3

South opens 1♥. If 5-card majors are set, North can support with 3 cards, and can count 16 or 17 points in support of hearts, depending on the value of the singleton King. Bridge V+ North bids game directly, with 4♥.

[NOTE: If 5-card majors are not set, North must first bid his club suit, and the bidding goes: 1© — 2§ —3§ — 5§. It would not be incorrect to bid 4©, but Bridge V+ tries to avoid contracts where the partnership has only 7 cards in the trump suit: here, 5§ makes with 2 over-tricks.]

2/1 forcing to game

This modern convention was invented in order to find a better way to handle the response to 1 of a major when using 5-card majors, and when holding 12 points, and either 3 cards in support of the major, or a hand that would be worth an opening bid. There are many variations on two-over-one forcing to game, including two major styles called “Lawrence” and “Hardy” after their inventors. Bridge V+ uses a simple system where natural bids are used after the initial 2/1 bid.

If you set this convention in Bidding Conventions, you will not use 2/1 forcing to game in the following circumstances:

Ø if an opponent has bid

Ø if you can bid one spade

Ø if you have four cards in support of partner

Ø if you can bid a jump-shift

Note also that Bridge V+ does not consider 1♦— 2♣ as 2/1 forcing to game, and that 1♠ — 2♥ requires five cards in the heart suit.

Then, if you hold just 3 cards in support of your partner, and 12 points including support points, or a hand that you would open, bid 2 of your longest suit. If you have 6-11 points you must bid 1NT: this totally artificial bid is forcing for one round.

Deal 987 is a good example:

West East

♠ A Q J 8 3 ♠ K 6 5

♥ K Q 2 ♥ 10 4 3

♦ 10 5 2 ♦ A 7 3

♣ 9 2 ♣ A J 7 5

West has a minimum opening bid of 1♠, and East has 12 HCP, and 3 spades. When 2/1 forcing to game is not set, the bidding is 1♠ — 3♠ — Pass. With 2/1 forcing to game set, however, East can show his strength perfectly at the 2-level: the bidding goes 1♠ — 2NT — 3NT — Pass. Both contracts make, but 3NT is of course better. However, it is not always better to bid 2/1 forcing to game. Here are E/W in deal 1192:

West East

♠ A K 6 5 2 ♠ 8

♥ A 7 3 ♥ J 10 9 5

♦ A 7 4 ♦ K 3 2

♣ 4 2 ♣ K Q J 9 6

West has 16 points, and opens 1♠. If 2/1 forcing to game is not set, East will reply 2♣, showing 10 points or more. The entire auction is 1♠ — 2♣ — 2NT — 3♥—3NT — Pass.

If 2/1 forcing to game is set, East is marginally too weak to bid 2♣, since he does not quite have an opening bid, so he must bid 1NT. West is forced to bid, but is not strong enough to bid 3♠ or 2NT: he thus bids 2♠, and the 3NT game is missed.

Bidding after the rebid is mostly natural, except for the fact that you must keep bidding if the reply was 2 of a suit, and the conditions are met for 2/1 forcing to game. Thus you would show a second 4-card suit, support the major at the appropriate level, or bid notrump. The details are given in the following sections.

Notrump Bids

Replies of 2NT or 3NT are true notrump bids, and show regular distribution. It is risky to bid notrump without stoppers in suits bid by the opponents. A stopper is four cards to the Jack, three to Queen, a King doubleton, an Ace, or any five-card holding (four is often adequate).

With Convention 2NT=11-12 set (this goes with five-card majors), 2NT quite naturally means 11-12 HCP, and 3NT is 13-15 HCP. A reply of 1NT shows a regular distribution only in certain precise circumstances:

Ø following an opening bid of 1 club, where the failure to bid a new suit at the 1-level, or to support clubs, almost certainly implies regular distribution

Ø following a bid from the right-hand opponents

In the above cases, the 1NT bid promises a minimum of 8 HCP. In all other cases, 1NT is used as a conventional negative response, when it is not possible to change suit, or to support partner. It normally indicates 5-9 HCP. (If 2/1 forcing to game is set the 1NT reply is always totally artificial, as explained in the previous section, showing only a points range of 5-11).

Take for example North's hand in Deal 11, introduced earlier for the suit-change reply, but with the spade Queen substituted for the Ace:

♠ Q 9

♥ J 10

♦ K 7 5 4 2

♣ Q 6 4 3

Here, with only 8 HCP, no suit-change reply can be made in clubs or diamonds, and so 1NT must be bid. (With 4 cards in spades, 1♠ would be the correct reply).

Choosing the Reply

Sometimes a hand will offer several valid replies; in particular, several suits may be biddable:

Ø with bids possible in two suits of different length, always choose the longer suit.

Ø with two or three suits of four cards, choose the suit that can be bid at the lowest level.

Ø with two suits of five or six cards, bid the higher-ranking suit.

When two different types of reply are available, the problem is somewhat more delicate. Consider for example, East's hand in Deal No. 544. West opens 1♥

♠ J 10 2

♥ K 10 3

♦ Q J 8 5

♣ K Q J

The rules will allow bids of 2♦, 3NT or 4♥. Which is preferable? Bridge V+ will choose 2♦ if 2/1 forcing to game is set, or 4♥ if it is not set. If 2/1 forcing to game is not set, there is no point showing the 4-card diamond suit, and it is generally easier to make 4 of a major than 3NT. The following list gives the general order of preference when several replies are available:

— a new suit at the 1-level over a minor opening

— a true notrump bid (2NT or 3NT), showing stoppers and regular distribution

— support of a major

— a new suit at the 2-level

— 1♠ over 1♥ when lacking heart support

— support of a minor

— conventional 1NT negative response

Some notes on competitive situations arising at the first reply

In most cases, an opponent's intervention does not alter the value of the reply. For instance, a new suit forced to the 3-level is roughly equivalent to the normal 2-level suit-change. However, this logic is not applied above level-2. A support reply will always be made if adequate points are held; 1♥, 3♠ (intervention), 4♥ shows 13-16 points in support of partner's hearts, despite the opponent's bid of 3♠. Similarly, following an opening bid of 1♠, and an over-call of 2♥, a simple raise to 2♠ still shows 6-10 points in support.

Two particular interventions are treated in a special manner:

Ø if the opponent bids 1NT, and you have 8 HCP or more, you should double for penalties.

Ø following a take-out double, redouble with 10 HCP or more; any other bid thus shows less than 10 HCP.

REBID AFTER OPENING 1 OF A SUIT

This is probably the most important bid made in an exchange following an opening bid of 1 of a suit. The opening bid can range in value from 13 to 23 points, and indicates a first suit. The rebid has two main purposes: to specify more precisely the strength of the hand, and to provide some new information: a second suit, for instance, or an indication of regular distribution. The rebid can also be affected by partner's reply.

Partner has supported opened suit

If the suit is a major, your main consideration is whether or not you can bid game. If game seems unlikely, you should pass; if the partnership is assured of game points, but cannot have enough for slam, you can bid game directly. An intermediate bid invites partner to bid game if he is in the top half of his promised range. If slam seems likely, you should try to find a slam-going bid, as will be described later.

A fairly common occurrence is illustrated by Deal 23, dealer South:

South North

♠ A Q 10 9 ♠ K 7

♥ J 7 6 4 2 ♥ A 9 3

♦ A ♦ 10 9 8

♣ A Q 7 ♣ J 10 9 4 3

North/South are using Five-card majors. South opens 1♥, showing 5 cards in hearts, and 13-23 points. North has 9 points in support of hearts, and thus bids 2♥ to show 6-10 points (not worrying particularly about West's 2♦ overcall). South now bids 3♥. This does not show undue hesitancy on the part of South: instead, it refines the points range to 17-19, and North will go to game with 8 points or more. The complete bidding sequence is: 1♥ — 2♥ — 3♥ — 4♥.

If the opened suit was a minor, there may still be a chance of a better contract in notrump, and you should examine this possibility before considering a rebid in the minor suit. The hand must be even (shortest suit has at least two cards).

Ø following a simple raise (1 of a suit — 2 of the suit), a 2NT rebid shows 18-20 HCP; your partner can be placed with 5-9 HCP, and as long as his distribution is not too unequal, game in notrump should be a reasonable proposition.

Ø support of a minor at the 3-level guarantees 9 HCP; therefore, you can bid 3NT with about 16 HCP, following 1♣ — 3♣ or 1♦ — 3♦.

Partner has bid a new suit

The preferred bid is support of partner's suit. Since partner can have 4 cards, you need at least 4 cards in order to support partner’s suit. Here again, the treatment of a major suit differs slightly from that of a minor. In general terms, the rebid is chosen at the level appropriate to the strength of the hand in support of the reply suit.

Ø a simple raise (1♦ — 1♥ — 2♥, or 1♥ — 2♣—3♣) shows 13-16 points

Ø double-raise in a major suit (1♥ — 1♠ — 3♠, or 1♠ — 2♥ — 4♥) is limited to 17-19 points

Ø double-raise in a minor suit (1♣ — 1♦ — 3♦, or 1♥ — 2♣ — 4♣) shows a minimum of 17 points, without upper limit

In all cases, you should take into account your support points or "dummy points" when evaluating your hand. A simple example is give by South's rebid in Deal 24. Here is the South hand:

♠ Q J 3

♥ 10 9 4 2

♦ A Q 10 8 7

♣ A

South opens 1♦, and North replies 1♥. South has just 15 points, and thus has to be content with a rebid of 2♥. Now West intervenes with 3♣. South can then compete with 3♥. North knows that South has at best 10 points, and passes. In tournament play, or if you are feeling confident, 4♥ would not be wrong...)

If partner's reply named a major at the 1-level, you can bid major game directly with 20-22 points. With 23 points or more, choose a bid which will keep the bidding open; notrump or, more likely, a bid in a new suit.

Notrump rebids

When partner has replied in notrump, and your hand is not too uneven (preferably, no suit with less than 2 cards), your rebid will be determined by a simple count of high-card points; with 25 HCP assured for the partnership, you can bid 3NT directly; with a reasonable chance of game, you should invite game with 2NT; otherwise, you should pass.

A single exception to the above should be applied when holding a 5-card major opposite a 2NT reply; then, repeating the major at the 3-level simply asks partner to choose between 3NT and major game.

When partner has bid a suit, a rebid in notrump is used to show a regular hand with precise high-card strength, according to the following rules:

Ø 1NT always shows 13-15 HCP.

Ø 2NT following a new suit at the 2-level generally shows 15-17 HCP. For 1♦ — 2♣, things are different, and the points range is most likely 13-15 HCP.

Ø 2NT following a non-forcing bid (simple raise of the opened suit, or 1NT), shows 18-20 HCP

Deal 960 with dealer South, gives us an example of a notrump rebid. This is East's hand:

♠ A 6 3

♥ A Q 6 5 2

♦ Q J 3

♣ A Q

East has 19 HCP, which is too much for an opening bid of 1NT, and in any case, since the hand contains a 5-card major suit (hearts), an opening bid in notrump is excluded. East thus opens 1♥, and West replies 1NT. East can now rebid 2NT, leaving West to conclude with 3NT.

Sometimes, it will not be possible to make a notrump rebid with a regular hand because the number of points in your hand does not correspond with the required range. If no notrump rebid is available, you will instead consider one of the bids described in the following sections.

