Learning to Play Bridge - one advantage of bad bidding is that you can practice playing atrocious contracts
Disclaimer: I've created these webpages on bridge from a wide collection of bits and pieces I've picked up over the years. Most of the original references, etc. I've lost, but if there is a problem please just send me a message and I will add any references and links needed. I claim no originality in the compilation on these pages, however the mistakes and mis-quotes are all my own work.
These pages are designed for people who play bridge, but would like to play better. I make no claim to being a good bridge player, what I've collected here is my own personal attempt at learning to play better bridge. Give me a lifetime and I might just make it.
What you see above is a standard SAYC (or Standard American Yellow Card) bidding 'cheat sheet' for what many people know in Europe as a version of the 5-card major system.
And below we have a different version of the same type of 'cheat sheet' filled in with one set of more or less standard bidding rules and conventions.
A 'cheat sheet' is a type of 'crib sheet', 'reference card' or System Card for the prior listing of a partnership's understandings. These cards can be consulted by the opponents in order to better understand the explanation provided by an opponent after a particular call (bid) or play is questioned.
'Cheat sheets' have nothing to do with cheating at bridge. Here is a Wikipedia article on the latest situation concerning Fantoni and Nunes, two of the worlds best bridge plays and now both accused of cheating. More prosaically we must note that cheating is about a pre-mediated act of illegally obtaining hand or card information from a partner without being detected. It is not the same as doing something which might be considered 'unethical', such as making an inference from a partner's hesitation. This type of thing can be sanctioned by a Tournament Director without establishing intent.
On these webpages we are going to describe the basic elements of bridge, using this 'cheat sheet' as a guide. The basis of the bidding system described on these webpages is the 'La Majeure Cinquième' by Michel Lebel, version 2015.
On this webpage we will first look at how simple bidding systems evolved and we will start on the long trip to understanding the meaning of each 'declaration' on the 'cheat sheet' (check out this list of bridge terms and expressions).
The core topic treated on this webpage is 'hand evaluation', which includes point counting, distributional points, controls, losing trick count, and total number of tricks. The last and largest section on this webpage concerns the understanding and evaluation of 'shape'. This topic is vital when looking to go beyond just adding distributional points to high-card points, and hoping for the best.
Over time I hope to add other webpages dealing with the techniques for playing the cards, interventions, conventions, signalling, defence, ...
A Bit of History
The game we know today, so-called contract bridge, is said to have been invented in 1925 by an American called Harold Vanderbilt. Whilst based upon a variety of earlier card games, contract bridge introduced the idea of an auction to determine a 'contract' or commitment for a partnership to try to 'make' a certain number of 'tricks'. Failure to fulfil the contract resulted in a scoring penalty given to the 'defenders', and success resulted in the awarding of points to the 'declaring side'.
The story goes that Vanderbilt invented 'contract bridge' whilst on a cruise in 1925. Originally in auction bridge the score was calculated on the basis of the number of tricks made, and there were no game bonuses, etc. However, the original idea of a bonus for a 'game bid' was in fact already mention in 1914 and the name 'contract bridge' was already in use in ca. 1920. What Vanderbilt actually did was revise the scoring system with 'results going above and below the line' and he also introduced vulnerability thus making sacrifices more expensive. After testing his ideas on the cruise he recommended 20 points for a minor, 30 for the majors, 35 for No Trumps, and 100 for game. There was considerable resistance to these changes from established bridge writers and experts, because they thought it would be too complicated and discourage beginners. But Vanderbilt sold the idea to the rich and famous, and the riffraff finally followed suit in 1927.
Initially bidding systems (the way the auction leads to the contract) were designed to permit a player to open one of a suit when they held a better than average hand, and to open at the two level with an even better hand, and at the three level with a very strong hand. This was the basis of the so-called strong-two bids. Today weak-two bids are common practice.
Again in the old days a simple reply at the two level could be made with 7-8 points, so a partner would have to bid at the three level with a good suit and 11-12 points or more. Then bidding systems introduced the idea that a two level reply was forcing to 2 No Trumps (NT), or even game forcing. Today many players use a 2-over-1 forcing (usually to game), which creates a wider variety of bidding sequences (hence greater accuracy) to move to game or a slam. This means that a hand that is worth a bid over 1♠, but is not worth a game forcing bid 2-over-1, must be bid 1NT (even if it is not a 'balanced' hand).