Combination rebids

Naming a new suit is a very useful bid. It specifies the number of points held, and gives valuable information about the shape of the hand. For instance, the 2♣ rebid in the bidding sequence 1♦ — 1♥ — 2♣ most likely shows a hand with at least 5 diamonds and 4 clubs, for the following reasons:

Ø with 4 cards in hearts a support rebid would normally have been chosen.

Ø with 4 cards in spades, 1♠ could have been bid.

Ø with a regular hand, 1NT could have been bid with 13-15 HCP, 2NT with 18-20 HCP, and with 15-17 the hand would have been opened 1NT.

The strength of a combination rebid is determined by the effect of the bid on partner's second reply. It is not the actual level of the rebid that is important, but the level at which the opening bidder’s partner must bid in order to return to the opened suit (“simple preference” - the most discouraging bid at his disposal). Compare the following two sequences:

1♦ — 2♣ — 2♥……………… ….(1)

1♠ — 2♦ — 2♥…………………..(2)

In each case the rebid is 2♥. However, the two situations are entirely different; in (1), in order to avoid a bad heart contract, partner must bid 3♦, whereas in (2) his bid would be 2♠. The first combination is "strong", while the second is "weak". A weak combination allows partner to return to the opened suit below the 3-level.

Ø a strong combination rebid shows 18-21 points.

Ø a weak combination rebid shows 13-19 points.

Finally, with a very strong hand, you should use a jump-shift rebid. If the suit combination is weak, a jump shows 20-23 points; with a strong combination, it is only necessary to jump when holding 22 or 23 points, a simple rebid of the new suit showing 18-21.

Consider North's hand in Deal No 19105:

♠ K Q 6 5 4

♥ A Q 8 5

♦ A 6

♣ A 6

North opens 1♠, and partner replies 2♣; a rebid of 2♥ is insufficiently strong, so a jump-shift is required:

1♠ — 2♣ — 3♥. The final contract is 3NT, which just makes.

Now exchange diamonds and spades:

♠ A 6

♥ A Q 8 5

♦ K Q 6 5 4

♣ A 6

Here, the sequence 1♦ — 2♣ — 2♥ would show a strong combination (18-21) points; it would then be unnecessary to jump following the 2♣ reply.

Repeat of the opened Suit

If none of the above bids can be made, you can repeat the opening suit, when holding at least 5 cards in the suit. A simple raise (2-level) shows 13-16 points; the double raise is stronger (17-19 points) and in addition shows a good suit, something like:

Ø 5 cards with 4 honours

Ø 6 cards with 3 honours (or Ace and King)

Ø 7 cards with 2 honours

At this stage, it is perhaps worth noting the effect of an intervening bid from the right-hand opponents. All bids other than the repeat rebid retain their same value, except that a notrump bid implies adequate stoppers in any suit bid by an opponent. The double raise repeat still shows the kind of hand described above, but you should bid a simple raise over an adverse bid only if the hand is reasonably strong, since partner will in any case have another chance to bid. Thus, you should pass with less than 16 points.

SECOND REPLY AFTER A SUIT OPENING

General Considerations

As responder you will usually approach your second reply with a clear picture of the opened hand: the likely range of partner's points strength, the probable length of the opened suit and some information on the shape of partner's hand. Your bid should in turn clarify the situation for partner.

You must consider the level of bidding in terms of the partnership holding. If a suit has been found, the combined partnership points will dictate whether to make a new bid. In competitive situations especially, it may be necessary to retire from the bidding before completely describing your hand, rather than make a bid at an unjustifiable level, except when it makes sense to double for penalties, or to make a sacrifice bid.

In tournament play, you can choose to bid even when almost certain of going down, in order to stop the opponents from making more match-points than you would lose by going down, especially if they have a chance of making game.

Support Partner's Suit

You should support your partner when you hold enough cards in partner's suit to assure a partnership total of eight. The number of cards held by partner can usually be inferred fairly accurately from the bidding. Sometimes, you may have no choice but to support a major with only three cards when partner has not promised more than four, but you should think of this as a last resort.

If partner's bidding has shown an upper limit which excludes game, or a lower limit that is too far from game, there is no point in continuing, and you should therefore make no encouraging bid (a preference bid may be necessary as will be explained below). If partner's bidding has been such that game points are possible if partner is in the top half of his promised range, an invitational bid is indicated. Bridge V+ only considers invitational bids below the 3NT level; above that, game points must be practically certain. In particular, support of a minor at the 4-level implies that game points for a minor are held; this bid is often made in the hope that partner can show deferred support for a major.

In general, once assured of at least eight cards and enough points for game in a major, you should bid game, except when you have enough points for slam, in which case a lower-level bid may be preferable in order to leave room for subsequent slam bidding.

On occasion it may be necessary to bid even though there is no chance of game. When partner's last bid showed a new suit for which no support is held, it may be better to return to his first suit rather than pass. In general, you should show preference for partner's first suit unless you hold two more cards in his second suit.

The sequence: 1♥ — 1♠ — 2♣ — 2♥, does not necessarily show any real support for hearts. The 2♥ bid may simply have been made to ensure against a poor contract in clubs. Simple preference like this never shows any new values. In order to show real support for hearts in this situation it is necessary to bid 3♥. Obviously, to do this the points held must make game a reasonable proposition.

Preference considerations do not apply when the previous bidding has already guaranteed game, or when the strength of the hand has already been clearly demonstrated. Thus, the 3-diamond bid in the sequence:

1♣ — 1♦ — 2♥ — 2♠ — 3♦

is just as strong as 4 diamonds, with the obvious advantage of allowing partner to bid 3NT. The 2♥ rebid already showed some 20-23 points, and so there is no danger in partner taking the 3-diamond bid as simple preference.

Partner has rebid notrump

To raise partner's notrump rebid, you should preferably have at least two cards in each of the four suits, or a picture card singleton if the distribution is 5-4-3-1 or 4-4-4-1, though you will often bid notrump with a singleton in partner's best suit. Before making your bid in notrump, you should estimate partner's probable strength in high-card points. If partner has shown an upper limit which excludes game (25 HCP), you should pass. If the partnership is certain to have 25 HCP or more, you can bid 3NT immediately. Bid 2NT over 1NT if game points will be assured as long as partner is in the upper half of his promised points range.

If you have a second suit with 4 cards, and that suit is major or your first bid suit was a major suit, you should bid the suit. Deal 2050, shows a case where V+ shows both majors:

West East

♠ Q 9 ♠ A K J 6 4

♥ A K Q ♥ J 10 9 5 2

♦ Q 10 7 ♦ J 6

♣ A Q 6 5 2 ♣ 7

West opens the bidding with 1♣, and after North has over-called with 2♦. East replies 2♠, showing at least four cards in spades, and 10-15 HCP. West's rebid is 3NT, and East bids 4♥ to show at least four hearts and at least five spades. West shows his preference for spades by bidding 4♠.

If partner bid 2NT, you can repeat a 6-card major suit. After 3NT, you can repeat a strong major suit (something like 6 cards including 3 honours; 5 cards with 4 honours). It usually makes no sense to repeat a minor suit after a 3NT rebid. In deal number 1861, East repeats a 7-card major suit:

West East

♠ A Q ♠ K 10 9 8 7 4 2

♥ J 10 3 ♥ A K 4

♦ A K 3 ♦ 9

♣ K Q 6 5 4 ♣ 9 7

The bidding goes 1♣ – 1♠ – 2NT – 4♠. The AQ of trumps in West's hand, allows him to make 12 tricks.

Partner has supported your reply suit

The simplest case is when partner has supported your suit; you just have to decide whether to pass, to invite game, or to bid game directly.

(An exception occurs when not using five-card majors, when the reply suit is minor, and the opened suit major: you can read about this, should you wish, in "Other Convention Settings". It's a good illustration of one of the many reasons for using five-card majors!).

In deal 59, East supports partner's second suit:

West East

♠ Q J 10 2 ♠ A K 8 3

♥ A K 8 6 3 ♥ Q 4

♦ 8 ♦ J 9

♣ 8 7 4 ♣ A J 9 5 2

East opens 1♣, and West shows his heart suit. East makes a combination rebid with 1♠, showing 13-19 points, and West, with excellent support for spades can go directly to game, with a bid of 4♠.

Combination-suit bids as second reply

If you can't bid a major suit, bid notrump or show a second suit. When possible, a combination-suit reply should show a true two-suited hand, at least 5-4. If the bid gives new information about a major suit you should prefer this bid to notrump, or support of partner's minor. You should also prefer to show a second suit than to bid a double raise of the reply suit even with 6-4, unless the 6-card suit is a major worth at least 5 playing tricks.

As we already saw for the rebid, a combination may be "strong" or "weak, " depending on whether it is possible for partner to return to the reply suit at the 2-level. Bidding a strong combination always implies a good chance of game; to show the same strength with a weak combination, you will probably need to jump in the second suit (depending on the level of the bid).

The two bidding sequences that follow show hands of similar strength, in spite of the fact that the second replies are at different levels.

1♦ — 1♥ — 2♣ — 2♠…………... (1)

1♦ — 1♠ — 2♦ — 3♥…………... (2)

In case (1) the opening bidder will only be able to return to his partner's suit by bidding 3♥; in case (2) he can bid 3♠. In both cases, the bidding would thus reach the 3-level. Both sequences are forcing, and a game contract is likely.

Repeat of reply suit

Opposite a suit repeat or combination rebid, a repeat of the reply suit usually shows six cards. This bid is discouraging when made at the 2-level. Otherwise, it is invitational, in particular when the bid is a jump-raise. You should also have six cards in order to bid a suit after making a conventional response of one notrump. If the rebid was in notrump, you can repeat a major to show a 5-card suit (partner has at least a doubleton). North's hand in Deal 15 illustrates repeating a major:

♠ Q 10 6 4 2

♥ 7 6

♦ A 10 3

♣ Q 10 3

North replies 1♠ after partner opens 1♥. When South rebids 2♣, North repeats spades, showing 5 cards in spades and 6-10 points.

When none of the bids described above is possible, but the partnership has enough points for game, you should look for a "compromise" bid in notrump, or perhaps raise a suit bid by partner with less than the normally required card support. With less strength, you should pass, unless partner has bid two suits, in which case you will apply preference rules and return to partner's first suit when necessary.

THE SECOND REBID, THIRD REPLY AND BEYOND

Most bidding sequences (excepting slam tries, which will be examined later) are effectively complete by the second reply. The cases where you need to go beyond the second reply while still exchanging basic information, are relatively exceptional. Nevertheless, we shall consider a few specific circumstances arising at the second rebid (that is, the third bid of the opening bidder).

If partner has supported your suit (or one of your suits, if you made a combination-suit rebid) you will bid game in your suit, invite partner to bid game, or pass, depending on the strength of your hand. If the second reply was in notrump, and your hand is not too uneven, you should bid 3NT, 2NT or pass. If your hand is very uneven, and thus probably unsuitable for a notrump contract, you will perhaps be able to support the reply suit, or make a repeat bid. In Deal 51, South repeats his spades after North bids 2NT:

North South

♠ K J ♠ A Q 10 9 6 2

♥ A J 7 2 ♥ Q 4

♦ K 10 9 7 5 ♦ A 8 2

♣ 8 3 ♣ 5 2

South opens 1♠, and the bidding goes: 1♠ — 2♦ — 2♠ — 2NT — 3♠ — 4♠. (East intervenes with 2♥ after North's 2♦). South's second repeat of spades shows 6 cards in the suit.

If the second reply was a repeat of the reply suit, partner has shown six cards, and you can support even with a doubleton (in this case, don't count the distribution point for the doubleton). You need to consider combined partnership points, including support points, to determine at which level you can show support for partner's suit, as described for the second reply.

If support is not possible, you should try for a notrump bid, or bid a new 4-card suit, (in which case you probably have a void or a singleton). Deal 375 gives an example:

North South

♠ K 9 5 4 2 ♠ A

♥ A 7 4 ♥ K Q 6 3

♦ — ♦ K J 8 7 6 5

♣ A Q 9 6 2 ♣ 5 4

South is dealer. The bidding is 1♦ — 1♠ — 2♦ — 3♣ — 3♥ — 4♥. South cannot show his hearts at the rebid, but once North has shown his strength with the 3♣ bid, he can bid 3♥. North supports with three cards to the Ace. The game contract makes.

Even if none of the above possibilities apply to your hand, you may still be able to make a useful descriptive bid. You can repeat the opened suit with six cards, or the rebid suit with five. In both cases, combined partnership points must justify the level of the repeat. Failing this, if game points are highly likely, you might try notrump, or raise a suit bid by partner. With less than minimum support, you should show preference for partner's first suit if you have insufficient length in his second suit.

From the third reply onwards, the only new distributional information that can be made known to partner is a five-card second suit in a two-suited hand. (In general terms, a repeat bid shows one more card than already promised by the previous bidding). Otherwise, and using all the information available from partner's bidding, the choice effectively reduces to responding to partner's support, supporting a suit bid by partner, or notrump.

BIDDING AFTER NOTRUMP OPENINGS

The precision of notrump openings usually guarantees early agreement on a reasonable contract. In addition, various conventions exist which have been designed to facilitate the bidding after a 1NT opening. The best known of these is the Stayman convention, which has been adopted as standard for Bridge V+. Also available in Bidding Conventions are Jacoby Transfers, which will be described at the end of this section. A convention which is rarely used, because it requires that both partners have a lot of points, is the Gerber convention, which is also included in Bridge V+ Bidding Conventions.

REPLY TO 1NT

The Gerber Convention

If you have a good long suit (at least 6 cards) and enough points to go for slam (16 points when 15-17 range is set), you can immediately try for slam in your suit, since partner must have at least a doubleton. You can check aces and kings by means of the Gerber convention, by using an artificial 4♣ response to the notrump opening, requesting partner to specify the number of aces in his hand by one of the following bids:

Ø 4♦: no ace, or 4 aces

Ø 4♥: one ace

Ø 4♠: two aces

Ø 4NT: three aces

If partner's rebid confirms that the partnership holds all four aces, and if the partnership has a minimum of 35 points, you should continue with 5♣ to request partner to specify the number of kings in his hand, in a manner exactly analogous to that used for aces. With just 3 aces guaranteed and grand slam out of the question, you can bid small slam directly. (The Gerber Convention can also be used after 2NT).

The Stayman convention

Bridge V+ uses the Stayman convention after an opening bid of 1NT. This extremely useful convention is designed to find a 4-4 fit in one of the major suits. If you have 4 cards in a major suit (or in both suits), you should reply with an artificial bid of 2♣, in the hope that your partner will also have 4 cards in that suit, since it is generally easier to play 4♥ or 4♠ than 3NT. You must have at least 8 HCP (if you have set 15-17 HCP for the 1NT open range in Bidding Conventions). Deal 193 gives an example:

West East

♠ J 3 ♠ A 8 7

♥ A K 10 3 ♥ 8 7 6 4

♦ A 8 4 ♦ K Q 9

♣ A 8 4 3 ♣ 9 7 5

West, holding a regular hand with 16 HCP, opens 1NT, and East replies 2♣ (Stayman). West then bids 2♥ to show the 4-card heart suit, and East can close with the game bid of 4♥ (or invite game with 3♥).

The player opening 1NT cannot have five cards in a major because of the rules of the 1NT opening. The 2♣ bid requests the opener to bid his 4-card major. Partner’s rebid should then be completely automatic:

Ø With no 4-card major, but with maximum opening points (17 HCP for 15-17): bid 2NT

Ø With no 4-card major, and less than maximum points, use the negative 2♦ response

Ø With 4 hearts and 4 spades, bid 2♥

Ø otherwise, bid your major at the 2-level.

If game is unlikely (0-7 HCP for 15-17), you should bid a 5-card suit other than clubs at the 2-level, in the hope that the suit contract will play more easily than 1NT. If this is impossible, (or if an opponent has over-called) just pass. The opening bidder will also pass.

Otherwise, with 5 cards in a suit and enough points in the partnership for game in the long suit (for example: 11 points for a major opposite a 1NT opening bid, or 13 points for a minor), bid 3 of the long suit.

If slam seems likely (16 points or more, opposite 15-17), bid 3 of any 5-card suit, or if you have no 5-card suit, bid notrump at the appropriate level:

Ø 3NT with less than 16 HCP

Ø 4NT with exactly 16 HCP

Ø 5NT with 17 HCP

Ø 6NT with 18-21 HCP

Ø 7NT with 22 HCP

Deal 231 shows 1NT—6NT:

West East

♠ K J 4 3 ♠ Q 10 9

♥ K Q 10 ♥ A J 4

♦ A Q 8 ♦ K J 4

♣ J 10 3 ♣ A K 9 6

If game points are certain, but slam unlikely, (11-15 points), bid Stayman with a 4-card major. Otherwise, with 5 cards in a major suit bid 3 of the major, or with at least 6 cards bid game immediately, partner having guaranteed at least a doubleton by his opening bid. In all other circumstances, bid 3NT (10-15 HCP). If game points are possible, but not certain (8/9 HCP for 15-17), bid Stayman with a 4-card major, 2NT otherwise.

[NOTE: Rather than trying to remember all the numbers in the preceding paragraphs (and elsewhere in the Handbook), you should start from the key numbers for game and slam: 25 HCP or 26 points; 33 HCP or 32 points, and work backwards, to calculate whether game, or slam, is "sure", possible, or unlikely.]

Jacoby transfers

The purpose of the Jacoby transfer bid is to arrange for the player who opened 1NT to be declarer, so that the stronger of the two hands is hidden from the opponents. Jacoby transfers can be set in Bidding Conventions.

With 5 cards in a major suit opposite a 1NT opening, bid 2 of the suit ranking just below the major; thus with a long heart suit, bid 2♦, and with long spades, bid 2♥. The opening bidder will then bid the next suit up; that is, your long suit. you then have a second chance to bid:

Ø if game is out of the question, pass

Ø with 6 cards in the major, bid game directly if game points are certain, or invite game at the 3-level

Ø if game points are possible, but not certain, bid 2NT

Ø if game points are certain, and you hold a second suit containing at least 4 cards, bid the second suit (with a jump if slam points are held). Partner should have no difficulty in choosing the correct bid.

Ø finally, with a distribution 5-3-3-2 and a total partnership count of at least 25 HCP, bid 3NT.

Deal 427 shows a Jacoby transfer sequence:

North South

♠ 9 6 ♠ K J 7 5 3

♥ A Q 6 5 ♥ K J 9 7 2

♦ A K 7 4 ♦ 10 8

♣ A 4 3 ♣ 2

With "Jacoby transfers" set, and with dealer North, the bidding goes: 1NT — 2♥ — 2♠ — 3♥ — 4♥. When South bids 3♥, North can deduce that his partner has at least five spades and four hearts, and that game points are certain. He of course bids game in hearts.

With 6 cards in a minor, and a weak hand excluding game, you should reply 2♠. When the opener then bids 3♣, you will pass if the long suit is clubs, (thus partially solving a problem inherent in the Stayman Convention), or bid 3♦. (Note that if the long suit is diamonds, the stronger hand goes down as dummy).

With long minor suits in stronger hands, you can still use the Stayman Convention (as you would when transfers are not used), or bid a long suit at the 3-level.

If an opponent intervenes after the 1NT bid, Jacoby transfers are invalidated, and 2♠ shows a spade suit with at least 5 cards and the range that would have applied for a 3♠ reply, since the only weak reply after the intervention is Pass.

Here are the East/West hands in Deal 2043:

West East

♠ K J 6 4 ♠ A Q 10 3 2

♥ K 10 8 ♥ —

♦ A J 7 ♦ K 8 4 3 2

♣ K Q 2 ♣ 8 5 3

West opens 1NT, but North decides to intervene with a 2♥ bid. Since East/West are using Jacoby transfers, East was ready to bid 2♥, so that West could transfer to the Spade suit. Instead, East bids 2♠, and West understands this as an encouraging bid showing 5 cards in spades, since otherwise East would have passed North's 2♥ bid. West bids 3♠ to show support for spades, and East bids game.

A special case Jacoby transfer occurs when you have enough points to guarantee game, and at least six cards in the major suit. You can then bid directly 4♦ or 4♥. This is the Texas convention.

Deal 134 (Dealer South) shows Texas:

South North

♠ K 2 ♠ A 6 4

♥ Q J 8 ♥ K 10 7 6 5 4 3

♦ A Q J 4 ♦ 10 5

♣ K J 8 6 ♣ 10

South opens 1NT, and the bidding goes: 1NT — 4♦ — 4♥.

REPLY TO 2NT

The 2NT opening is not forcing, and you can pass with a very weak hand (usually 0-3 HCP). The play of the hand is particularly difficult when practically all the strength is in one hand, and so you should try to have one or two more points than the normal game minimum. The value to be assigned to partner's opening depends also on whether the partnership is using five-card majors; if it is, 2NT shows 20-22 HCP. This is the default choice for Bridge V+.

If slam seems possible, bid a 5-card suit at the 3-level or choose an appropriate notrump bid. Otherwise, show a long major suit (bidding game directly with 6 cards), or else bid 3NT.

REBID AFTER 1NT OR 2NT

Rebids following opening bids of 1NT or 2NT follow the same basic logic. We don't need to specify which range of points was set for the 1NT opening in Bidding Conventions, as long our explanation makes no explicit reference to the number of points required, since the reply will have been made with full knowledge of the strength of the opening bid.

You will often be able to decide immediately on the contract to be played. The following replies demand a pass on rebid:

Ø any 2-level bid other than Stayman, if you are not using Jacoby transfers.

Ø any game bid (3NT or 4 of a major).

Following a Stayman reply, you should show your 4-card major, or if you don't have a 4-card major, bid 2NT with maximum points (17 HCP for range 15-17), or 2♦ with less than maximum. If you have 4 cards in both hearts and in spades, bid 2♥.

Deal 2155 gives an example of this last case:

West East

♠ A K J 4 ♠ 10 8 7 3

♥ 10 8 7 3 ♥ A 9

♦ A 6 2 ♦ Q 9 5

♣ A 5 ♣ K 7 4 2

East bids 2♣ (Stayman) after West's opening bid of 1NT, and West rebids 2♥. When East refuses the heart suit by bidding 2NT, West can conclude that East has 4 cards in spades, and since East has shown maximum points, West bids 4♠.

If partner has bid a major suit at the 3-level (after a 1NT or 2NT opener), you should support with 3 cards minimum. If the suit is minor, it is preferable to have good 4-card support. Otherwise, bid 3NT.

Here's Deal 431:

South North

♠ Q 8 6 5 2 ♠ K J 7

♥ K 2 ♥ Q 10

♦ Q J 10 3 ♦ A K 6

♣ 8 3 ♣ A K Q 10 5

North opens 2NT. The bidding is: 2NT — 3♠ — 4♠.