Example: ♠A-K-3-2 ♥K-10-2 ♦K-J-3-2 ♣3-2
This hand has 14 HCP, enough for a game-forcing 2-over-1 bid over an opening major. The game forcing bid would be 1♠ - 2♦ forcing game and showing a 4-card side suit. Over an opening 1♥ many players would prefer to bid game-forcing 1♥ - 2♦ rather than show a 1♠.
Four card major suits were once the standard opening one-level bid, and the search for a 4-4 fit was the cornerstone of many bidding systems. Now many of the popular bidding systems use an opening 5-card major, and search for an early 5-3 fit.
Today bridge hands are usually evaluated according to high-card points (or honour point count) HCP and some form of distributional points system designed to improve the accuracy of the bidding process. There are many different ways of defining bids in the bidding process, one of the most commonly used set of descriptors include descriptive bids, informatory bids, sign-off bids, pre-emptive bids, invitational bids, forcing bids, asking bids, transfer bids, relay bids, take-out bids, cue bids, splinter, game-try, quantitative bids, and lead directing bids (including doubles). Not forgetting all the artificial bidding and conventions, in opposition to a 'natural' bid.
Modern day bidding systems are now focussed on what is more successful when 1,000's of hands are analysed. And bidding systems evolve as new forms of defence are found to counter the advantages of a bidding innovation. Initially the weak No Trump (NT) was popular, but new styles of defence were introduced making the strong NT a better alternative today (see Quantitative No Trump Bids). All NT bids should define no more than a 3-point range (better still a 2-point range) and a very specific set of distributions, and above all should inform the partner as to whether to continue bidding or not.
Weak-two's, No Tumps, pre-emptive bids, are all limited bids in that they are made with specific types of distributions and a fixed maximum number of points (high-card points or otherwise). No Trump bids define a narrow range of high-card points. The idea is that a limit bid tells partner an exactly maximum limit both in terms of distribution and points.
Example: ♠A-J-6 ♥9-6 ♦Q-5-3-2 ♣Q-6-4-3
This is a typical limit bid with partner bidding 1NT over an opening 1♥. Partner promises 6-9 HCP and no fit in Openers suit. A balanced hand is not a requirement for this type of bid.
Opening bids once required 13 points with a 4-card suit, 12 points with a 5-card suit, and only 11 points with a 6-card suit. Today bridge players want to enter the bidding as quickly and as often as possible. More than 50% of computer dealt bridge hands have partnership point counts between 17-23. Aggressive players are willing to bid game with a 10-card suit and a 20-20 point split. But if one pair is holding a 10-card suit, then it is likely the other pair also holds a 10-card suit, and therefore there is a potential for a double game swing. All the more reason to get in quick.
An opening weak-two bid should be about 8 points (range 6-10) with a robust 6-card suit with two of the top three honours, or three of the top five honours (the 10 is a honour). If the remainder of the cards are dealt out, the partner should receive about 10-12 high-card points and 2 cards in the opening suit, precisely the combined points and cards to justify a 2♥ or 2♠ contract. The same logic applies with the same number of combined points and a distribution 5-3, or 4-4 with the possibility to ruff. Computer simulations show that 2♥ or 2♠ will make, or go down with a profit. So in all cases it is desirable to get to a two level contract as quickly as possible.
Take a good hand with a 6-card major in front of a partner opening a weak-two in the other major. If the respective fits are 6-1 in both majors computer simulations show that it is better to play the contract in the 6-card major of the weaker hand. In fact computer simulations strongly suggest that if there is a misfit (type 6-1), it is always better to play in the long suit of the weaker partner.
Another good reason to allow the opening weak-two bid is that it allows partner to make a T.N.T. (Total Number of Tricks) raise based upon the number of cards they are holding in that suit. So in front of a weak two, partner should pass with a weak hand and only 2-card support, but raise to the 3-level with 3-card support, and to the 4-level with 4-card support, taking into consideration the vulnerability. The raise to game over a weak-two can also be because partner is strong, so often the opponents are not willing to double because they are uncertain about the exact nature of the game bid.