Replies in notrump at all levels are very precise, so you should never have a problem to decide at what level the contract should be played. Thus, if partner has replied 2NT to an opening bid of 1NT, game should be bid only if the exact maximum high-card points for the range are held (17 HCP if the range was set at 15-17).

Notrump rebids after 2NT follow the same logic as those for 1NT:

Ø 2NT — 4NT invites opener to bid 6NT with 22 HCP (maximum for the 2NT range 20-22 HCP).

Ø 2NT — 5NT requires 1 point less, that is 21 HCP

Ø 2NT — 6NT shows that the responder guarantees a total of 33 HCP even for a minimum opening bid.

Here is Deal 38076. South is dealer, and the bidding goes 2NT— 5NT — 6NT:

South North

♠ A Q 6 ♠ K 3

♥ A Q ♥ 9 5 4 2

♦ K Q 7 4 3 ♦ A J 6 2

♣ K Q 3 ♣ A 10 4

SECOND REPLY AFTER A NOTRUMP OPENING

If you replied with 2♣ (Stayman), and partner bids your major suit, you will either pass, invite game by bidding 3 of the major, or go straight to game, depending on your points. If partner bids the other major, or has denied a 4-card major by bidding 2♦ or 2NT, the contract will usually be in notrump, at an appropriate level.

With 4 cards in hearts, and 4 cards in spades, partner will first bid 2♥. As we saw above for deal number 2155, if you then bid 3NT, partner can deduce that your major suit is spades, and bid 4♠.

If the reply was not Stayman, and not notrump, the sequences requiring further bidding are relatively rare.

Deal 948 ends up in a minor suit:

West East

♠ K Q 7 ♠ 5 2

♥ K Q J ♥ 4 3

♦ Q 7 5 2 ♦ A K J 10 9

♣ A K Q ♣ J 9 8 4

West opens 2NT with the maximum (22 HCP). The whole sequence is: 2NT — 3♦ — 4♦ — 5♦.

BIDDING AFTER AN OPENING OF 2 OF A SUIT

Bridge V+ uses Benjamin 2-bids, (Strong 2-Diamonds set in Bidding Conventions). The bidding after Demand 2-bids, Strong 2-Clubs, and Limited 2-bids is described in Appendix I "Other Convention Settings".

BIDDING AFTER STRONG 2♦

The weak reply is 2♥; this shows 0-7 HCP, and often removes any hope of slam. All other bids will be looking for slam, and in any case, you must not pass below game, even with zero points:

Ø show a good suit (at least 5 cards and three honours): partner will then either show his own strong suit, support your suit, or bid notrump: a 2NT rebid shows 23-24 HCP, and 3NT shows 25-26 HCP.

Ø reply notrump: 2NT shows 8/9 HCP; 3NT is 10-12 HCP.

BIDDING AFTER BENJAMIN 2♣

Benjamin 2§ shows 20-23 points, and a long as yet unspecified suit. Your reply is always 2♦: this is a "relay" bid, allowing partner to show his long suit (2♥, 2♠, 3♣ or 3♦). The relay shows neither hand points, nor the diamond suit. Your second reply is your first opportunity to make a decision:

A simple raise of partner’s suit shows slam potential, but requires 11 points or more, including support points. You can bid major game directly with 7-10 points. 2NT shows 4-7 HCP, and 3NT promises at least 8 HCP. You should pass with less than 4 HCP.

Your partner has shown a hand with a very good suit which he will name with his rebid. He will therefore either respond to your second reply, or say a little more about his own hand:

Ø with at least 4 cards in your suit, he can show support

Ø if you have bid game in partner's long suit, he will pass unless the opened suit is exceptionally strong

Ø he will likely go for slam with any other support bid

Ø he might show a second suit with at least 4-cards.

Ø he might repeat the opening suit, in particular with a 6-card major over your 3NT response.

Look again at Deal 89:

West East

♠ A K Q J 9 3 2 ♠ 10 5 4

♥ 7 3 ♥ J 10 9 8

♦ J 3 ♦ A K 7

♣ A 10 ♣ 9 3 2

West first bids Benjamin 2♣, and after East's 2♦ relay, West bids 2♠ to show the spade suit. East is missing just one point in order to bid the slam-going response of 3♠, which would show at least 11 points. He thus bids 4♠ directly, to close the bidding.

BIDDING AFTER WEAK 2♥ or 2♠

Partner has said more or less everything about his hand with the opening bid. It is up to you as responder to decide on the contract.

With less than 14 HCP, pass. Otherwise, with 20 points or more, and at least two cards in partner's suit you can try for slam. With at least an honours doubleton and 15 points in support of partner's suit (17 points for a 2♦ opening) you can bid game directly.

In Deal 91, North/South bid game in spades:

South North

♠ Q J 10 9 7 3 ♠ A K 4 2

♥ 2 ♥ A 6 4 3

♦ Q 8 7 5 ♦ A 6 4

♣ A 10 ♣ K 2

With South dealer, the opening bid is 2♠ (Weak 2-bid), and partner immediately bids game with 4♠.

With a doubleton in partner's suit, and a regular hand, you can bid 3NT with 17 HCP, or 2NT with 14-16 HCP: partner will then bid 3NT only with at least 11 HCP. Again, when lacking support in partner's suit you can bid a new suit with a minimum of 5 cards in the suit, and a good honours holding, at least AKJ or similar. If partner has at least 3 cards in your suit, he will bid game; otherwise, he will show a second suit, or repeat the opening suit.

COMPETITIVE BIDS

We have so far only considered auctions where the opponents kept relatively quiet, with only passing references to the possible effect of an opponent's bid on the natural development of a bidding sequence. Bridge V+ has been programmed to bid competitively, entering into an auction started by the opposing partnership whenever possible. This does not mean making "nuisance" bids in any and all situations; on the contrary, to guard against making ill-founded interventions that could lead to a contract at a dangerous level, the hand is evaluated for such bids in stricter terms than the simple points-count evaluation used for the opening partnership.

You can enter an auction started by the opponents in two ways:

Ø first, by using an intervention bid, to compete from an early stage with the opponents in order to reach a contract, and to prevent them from reaching theirs.

Ø second, by reopening the bidding when the opening partnership stops bidding at a relatively low level, showing comparative weakness in both hands. You can reopen the bidding with relatively few points in your hand, on the assumption that the high cards are more or less divided between the two partnerships, and that partner must in consequence have a reasonably good hand.

You are in a position to reopen when neither you nor your partner have bid (you may have passed), and where the last opponent's bid has been followed by two passes, one from your partner, who has thus failed to intervene, and the other pass from your right-hand opponent. Since the rules for an intervention are quite strict, and may cause a relatively strong hand to be passed, every occasion to reopen should be taken. In this way, if your partner would like to intervene, but does not have the right sort of hand, he may pass with confidence, knowing that you will reopen whenever the bid is indicated, thus giving him a second opportunity to show the strength of his hand.

We shall first describe the two principal intervention bids, the take-out double and the overcall, then go on to treat reopening bids. In each case, the possible replies and rebids will be dealt with at the same time as the bid which begins the competitive sequence.

THE TAKE-OUT DOUBLE

The take-out double is made by doubling an opening bid or reply. The take-out is never intended for penalties, but serves to show a certain type of hand in relation to the bidding of the opposing partnership. It is a very convenient bid, in that it conveys information without raising the level of the bidding.

The take-out is used only following a suit opening (doubling a notrump opening is always for penalties). Doubling the opening bid shows shortness in the opened suit (usually at most a doubleton), together with reasonable support in the unbid suits. The ideal distributions for a take-out double are 4-4-4-1 and 5-4-4-0, with the singleton or void in the opened suit. If you double the opponent's reply, you promise support in the suits not bid by the opponents.

You should make a take-out double if the following conditions are satisfied:

Ø the hand is worth at least 13 points (or 16 points if the shortest suit is a doubleton).

Ø no suit contains more than five cards.

Ø you have at least two unbid suits available for partner to bid.

Ø you hold reasonable support in each of the unbid suits, and no more than one of these suits has less than 4 cards. (For a take-out over two suits, you should have at least 4 cards in each unbid suit).

Here is North's hand in Deal 143:

♠ J

♥ A K J 2

♦ Q 10 5 2

♣ J 10 5 3

West has opened 1♠. North has 14 points (including support points) in support of any of the unbid suits. He also has 4-4-4-1 distribution with a singleton in spades: a perfect take-out double. South bids, and makes 3♦.

REPLY TO A TAKE-OUT DOUBLE

When your partner doubles for take-out, you can rely on support in any suit not bid by the opponents. The level of your response depends on the strength of your hand:

With a Weak Hand (0-7 points)

You should reply to a take-out double even with zero points, unless the right-hand opponent has made a bid. If the opponent has bid a suit or notrump, you can pass with less than 4 points. You can also pass in some hopeless cases where no reasonable bid is available (for instance, if you would be obliged to bid a 3-card suit at a relatively high level). Otherwise, choose your longest suit, or with two or more 4-card suits, the one that can be bid at the lowest level. Deal 58 is fairly typical:

North South

♠ A K J 3 ♠ 10 9 4 2

♥ K Q 9 7 ♥ 10 8 4 2

♦ A K J 7 ♦ 5 3

♣ A ♣ Q J 7

West opens the bidding with 1♣, and the auction goes 1♣, Double, Pass, 1♥, 2♣, 4♥. North has an ideally shaped hand for a take-out double with the singleton club Ace and 4-4-4-1 distribution. East passes, and South with 3 HCP bids his lower-ranking 4-card suit, which is hearts. West repeats his long clubs, but North jumps straight to game in hearts.

With a Medium Hand (8-10 points)

If your right-hand opponent has bid a suit in which you hold at least 4 cards, it may well be a "psychic bid" (a bid made with few cards in the suit, intended to confuse and harass the next opponent). In this case, with medium strength you can double for penalties.

Otherwise, make a jump-bid in your best suit, to show the encouraging strength of the hand, or bid 1NT with at least 7 HCP and stoppers in the opponents' suits. In Deal 233 a jump-bid reply with just 10 points results in a game contract.

West East

♠ 10 5 ♠ K 6 4 2

♥ A Q J 7 6 ♥ K 8 5

♦ 9 4 ♦ K 3

♣ J 8 6 3 ♣ A 10 9 4

North opens 1♦. East has 14 points and a doubleton in diamonds, and doubles for take-out. West must jump to 3♥, showing 8-10 points. East has no hesitation bidding game in hearts.

With a strong hand (at least 11 points)

Having a strong hand in response to a take-out double is quite rare, since the two preceding players both have opening hands. With 5 cards in a major suit, and at least 11 points, you can immediately bid game. East does so in deal number 1877:

♠ A 10 7

♥ K Q 8 5 4

♦ K 8 6 4

♣ 8

South is dealer, and opens 1♦. West doubles, and North bids 1♠ in response to South's opening bid. East then jumps directly to 4♥,

You might bid a minor suit at the four level, but this will be extremely rare. This happens in deal 2898, which is interesting in many respects:

West East

♠ 10 4 ♠ K 9 7

♥ K 7 4 ♥ 5

♦ Q J 9 7 4 2 ♦ K 10 8 6

♣ Q 2 ♣ A K 10 5 4

North opens the bidding with 1♥. East has a singleton heart but only three cards in spades. However, the three cards include the King, and East has a strong hand with 14 HCP concentrated in Aces and Kings. The bidding goes 1♥, Double, 3♥, 4♦, Pass, 5♦. The contract goes down 1 trick, but note that if East had not bid double, North/South would have made game in hearts.

[NOTE: a reply in notrump is not impossible, but it is very rare, and if it happens it is usually after the right-hand opponent has redoubled.]

REBID AFTER TAKE-OUT DOUBLE

If partner bid game, or doubled for penalties, you can normally pass. If partner replied in notrump, consider a raise in notrump according to the number of high-card points that you hold, or bid a long suit when the hand is uneven (5-4-4-0, 5-4-3-1). You can support a suit bid by partner with one or two less points than following a normal opening. You know the strength of partner's hand from the level of the reply, and so you can calculate the combined partnership points, adding support points where necessary, to decide at what level the contract can be played.

OVERCALLS

You can overcall an opponent's bid either in a new suit or in notrump. Overcalls in notrump are always strong (16-18 HCP for 1NT; 20-22 HCP for 2NT). You should have a stopper in the opponent's suit.

When you overcall, at least one of the opponents has already shown some strength, so the likelihood of finding partner with a very weak hand is increased. You must therefore be aware of the risk of getting into a poor contract. In addition, because of the competitiveness of the situation, there will normally be little time for exploratory bidding. You should therefore never make an overcall with less than a good 5-card suit, or a 4-card suit with at least two honours. Partner will be able to support with three small cards. As well as having a good suit, your hand should have general playing strength in tricks to guard against going down too seriously.

The number of tricks required depends on the level of the overcall: for a bid of 1♥ or 1♠ you need at least four playing-tricks, and slightly more for the minor suits. For an overcall at the 2-level, you need at least five playing tricks. Count one more trick in all cases when you are vulnerable.

The overcall suit should contain high-card values corresponding to the level of the bid: at the 1-level, something like a 5-card suit with two honours, or a 6-card suit with at least one honour is good, while at the 2-level, the suit should be better still, say three honours or two good honours in a 5-card suit, or two honours in a 6-card suit. With a strong hand worth 7 or 8 tricks, including a very good suit, a jump-overcall should be used to inform partner of the exceptionally strong holding.

The following comparison will explain the difference between a hand suitable for an overcall, and one that is not:

(1) (2)

♠ Q 8 7 ♠ 7

♥ J 10 5 ♥ Q J 10 5

♦ K J 9 3 2 ♦ K J 10 9 3 2

♣ K Q ♣ 8 7

Hand (1) has 13 points. and 12 HCP; it would, however, be very unwise to overcall with this hand, even at the 1-level, for it is worth barely more than 3 tricks. Hand (2), with 11 points (and only 7 HCP) is a very good proposition for a 2♦ overcall following a spade opening; the well-linked heart and diamond suits can between them be counted upon for 6 tricks however weak partner should turn out to be.

You should apply the same rules for a pre-emptive intervention as for the normal pre-emptive opening, as long as the pre-emptive bid does not go beyond the 3-level. You need a seven-card suit and a weak hand (4-8 HCP). The pre-emptive bid is a double-jump overcall, for example: 1♦, 3♥ or 1♥, 3♠. (A single jump would show a strong hand, as described above).

North in deal 97 has a good hand for a strong jump overcall:

♠ A K 7 6

♥ 8

♦ A 4

♣ K Q 7 4 3 2

North can count just 7 playing-tricks, and 20 points. This is minimum for a strong overcall, but the high honours add some extra assurance.

Weak Jump Overcalls

Strong jump overcalls are fairly rare. A modern development is to jump instead with weaker hands in order to hinder the opponents' bidding, and to bid all other overcalls at the minimum level, knowing that stronger hands can be shown later in the bidding. If the “Weak jump overcalls” convention is set, a jump overcall shows a good suit with at least 6 cards, and 6-12 points, about the same as required for a weak 2-bid.

Consider deal 161:

North

♠ A 7 4 3

♥ K

♦ Q 9 8 6 5

♣ K 10 4

West East

♠ 6 5 2 ♠ 10 8

♥ 10 7 ♥ Q J 9 8 6 4

♦ A K 7 4 3 2 ♦ 10

♣ J 9 ♣ Q 7 6 5

South

♠ K Q J 9

♥ A 5 3 2

♦ J

♣ A 8 3 2

South is dealer. If Weak jump overcalls are not set, West can overcall at the 1-level, having 5 or 6 playing-tricks. The bidding in this case is: 1♣, 1♦, 1♠, Pass, 2♠, Pass, 3♠ Pass, 4♠. When Weak jump overcalls are set, South still open 1♠, but this time West will bid 2♦, which is a jump-overcall. North and South both now consider themselves too weak to bid at the 2-level, and the contract is stolen!

In the previous section, deal 97 was used as an example of a strong jump-overcall:

North South

♠ A K 7 5 ♠ 10 9 4 2

♥ 8 ♥ 10 8 4 2

♦ A 4 ♦ 5 3

♣ K Q 7 4 3 2 ♣ Q J 7

West is dealer, and opens the bidding with 1♥. With Weak jump overcalls not set, North makes a strong jump overcall of 3♣, and everyone passes. In a way, the strong jump overcall has pre-empted the East/West bidding (West as declarer can make game in hearts). However, with Weak jump overcalls set, North overcalls with 2♣. This is not enough to prevent East from supporting his partner by bidding 2♥, but North can now compete by bidding his second suit, and his partner concludes with 4♠, which makes! (Note that in this deal North/South have fewer honours points than East/West).

Bridge V+ testing has shown that Weak jump overcalls work better than strong jump overcalls, at least in the context of Bridge V+ bidding. For this reason, Weak jump overcalls are set for the East/West partnership in tournament mode. Of course, you can choose whether to use Weak jump overcalls and all the other convention settings for the North/South partnership, with you as South.

BIDDING AFTER A SUIT OVERCALL

Support reply

An overcall necessarily shows a good suit, so the preferred reply is to support that suit, even with only 3 small cards, or a doubleton containing an honour. However, since the overcall is based on a count of playing tricks, it may have been made with a hand relatively weak in points, so you need to have a few more points than you would need for a reply to a normal opening bid. You should count support points, of course.

Ø simple support 9-12 support points

Ø jump support 13,14 support points

Ø double jump 15 support points or more

Deal 95 shows a successful intervention by East

West East

♠ 10 8 6 5 ♠ A K 9 4 3 2

♥ A K 7 3 ♥ Q J 4

♦ 6 ♦ K 9 8

♣ 8 6 5 4 ♣ 7

North is dealer, and opens 1♦. East overcalls with 1♠. West has good support for spades, and 10 points counting an extra point for support, and can bid 2♠ over South's 2♣. East invites game with 3♠, and west concludes with 4♠.

Reply in notrump

Notrump bids opposite an overcall always show a regular hand, preferably with a stopper in the opponent's opened suit. 1NT shows 8-9 HCP and 2NT shows 10,12 HCP. The opener can then repeat a 6-card suit, or bid 3NT if holding the adequate number of honours points.

Deal 581 shows a 2NT reply to 2-level overcall:

West East

♠ Q 7 ♠ 6 5 4

♥ Q 5 4 3 ♥ A 8 6

♦ 6 ♦ A K 7 5 2

♣ A K Q 7 3 2 ♣ J 8

South is dealer, and opens 1♥. West overcalls with 2♣. East has 12 HCP and a doubleton in partner's suit, and so bids 2NT. West is then happy to go to 3NT game, knowing that the club suit will probably bring six tricks.

Suit-Change Reply

A minimum level bid in a new suit is normally a sign of weakness, always denying support of the overcall suit. You should not use it with less than a 6-card suit. It informs partner of a probable misfit, and requests him to pass, thus allowing the contract to be played in your long suit, rather than the overcall suit.

There is one important exception: with a good major suit opposite partner's minor overcall you can use a suit-change bid in the hope of finding a better contract in the major. The major should be good enough to itself warrant an overcall. Deal 671 gives a nice example of this special case:

West East

♠ 9 3 2 ♠ K Q J 8 6 5

♥ 9 ♥ 8 5 4

♦ A 7 5 4 2 ♦ Q 3

♣ A Q 10 5 ♣ 8 6

South is dealer and the bidding goes as follows: 1♣, 1♦, 1♥, 1♠, 2♥, 2♠, 3♥, 3♠, 4♥, 4♠, Pass, Pass, Pass

West's overcall of 1♦ is based on the good minor suits. East has a good spade suit, and can definitely afford to show it. West has 3 cards in spades, and can support partner with 2♠ over South's 2♥ bid. The two partnerships then compete all the way to game in spades for East/West, which just makes.

With a strong hand (at least 13 points), and a 6-card suit (major or minor), you should use a jump-shift. With 13 points but no 6-card suit, a cue-bid should be made in the opened suit, to invite partner to say more about his hand, in particular to show a second suit if one is held.

Deal 4557 shows how a cue-bid reply can help a partnership to an impressive slam contract:

West East

♠ K 7 5 4 3 ♠ 10 8

♥ A 4 ♥ 10

♦ A K 7 6 ♦ Q J 9 8 5

♣ 10 9 ♣ A K Q 5 4

South opens 1♣. West has a decent diamond suit, and can count 5 or 6 playing tricks, so overcalls with 1♠. East has only a doubleton in spades, but has two or three quick-tricks, 13 points, and two good suits. Since East has no real reason to prefer diamonds, a cue-bid makes sense: East therefore bids 2♣. This is a cue-bid because the opponent opened a club: the fact that East has such a good club suit is incidental. West shows his other good suit (diamonds), and the partnership gets to game in diamonds!

Here is the full auction: 1♣, 1♠, Pass, 2♣, Pass, 2♦, 2♥, 4♦, Pass, 5♦, Pass, Pass, Pass

REOPEN

Because of the restrictions imposed on intervention bids, partner may have passed with a fairly good hand; you should miss no opportunity to re-open the bidding. Remember, though, that re-opening does entail a certain amount of risk, and should only be attempted when there is good reason to suppose that the opponents are weak, and when the level of bidding does not present any particular danger. Typical opening sequences showing weakness are the following:

1) A passed opening of 1 of a suit (e.g. 1♠, Pass, Pass) — your right-hand opponent has probably less than 5 HCP, and even though the opening may be quite strong, there is a reasonable probability that the points are divided between the two partnerships.

2) A pass at the rebid following a weak reply. Examples:

1♦, Pass, 1NT, Pass, Pass;

1♦, Pass, 2♦, Pass, Pass.

3) A weak rebid following a 1-level reply. Examples:

1♦, Pass, 1♠, Pass, 2♦, Pass, Pass;

1♥, Pass, 1NT, Pass, 2♥, Pass, Pass.

4) Simple preference as second reply following a weak combination rebid. Example:

1♦, Pass, 1♠, Pass, 2♣, Pass, 2♦, Pass, Pass.

Here, the only reasonable re-opening is a bid of the missing suit (hearts in the example given).

If you find yourself in one of the above situations, you should reopen the bidding according to the following rules:

Ø with less than 7 HCP, pass.

Ø bid 1NT with an even hand worth 10-12 HCP, when holding a stopper in the opening suit.

Ø with 7-10 HCP, and a 5-card suit not bid by the opponents, bid the suit at the lowest level (only go to the 3-level if the suit has at least 6 cards).

Ø in all other cases, double as long as the bidding has not passed the 2-diamond level (remember that doubling 2 of a major can be risky); also, if the opponents have bid two suits, you should hold at least 4 cards in each of the unbid suits.

Finally, you can double a pre-emptive bid when holding at least 16 points, and a strong suit.