A final reason to use the opening weak-two bid is that otherwise the player would be forced to pass and then later be forced to reply 1NT despite holding a 6-card suit (remember many partnerships play the 2-over-1 forcing game).
The Stayman Convention, despite being first published in 1945, is still an essential part of most bidding system. In its simplest form it looks for a 4-4 card suit fit in a major after an opening 1 No Trump or 2 No Trump. The 2♣ is a convention and since it is artificial, it is a forcing bid. The replies 2♦ and 2 NT are also artificial, and thus forcing. Whilst the basic convention is easy to follow, there are numerous variations.
Example: ♠A-J-9-2 ♥7-6 ♦Q-10-5-3-2 ♣Q-6
This is a typical Stayman 2♣ hand. Partner will raise Opener's reply in ♠, otherwise they will bid an invitational 2NT.
Transfers (Jacoby) and relays are now common in most bidding systems, simply because they significantly extend the range of possible bids open to the partnership. For example, a 2NT following a transfer bid over an opening 1NT can have additional meaning based upon the partnership agreement.
Example: ♠A-J-10-6-5 ♥9-6 ♦8-5 ♣10-6-4-3
This is a typical 2♥ transfer. Partner will pass Opener's reply in 2♠.
Variations on the slam convention Roman Blackwood are also now common and provide a powerful way to quickly determine the number of 'key' cards held by partner, and even if partner is also holding the Queen of trumps. Given that 3NT+1 is always better than 5♣ or 5♦, some partnerships are using 4♣ or 4♦ as a Roman Blackwood request for a slam in a minor suit.
Very strong suits are usually opened with a strong-two bid (or forcing two bid). Many, if not most players, have now moved to the weak-two bid with 2♥ and 2♠. Concerning the opening 2♣ and 2♦, some players use an artificial strong 2♣ as a single convention defining a hand that is too strong for a one-level bid. This declaration is forcing and covers a wide variations of points and distributions, and with this the opening 2♦ becomes another weak-two bid.
Other players have retained both artificial 2♣ and 2♦ as conventions show strong hands, 2♣ becomes a forcing 'indeterminate' (20-23 HCP+distribution) and 2♦ forcing game (24 HCP+distribution). Some players have retained the strong 2♣ and 2♦, but have defined 2♣ as 'intermediate' 18-20 HCP+distribution, and 2♦ 21+ points. The 2 No Trumps bid is natural and defines high-card points of 20-21 points.
Example: ♠A-K-Q-9-8 ♥A-K-6 ♦A-3-2 ♣5-2
This is a typical 2♣ forcing hand. Opener has 20 HCP, a solid 5-card ♠ and 5 losers.
Example: ♠A-K-Q-J-9-8-6 ♥A-K-10 ♦6-5-3 ♣-
This is a typical strong 2♦ game forcing. Despite having just 17 HCP, this hand has only 4 losers.
One finally point concerns game contracts in the minor suits. Today the view is that with something like 28-29 points needed for a successful game contract in a minor, the better contract will usually be 3NT with probable over-tricks. Even playing 1NT has the same score (40) as a 2-level part-score in a minor, and to beat 1NT + 1 (70 points part-score) a partnership will need to win 10 tricks in a minor suit.
The above 'little history' is just to remind the reader about some of the key principles that they will be expected to apply in adopting a bidding system and conventions.
A very good starting point is to think of all bids (including Pass) as having an approved range of points, and as being defined as either sign-off, encouraging, invitational, forcing, or forcing to game (or eventually slam).
Silly contracts are always linked to one partner forgetting one or more of the basic rules of their agreed bidding system.
Good bidding is based upon knowing and using a well-structured system. But the application of a good bidding system needs good judgement, and the basis of good judgement is intelligent hand evaluation.
All bidding systems rely on a player evaluating their hand, determining the hand's 'value' (usually a number), and communicating (bidding) this number to their partner. The trick is to pass the maximum information (within the rules), but keep the hand evaluation simple yet meaningful.
So hand evaluation is about how partners assess their hands and describe them to each other so that they can reach the optimum contract (i.e. best chance of scoring the most points with a reasonable risk).