In deal 622, South reopens with 1NT:

♠ Q 6 5

♥ A 10 9

♦ Q 10 8 4

♣ Q 10 7

West opens 1♣, bidding goes 1♣, Pass, Pass, 1NT,...

BIDDING AFTER RE-OPEN

You should be very careful when replying to partner's re-opening bid, since it may have been made with relatively few points.

If partner has bid a suit at level 1, he has a relatively weak hand with only 7-10 points. Three cards are sufficient for a support bid, but to have a reasonable chance of game, the hand must be quite strong, say about 17 points, counting support points. Then with some kind of strength of his own, partner will rebid.

If partner has bid 1NT, count high-card points to determine at what level the partnership can play a notrump contract. Normally, you would bid 3NT with 14 HCP, or 2NT with 12-13, expecting partner to go to game with maximum points. With an irregular hand unsuitable for notrump, a simple raise of your suit is discouraging. A jump-bid should be used to show 14 points or more. Partner will raise with good support.

You can pass a reopen double for penalties, only with a strong holding in the opponent's suit (at least 4 cards including QJ or better), and if the opening bid was not 2 of a major suit. Otherwise, you should show a suit, or bid notrump, unless released from the obligation to reply by a bid from your right-hand opponent. With 14 points and a good suit, you should make a jump bid, and with 14 or 15 HCP and a regular hand, bid 2NT. Partner should have no problem in deciding whether or not to rebid.

Deal 792 shows an example of reopening with a suit:

West East

♠ Q J 9 8 5 4 ♠ A K 10

♥ Q J 8 ♥ 7

♦ J 5 2 ♦ A 9 7 6

♣ 7 ♣ K J 6 5 3

When North opens with 1♣ East has a difficult decision to make. Clubs are his best suit, and diamonds don't look very good for an overcall. Here, Bridge V+ passes, knowing that his partner will reopen if he can. West has only 7 HCP, but can show his 6-card spade suit: he bids 1♠. North competes with 2♥, and East supports spades with 2♠.

Now take a look at deal 191:

West East

♠ A 6 5 4 ♠ K Q 8 2

♥ 10 3 ♥ J 8 6

♦ J 10 8 4 3 ♦ A Q 6

♣ A 8 ♣ Q 10 6

South opens 1♥, and the bidding goes 1♥, Pass, 1NT, Pass, 2♥, Pass, Pass. West is clearly too weak to overcall this time and so had to pass the opening bid, but East has 14 HCP, and both North and South have shown that they are relatively weak. East doubles, and West can now show his diamond suit with 3♦.

SLAM BIDDING

You should verify two critical conditions before making a slam-going bid:

Ø the partnership must have agreed on a suit; you have good support for a suit bid by partner; or you have a suit that can stand alone

Ø the partnership must be assured of 32 points for slam in a suit, or 33 HCP for a slam in notrump

You need to be sure of the trump suit before trying for slam, because 32 points is a good statistical minimum only if a solid trump suit (8 cards in the two hands) is held.

Before you actually bid slam, however, you need some extra information; you must be reasonably confident that the opponents cannot defeat the contract by cashing quick tricks against which the partnership has no defense. In particular, the opponents must not hold two aces, unless you have a void in one of the suits. If the partnership definitely has at least 33 HCP, the opponents cannot have two aces; however, a partnership total of 32 points cannot guarantee two aces, and so more information is needed.

Slam bidding is designed to elicit the suit controls held by the partnership. An ace is a first-round control, and a guarded King or a singleton is a second-round control. A void guarantees both first and second round control of a suit.

THE BLACKWOOD CONVENTION

This well-known convention is frequently misused. You should bid Blackwood only in strictly defined circumstances:

Ø 32 points in the partnership hands must be guaranteed, or at least highly likely.

Ø your hand must not contain a void suit.

Ø you must have first or second-round control in each suit (or, where missing both controls, partner's bidding must have shown that he probably controls the suit).

The Blackwood Convention uses the 4NT bid to request partner to specify the number of aces he holds. He must make one of the following responses:

5♣ no aces, or all aces held

5♦ one ace

5♥ two aces

5♠ three aces

The level of these responses imposes further restrictions on the use of Blackwood. Thus, if the agreed trump suit is clubs, you must hold at least two aces in order to contemplate using Blackwood (otherwise, a 5♦ reply would render an eventual slam bid inevitable, even though the partnership is missing two aces). Similarly, with diamonds as trumps, you should have at least one ace.

If partner's reply guarantees that the partnership holds all four aces, and if the minimum partnership strength is 35 points, grand slam is possible, and you can bid 5NT to ask partner to specify the number of kings in his hand. He does this in the same way as for aces, though bidding at the 6-level.

There are very occasionally cases where you will use Blackwood to bid to slam, even though the hand does not satisfy all of the restrictions listed above. This will usually be when you are sure of having much more than the minimum number of points for slam, have no alternative way of checking suit controls, but want to check that partner has at least one ace.

First, though, let's look at an example where Blackwood is justified, and functions correctly, (deal 567):

West East

♠ A 10 9 7 4 3 ♠ K J 2

♥ J 9 ♥ A K Q 8 6 2

♦ K 2 ♦ A Q 7

♣ A K 3 ♣ 10

South has dealt, and West opens the bidding with 1♠. East has 19 HCP, and 22 points, and jump-shifts to 3♥. When West rebids his spades, East, with KJ2 in spades, knows that slam is highly likely. He has 2 aces, and 2nd-level control in the other two suits, and so bids 4NT. West shows the two remaining aces with his 5♥ bid, so East can ask for kings with 5NT, and does so. East indicates that he has the two remaining kings, and East can bid the grand slam with relish, though perhaps disappointed that partner is playing the contract!

The entire bidding sequence is: 1♠ — 3♥ — 3♠— 4NT — 5♥— 5NT— 6♥— 7♠.

Having seen an example of when to use Blackwood, let us now examine a case where Blackwood should not be used. First, to illustrate the folly of using Blackwood with a void, consider North's hand in deal 72:

♠ A Q 10

♥ A K 6 3

♦ —

♣ Q 10 8 7 6 3

North as Dealer has opened the bidding with 1♣, and the bidding sequence up to the second rebid has been:

1♣ — 1♦ — 1♥—4♥. Suppose North now bids 4NT; South will bid 5♦ showing one ace. Should this be the ace of diamonds, a slam contract is hopeless. The use of the Blackwood convention has helped the bidding in no way; indeed, the player is in exactly the same situation as before bidding Blackwood, in that he has to take an uniformed guess on which ace partner is holding. The solution to this problem is to use control bidding, as will be explained in the next section.

The Blackwood convention is also not the best way to get to a slam when you have a suit lacking both first and second round controls: that is, a suit of two cards or more that contains neither the King nor the Ace.

Take a look at deal number 123, with North dealer: East/West have a good chance for slam with the following holdings:

West East

♠ A K J 5 ♠ 8 3

♥ A K J 9 7 3 ♥ Q 8 5 2

♦ 8 6 ♦ 2

♣ 9 ♣ A K J 6 4 3

East opens 1♣, and West jump-shifts to 2♥ (over South's 1♦ intervention), showing at least four hearts, and a minimum of 16 HCP. East supports hearts, and West obviously wants to get to slam, but how?

West has no void suit, so Blackwood might seem reasonable, but what about that diamond suit? East will reply 5♦ to a bid of 4NT, showing one ace. So, West now knows that the partners have three aces between them. The problem is, that East may be showing the ace of clubs, and West can be sure that his smart opponent will lead diamonds, possibly meaning that the contract will go down in the first two tricks.

There is, of course, a surer way of finding a slam in this situation: you can use control bids.

CONTROL BIDS

When you cannot use Blackwood, you might instead be able to show control by bidding a suit which includes the Ace, or has no cards at all. You can only make a control bid once a trump suit has been clearly agreed; this usually means that a suit bid by one partner has been supported by the other.

Exceptions to this rule occur when show, or support, a major suit when a minor seems to have been agreed. For example, consider the sequence: 1♦— 2♣ — 3♣ — 3♥. Responder has first shown a long suit in clubs; when he later bids 3♥, he is showing at least 4 cards in hearts in the hope of playing a major contract.

Here the partner of the opening bidder shows a natural preference for game in a major over a minor contract. Contrast this with 1♥ — 2♣ — 4♣ — 4♦, which is a definite slam attempt, showing first round control in diamonds (ace or a void).

Once one player has shown a control, his partner should respond by showing a control in his turn at the lowest level possible, or, if no control is held, by returning to the trump suit. It is then the turn of the first player to show his next control, return to the trump suit, or pass. This exchange of information will eventually end with a bid in the agreed trump suit, or possibly in notrump.

Now let us return to the example introduced in the previous section (deal 123), to illustrate one of the limitations of the Blackwood convention. Here again are the East/West cards:

West East

♠ A K J 5 ♠ 8 3

♥ A K J 9 7 3 ♥ Q 8 5 2

♦ 8 6 ♦ 2

♣ 9 ♣ A K J 6 4 3

West prefers not to use the Blackwood convention after East’s support of his heart suit, since if East shows only one ace, it could well be the ace of clubs, and the slam contract might be hopeless.

Suppose that instead of bidding 4NT, West bids 3♠. Clearly this bid does not show a second suit, since a good major has already been found: instead, it shows first-round control in spades, either the Ace or a void.

East can now bid 4♣, showing the Ace of clubs. Since East opened with the club suit, the control bid cannot possibly show a void in clubs.

Ignoring South's 1♦ overcall, the full sequence of bids for East / West is as follows:

1♣ — 2♥ — 3♥— 3♠— 4♣ — 4♠— 5♣ — 5♥— 6♥

When West bids 4♠ East knows that West has either AK of spades, or a void, and when East continues with 5♣, he shows AK of clubs, since he cannot be void in clubs, having bid them. Notice, however, that with these last two bids both players have denied having a first-round control in diamonds. For West, this means that he cannot call slam, since the opponents could possibly take two tricks right at the start, so he must sign off with 5♥.

East, however, has a singleton diamond, and knows that he can trump a second diamond lead. The only question remaining is whether or not West holds the ace of trumps. Since he showed 16 HCP with his jump-reply, that seems a reasonable bet, and East goes on to slam in hearts.

Most control sequences are much simpler than this one, but much essential information was exchanged between the partners, and the final slam bid is a very reasonable one. In fact, Declarer makes 13 tricks.

You can usually reach slam without making as many bids as in Deal 123, and sometimes you don't even need to explicitly check the controls. Deal 62 gives an example of this:

South North

♠ K Q 6 ♠ A 10

♥ A J 9 7 ♥ K Q 2

♦ 6 ♦ A K 10 4 3

♣ 10 8 6 5 3 ♣ A Q J

Using Benjamin 2-bids, North opens 2♦ and the bidding goes: 2♦— 2NT—3NT— 6NT. When North rebids 3NT, showing a regular hand with at least 23 HCP, South goes directly to 6NT.

How can South, who only has one Ace, make this decision? He simply counts combined honours points: he has 10 HCP which when added to North's guaranteed 23 HCP, make 33 HCP. It is thus impossible, with only 7 HCP remaining in the deal, for East/West to have more than one Ace. It would not even be unreasonable for South to have replied 3NT showing 10-12 HCP, in which case North could have also gone directly to 6NT: 2♣ — 3NT — 6NT!

In deal 1181, just one bid serves to clinch a slam contract:

West East

♠ K Q J 5 ♠ A 7

♥ 10 8 4 3 ♥ A J 9 5

♦ A 5 ♦ K 10 9 6 3

♣ J 6 2 ♣ A K J 6 4 3

East opens 1♦, and West bids 1♥. When East bids 4♥, showing at least 20 points in support of hearts, West sees a possible slam. He can't use Blackwood, because of the weak club suit, but can suggest slam by bidding 5♦ to show the ace. East gladly accepts the invitation by bidding 6♥.

Finally, let us take a last look at deal 123, which has already been such a fruitful example for slam bidding. Here, once again are the East West hands:

West East

♠ A K J 5 ♠ 8 3

♥ A K J 9 7 3 ♥ Q 8 5 2

♦ 8 6 ♦ 2

♣ 9 ♣ A K J 6 4 3

This time, West is dealer, and starts with 1♥ to show his strong heart suit, which East supports with 4♥. West shows his first control with 4♠, and East follows with 5♣, for the Ace of clubs. West cannot bid slam because of the useless diamond doubleton, and so returns to the agreed suit with 5♥. East, however, controls has second-round control of the diamond suit with his singleton, and bids slam on the strong possibility that West has the Ace of trumps.

In this deal, you could also bid 2♣ Benjamin with West's hand, showing 20-23 points and a strong suit. East would make the 2♦ relay bid, and you could then show that hearts are your long suit. East then knows that the partnership has a slam in hearts. He can't show his control in clubs, because partner could mistake that for a natural bid (which it also could be!). East reckons the partnership has over 35 points, and knows he must bid slam, except in the almost impossible case where West has only one ace. So, as a safety precaution he could bid Blackwood, and would be rewarded by the knowledge that the partnership has three aces, and his singleton diamond.

There is a category of hands where Bridge V+ will bid a slam directly, and which you may come across (especially, of course, if you use the "Select hand" Menu option and search for slam bids). Deal 4984 gives us a nice example:

West East

♠ 10 9 7 ♠ K Q 8 2

♥ 2 ♥ A K Q 10 6 5 4

♦ 9 8 5 4 3 ♦ —

♣ K 10 9 8 ♣ A Q

East opens 2♦ (Benjamin), and West makes the weak reply of 2♥. This happens to be East's long suit, and East bids 3♥, knowing that partner must bid. West has a singleton heart, but the Club king might be useful, and the hand is not too uneven, so 3NT seems reasonable. Now, what can East do? Blackwood would give useful information only if West has 2 aces, and he can't have two aces since he replied 2♥, and if West has one ace, Blackwood changes absolutely nothing. This is a "go for it" situation (the algorithm is a little more complicated than that!), so East bids 6♥ directly.

PENALTY DOUBLES, AND SACRIFICE BIDS

Deciding on when to double for penalties is more an art than a science. It is hard to find rules that work more than 50% of the time. Indeed, it is perhaps more important to know your opponents in order to guess whether they have gone too far on a given deal (and Bridge V+ can't do that yet!).

Bridge V+ will double for penalties when there is reasonable justification for thinking that the partnership together have enough defensive tricks to defeat the opponent's contract. Defensive tricks are counted as follows:

➢ count any playing-tricks in trumps as defensive tricks. High-card tricks are rare, but do occur. Count four cards in the trump as worth half a trick; even if none of the trumps actually makes, declarer's play is likely to be appreciably handicapped by the need to deal with a long adverse trump holding. Each trump card beyond the fourth (a relatively rare occurrence) counts as a full defensive trick.

➢ count all quick-tricks in side suits (playing-tricks are counted in the trump suit), to a maximum of two quick-tricks per suit.

➢ the number of defensive tricks held by partner can never be known with confidence; however, some reasonable suppositions can be made. An opening bid in a suit, or a strong 1NT opening, can generally be relied on for 1½ tricks .

If you follow these rules, you should get a positive result from your penalty doubles. Bridge V+ does this, and is thus fairly conservative about doubling. However, if you get to a really bad contract, you can expect to be punished! Bridge V+ does not know its opponents of course, and so cannot take relative playing strengths, or flamboyant characters into consideration.

High-level bids are special: you should not double slam contracts unless certain or practically certain of defeating the contract: for example, with ace of trumps against a grand slam, or two aces against 6NT. (Note that no conventional play-related doubles are currently used by Bridge V+).

Deal 206 shows a difficult case for deciding whether to double, or bid at the 5-level:

South North

♠ K Q 9 6 3 2 ♠ A 8 7 5 4

♥ J 10 5 4 ♥ K 7 6 3 2

♦ 4 ♦ 9 3

♣ A J ♣ 8

This is a very typical situation. South opened 1♠, and North can hardly believe his luck: five cards to the Ace in partner's major suit! East intervenes with 2♦, but North is just strong enough to bid 3♠. East passes, and South bid bids game in spades. Everything looks good for North/South until West bids 5♦. This could be a sacrifice bid, but neither North nor South has ever shown anything more than minimum points for their bids. North's 3♠ bid in particular is justified only by the singleton club.

So, 5♠ may be difficult to make. What about a penalty double of the 5♦ bid? North counts 1½ quick-tricks. His partner has opened, so maybe the partnership can take the three tricks necessary to defeat the 5♦ contract. Sometimes, instead of doubling, it is better to bid beyond an opponent's game contract, knowing that you will probably go down, but calculating that you won't go down too much (even doubled), and that your opponent would have made his game contract. This is called a "sacrifice bid". Judging when to double and when to sacrifice is very difficult, and yet an important part of the game, especially in duplicate tournaments.

[At the time of writing (first update), Bridge V+ bids 5ª, but at the time of the first version it doubled. As the code evolves it might go back to preferring the penalty to the sacrifice bid. It is hard to know what is the “correct” bid...].

In deal 1355, East makes a good sacrifice bid:

West East

♠ 8 3 ♠ 10

♥ K J 7 3 ♥ 2

♦ A Q 7 5 4 ♦ K 10 9 8 2

♣ Q J ♣ K 9 8 7 3 2

With dealer South, the first time East gets to bid, he has a difficult decision to make: the bidding has so far gone: 1♠, 2♦, 4♠... It really looks like North/South will make their contract in 4♠, but East has excellent support for West's diamonds, and West's bid was relatively strong. It is highly unlikely that the partnership will make 11 tricks in diamonds, and they will probably be doubled by an opponent, but perhaps the risk is acceptable (we'll assume for now that East/West are not vulnerable).

East bids 5♦, and North doubles for penalties. East/West lose 100 points for going down 1 trick, whereas the 4♠ contract would have cost 420 match-points. The sacrifice has succeeded (and would have succeeded even if East/West were vulnerable).

Sometimes, a sacrifice bid is not reasonable, and you have to take the chance on defeating the contract with good defensive values. West's hand in deal 326 is a good example:

West East

♠ A Q 10 5 ♠ 7

♥ — ♥ 9 6 2

♦ A J 8 7 5 ♦ 9 6 4 3

♣ A 10 8 7 ♣ 9 6 4 3 2

South opens 1♠, and West very reasonably overcalls with 2♦. North bids 3♠, and his partner takes it to game. What should West do? He has perhaps 7 playing tricks, but partner has always passed, so there is no reasonable bid over 4♠. However, West has 4 cards, including A,Q,10 in the trump suit, as well as two other Aces. Clearly he must double, and sure enough, North/South go down 2 tricks in their 4♠ contract.

[East has a "Yarborough", with no card above the nine-spot. The name comes from the Earl of Yarborough, a 19th century Whist player, who offered his co-players odds of 1000:1 on getting such a hand. Since the odds are actually about 1400:1, the Earl was able to make a good profit during his card-playing years!]

APPENDIX I: OTHER CONVENTION SETTINGS

In the main part of the Handbook, we chose to describe the set of conventions used by Bridge V+ in Tournaments mode. This has kept the explanations as simple as possible, (Bridge bidding is not at all easy to learn!), and has avoided the confusion that could be caused by trying to consider too many variants and combinations of variants, while trying to understand the overall logic of the bidding system.

In this Appendix we shall discuss the effects of Conventions settings other than those used by Bridge V+ in Tournaments mode, when they have not already been covered in the main text.

Five-card majors convention not selected

This is basically "Standard American": all suits are treated in the same way; the suit chosen to be opened depends on the distribution: a perfectly flat hand (card distribution 4-3-3-3) is always opened 1♣. With a distribution of 4-4-4-1 the choice of suit is determined by the singleton:

Ø With a singleton heart or spade, open 1¨

Ø With a singleton diamond, open 1§

Ø With a singleton club, open 1©

These rules aim to facilitate the early discovery of a 4-4 fit with partner. Otherwise, the hand is treated as for 4-4-3-2 distribution. That is, the suit of higher rank is opened when the 4-card suits are adjacent, the lower-ranking suit otherwise.

For all other distributions, you should open the longest suit, or with two suits of equal length, open the higher ranking suit.

In the description of the Better Minor, and Short Club conventions for choosing which of two minor suits to open at the 1-level, we used deal 343 to explain the difference between the two systems. Here again is the South hand in deal 343:

♠ K 8 7 6

♥ A K 5 4

♦ Q 7 3

♣ 4 2

Using five-card majors, you will choose one of the minor suits, depending on whether you use Better Minor, or Short Club. When not using five-card majors, (Standard American), the rule to be applied is the one cited above for 4-4-3-2 distributions: therefore, you will open 1♠.

Now, suppose that we switch around a few card values, so that there are five cards in the diamond suit.

♠ K 8 7 6

♥ A 5 4

♦ K Q 7 3 2

♣ 4

1♦ should be opened whether using five-card majors or not.

Deal 343 is actually very interesting.

If 5-card majors are used, the bidding is: 1♦— 2♠ —3♠ — 4NT — 5♦ — 6♠.

Without 5-card majors, we have instead: 1♠— 3♦ —3♥ — 4NT — 5♦ — 6♠.

Notice that in both cases, N/S reach a small slam in spades. The only difference is that with the 5-card major convention, North is declarer, and when not using 5-card majors, South is declarer. As it turns out, the consequence of this change of declarer is enormous. In the first case, with North declarer, East leads the Jack of diamonds, and the contract goes down 3 tricks! With South declarer, West cannot lead diamonds (he has none!), and quite reasonably chooses a small heart instead. South is able to draw trumps, and goes on to make the small slam.

This does not mean that Standard American is better than five-card majors; it just means that there is a real element of luck in Bridge, and that adds to the fun! In other situations, using five-card majors will give better results than using Standard American. Remember also, that while Bridge is primarily a game of skill, chance does play a fairly large part in the game.

1NT openings

When I first learned Bridge, almost everyone used the "Strong 1NT" convention of 16-18 HCP. Some players were experimenting with "Weak 1NT" (as well as weak 2-bids). For some of these, Weak 1NT meant 13-15 HCP, and for others 12-14 HCP, evolving to this latter range over time. Now, many people have adopted a range of 15-17 HCP. To handle all of this, Bridge V+ offers 4 different ranges for a 1NT opening: 12-14, 13-15, 15-17, 16-18.

Consider deal 207:

North

♠ Q 9 2

♥ 10 8 3

♦ 10 9 8 7 6

♣ K 3

West East

♠ A 4 ♠ J 10 6 5 3

♥ K J 9 7 5 ♥ Q 4 2

♦ 4 2 ♦ A 5

♣ Q 10 9 6 ♣ A 5 4

South

♠ K 8 7

♥ A 6

♦ K Q J 3

♣ J 8 7 2

South is dealer. With 1NT range set at 15-17, the auction is: 1♦, 1♥, 2♦, 2♥, Pass, Pass, Pass. West just makes the 2♥ contract. However, if the 1NT range is set at 12-14, South opens 1NT, and all the other players pass. South's bid has successfully prevented the East/West partnership from finding their heart suit (and even makes 9 tricks!

So, what is the best range for 1NT opening bids? The statistical answer is that it really doesn't matter which one you choose, as long as your partner chooses the same one! Bridge V+ of course will play whichever system you prefer. Note that whatever the range setting, Bridge V+ won't open 1NT with 5 cards in a major suit, and it will only bid 1NT with one of the distributions 4-3-3-3, 4-4-3-2 or 5-3-3-2.

Demand 2-bids

If neither Strong 2-Clubs, nor Weak 2-Bids are chosen, an opening bid of 2 of any suit implies a very strong hand, with at least 24 points. All 2-bids are forcing to game, and so partner must reply, even with zero points. In most cases, the eventual contract will be in the opened suit; it must therefore be solid: five cards with 4 honours, six cards with 3 honours (or Ace and King), or seven cards with 2 honours.

In deal number 145, South’s hand is:

♠ A K Q 10 5 4

♥ —

♦ A K 7

♣ A Q 8 4

With Strong 2-Diamonds selected, Bridge V+ opens 2♦; if Strong 2-Clubs selected is selected, Bridge V+ opens 2♣; if neither are selected, Bridge V+ will use the demand 2-bid of 2♠.

The Strong 2-Clubs convention

The demand 2-bid certainly succeeds in showing a very strong hand. Unfortunately, it can be used only very rarely. The Strong 2-Clubs convention was invented (by Pierre Albarran and David Burnstine) to make better use of level-2 opening bids. Thus, 2♣ indicates that a very strong hand is held, but does not specify which is the strong suit. It can at the same time be used to show a very strong regular hand with 23-24 HCP (and hence too strong to open 2NT). Subsequent bidding will determine whether the opening showed a very strong suit, or a hand with lots of high cards.

The remaining 2-bids, 2♦, 2♥, and 2♠, are thus freed for other bidding purposes: they can either show very good hands, not quite good enough for a strong 2♣ opening (Limited 2-bids), or alternatively, hands not strong enough even for a normal opening of 1 of a suit, but with a very nice six-card suit: these are Weak 2-bids, already described for Benjamin 2-bids. Note, however, an important difference: this time, 2♦ is also a weak opening bid

Thus, if you choose Strong 2-Clubs in Bidding conventions, and set Weak 2-bids, all 2-bids other than 2♣ are weak openers; if you unset Weak 2-bids, you are using Limited 2-bids.

Limited 2-bids

When the Strong 2-Clubs convention is used, but Weak 2-bids are not set, a bid at the 2-level in another suit promises just 20 to 23 points, and a solid suit: five cards with 4 honours, six cards with 3 honours (or Ace and King), or seven cards with 2 honours. When the long suit is not sufficiently strong, you should open the suit at the 1-level, and then show the strength of the hand with a powerful rebid.

Take a look at Bridge V+ deal number 1012:

South North

♠ 3 2 ♠ A K Q 8 7 4

♥ A 10 7 5 2 ♥ J

♦ 10 4 3 2 ♦ A K 8 5

♣ A 6 ♣ J 2

With Strong 2-clubs set for N/S, and Weak 2-Bids not set, Bridge V+ opens the North hand with 2♠, and South replies 4♠.

Rebid after 1 of a suit, not using Benjamin 2-bids

With a very good suit and 20 points or more, and no other reasonable rebid, you can repeat the opening suit at the 4-level, even with a minor suit. Partner has a pretty clear idea of the opening hand, and can decide whether to continue or not, either to game in the minor, or slam.

This is North's hand in Deal 67:

♠ A 5 2

♥ A

♦ Q J 8

♣ A K Q 5 4 3

If you are using Benjamin 2-bids, you will open this hand with 2♣, then rebid 3♣. If you are not using Benjamin 2-bids, but are using the Strong 2-Clubs convention you are forced to open this hand 1♣. Similarly, if you use neither Benjamin nor Strong 2-Clubs, the hand is not strong enough for a Demand 2-bid, and you must open 1♣.

In both cases, when partner replies 1♦, it's hard to see any other rebid than in clubs, especially given the very strong honours holding. Some authors might suggest a jump-shift in spades to show 20-23 points, but this kind of bid backfires quite frequently, and Bridge V+ will not make it. You should thus rebid 4♣, showing a long, strong club suit, and 20-23 points.

Rebid when not using five-card majors, when partner has supported minor reply suit

If you are not using five card majors, and when the reply suit is minor, and the opened suit major, with 3 cards in partner's major suit you should show deferred support in the major, in the hope of finding a more favourable contract.

In deal 6940, East supports partner's second suit:

West East

♠ 10 ♠ J 6 4

♥ 10 5 2 ♥ A K J 9 7

♦ K Q J 9 4 ♦ A 7 5 3

♣ K 9 7 3 ♣ Q

East opens 1♥, and West bids 2♦ over South's 1♠ intervention. East supports diamonds with 3♦, showing 13-16 points and at least 4 cards in diamonds. West can finally show his support for hearts with 3♥, and East concludes with game in hearts, making an over-trick.

With five-card majors, of course, things are different: 1♥, 1♠, 3♥, Pass, 4♥, Pass, Pass, 4♠, 5♥, Pass, Pass.

East makes 5♥.

Bidding after a Demand 2-bid opening

Remember that in order to use demand 2-bids you will have unset Strong 2-Diamonds, Strong 2-Clubs and Weak 2-bids in Bidding conventions.

The demand 2-bid is forcing to game: you must therefore reply, even with zero points. With less than 7 points, and fewer than 3 cards in the opened suit, you should use the negative response of 2NT. 3NT is a true notrump bid, showing regular distribution, a doubleton in partner’s suit, and at least 8 HCP.

A new suit shows at least 7 points, and a possible slam: this is the preferred reply, as long as a good suit is available – for a bid at the 2-level, the suit should have at least 4 cards and an honour, while for a bid at the 3-level, a 5-card suit is normally required, with at least QJ (a 4-card suit should have at least two good honours).

You can support partner’s suit when holding at least 3 cards. A simple raise shows slam potential, at least 8 points counting support points. With 4-7 points in support of a major, bid game directly. Otherwise, simply bid 2NT. Subsequent bidding follows the general rules that we have covered in the main text, ending up in major game, 3NT, minor game, or slam.

Deal 687 gives us a nice example of a demand 2-bid:

South North

♠ 6 ♠ K 9 7 5 3

♥ A K Q J 6 4 ♥ 10

♦ A J 10 9 ♦ K 7 6 5 4

♣ A 10 ♣ 5 3

If South is playing demand 2-bids, it will bid 2♥ with this magnificent hand. North has only the 10-spot in hearts, but he does have two biddable suits. He thus first bids 2♠. South then shows his second suit with 3♦, and North realizes that a slam is possible: he uses the Blackwood convention (see Slam bidding) to check how many Aces South holds, and the partnership ends up in 6♦.

Bidding after a Strong 2§ opening bid

If you are using the Strong 2-Clubs convention, and your partner has opened 2♣, you should reply 2♦ with 0-7 HCP. All other bids will be looking for slam, and in any case, you must not pass below game, even with zero points. You can show your best suit, bid 2NT (8-9 HCP) or 3NT (10-12 HCP). Partner will then support your suit, or show his own long suit, or bid notrump: a 2NT rebid shows 23-24 HCP, and 3NT shows 25-26 HCP.

Bidding after a Limited 2-bid

A Limited 2-bid shows precisely 20-23 points, and so as responder you can pass with a hand containing less than 4 HCP. The replies to Limited 2-bids are generally less slam-oriented than those for demand 2-bids, and a biddable suit can be shown at the 2-level with as little as 4 HCP. To bid at the 3-level, you should have at least 7 HCP.

A simple raise of partner’s suit still shows slam potential, but requires 11 points or more, including support points. You can bid major game directly with 7-10 points. 2NT shows 4-7 HCP, and 3NT promises at least 8 HCP. You should pass with less than 4 HCP.

An opening bid at the 2-level shows a strong hand, and a very good suit. Your rebid will therefore either respond to partner’s reply, or say a little more about the type of hand held:

Ø with at least 4 cards in partner’s suit, show support

Ø if partner has bid game in the opening suit, pass unless the opened suit is exceptionally strong. Go for slam with any other support bid from partner

Ø show a second suit with at least 4 cards whenever possible

Ø repeat the opening suit with 6 or more cards; in particular, repeat a 6-card major over partner’s 3NT response.

APPENDIX II: SOME FUN NUMBERS

You may have noticed that the majority of examples in the Handbook are taken from the first 1000 deals. When you tap on the "Next Deal" menu option Bridge V+ generates a deal number in a set of just over 2 billion deals (because the deal number is expressed as a 32-bit binary number). This means that if 1 million people all over the World played 10 Bridge V+ deals during the course of the day, only a handful of them would hit on a deal in the first 1000. You would find (if you cared to look) that about 94% of the deals you play have deal numbers with 9 or 10 digits: generated deals with deal numbers of less than even a million are quite rare.

I mentioned the Earl of Yarborough in the chapter on Penalty Doubles. He offered his Whist opponents 1000 to 1 odds on their being dealt a hand containing no card above the nine. The first hand in the Bridge V+ set that is a "Yarborough" is West's hand in deal 273 (take a look if you've never seen a Yarborough!). If the Earl of Yarborough were still around today and challenged a Bridge V+ user entering deal numbers in order from deal 1, and the bet adjusted to refer to all four hands in each deal, he would be winning even once he paid up on deal 273. As it happens, if the bet continued until deal 4000, they would encounter 16 hands without any card above nine, and so the Earl would just break even!

Getting a really good hand is much harder. You would have to play Bridge an awful lot (about 2½ million hands) to hope being dealt North's hand in deal 1379423 (North/South get to 6NT):

♠ A K Q

♥ A

♦ A K

♣ A K J 10 7 5 2

I have never seen a Bridge book that talks about hands like this, for the good reason that most of the people reading the book will never get a hand like this in their lives! However, the Bridge V+ bidding engine has to at least bid something not too stupid.

Going back to statistics for a moment, the first deal with a suit holding of 11 cards is the North hand in deal 301366, where North is missing only the 8,4 of spades, and has the heart Queen and club 7. North eventually bids 6♠, on the "are you kidding me?" principle, and finds partner with 2 aces, but loses a trick when East leads the heart Ace.

Statistically, we would expect a deal containing a suit with 12 cards, about every 78 million deals, and there is probably not a single 13-card suit in the whole of the Bridge V+ set. Actually, the first suit with 12 cards occurs in deal 28103138. With South as dealer, West opens 1♣, and Bridge V+ pre-empts with 6♠! In fact, South has all the spades except the 8-spot, along with the 5 of diamonds. Amazingly, South has the diamond ace, so North is bound to make 13 tricks!

To end on a cheerful note, take a look at deal 5967320, where North/South take all 13 tricks, even though the partners have only 13 HCP between them!

South North

♠ 10 8 2 ♠ —

♥ J 10 6 4 3 ♥ A Q 9 8 7 5 2

♦ J 10 7 6 ♦ —

♣ Q ♣ A J 7 6 4 2

Bidding is: 1♠, 3♥, 4♠ Pass, Pass, 5♥, Double!