The value of a hand depends upon the quality of its high-card strength (honour point count or high-card points) and the length of the suits (distribution), and to a lesser extent the location of the honour cards. What each player needs (and each partnership must agree on) is a way to evaluate the combined high-card points and distributional strength of a variety of different types of bridge hands.
Another important feature is the way hand evaluation must change during the bidding. Hand evaluation is about determining the playing strength of the hand in relation to the other three hands. There are three situations which will always influence hand evaluation during the bidding: usefulness or disadvantage of short suits, the fit with partner and/or the opponents finding a fit, and the favourable or unfavourable position of high cards. The goal of the bidding is to find a 8+ card fit in a major suit, and all the players at the table will evaluation their hands with that in mind. Without an 8-card fit, the players will move their focus to the next best thing, a contract in No Trumps. This will require a re-evaluation of the strength of the hand. If that fails then the remaining option is a contract in as minor suit. That again will require a new re-evaluation. Finding support with partner, finding a strong hand with partner, a double, the interventions of the opponents, even a pass, all will require each player to re-evaluate their hand 'on-the-fly'.
As an example, this hand ♠ 10-5-3-2 ♥ Q-J-10-7 ♦ 8 ♣ 9-8-5-3, has 3 high-card points (HCP) plus 2 distribution points for the singleton (so 5 points DH for distribution+HCP). A good initial position is that this is a 'Pass' hand, however it could be interesting in defence (4-4 majors, a singleton, and a possible bad HCP split against the opponents). But Partner opens 1♥, so what to do now? 'Pass' or re-evaluate. Many players will not 'see' beyond the 3 HCP or the 5 DH. However, this hand has 3 HCP, 3 points for the singleton, an extra point for the 4-card support, and the couple of 10's and a 9-8 sequence could be worth an extra point. So now the hand has a worthwhile 7-8 DH, and Partner should support Opener with a bid of 2♥. This logic would be just as valid if Opener bid 1♠.
Below we look at ways to evaluate both the high-card strength of a hand and its distributional strength. We will also look rapidly at different ways to evaluate a hand by its controls or by the so-called 'losing trick count'. The Wikipedia article on hand evaluation is a good companion text. And finally we will focus on a long section on determining and exploiting a hand's 'shape'.
Milton Work Point Count
Bridge players need some simple and practical way to start evaluating a bridge hand. What to take into consideration - high cards, suit distribution, quality of suits, controlling cards, fit with partner, general 'shape', …? The most basic and certainly the most popular evaluation method (initially conceived for a 'balanced' hand) is to assign numerical values to the top four honour cards.
Point Count: Ace = 4 HCP King = 3 HCP Queen = 2 HCP Jack = 1 HCP
There are 40 total high card points (honour point count) in the deck, and the addition of the points in a particular hand is known as the high-card point (HCP) count. An 'average' hand would be expected to hold 10 HCP in the form of 1 Ace, 1 King, 1 Queen, and 1 Jack.
Simply put, you need a better than average hand (say 12 HCP) to open the bidding.
Based upon a large sample of real world bridge hands just using HCP is insufficiently precise. It does not take hand shape into account, and there are several ways to refine the way players should assess (or re-assess) the exact distribution of cards in any specific hand. Statistical analysis of hands show that HCP undervalues Aces and 10’s, other analyses prefer to consider Queens and Jacks are overvalued. In the real world Queens and Jacks often fall under Aces and Kings rather than win tricks, and in defence a Jack hardly ever wins a trick. There are several ways to 'adjust' HCP, the ones I like are (i) add 1 HCP when holding all 4 Aces, (ii) deduct 1 HCP if a hand has no Aces, (ii) add ½ HCP for each 10 in a hand.
Many texts mention Charles Goren as the creator of the 4-3-2-1 point-count system. As Wikipedia points out Goren developed the ideas of Milton Work and again as Wikipedia rightly notes the point-count system was based upon a suggestion made in 1915 by Bryant McCampbell as a way to evaluate balanced hands. Initially Work opposed the point-count system, but finally he was responsible for promoting the system from 1927. Goren was an employee of Work and it was he that applied the point-count to value all types of hands.
The reality is that the Work point-count is just one of many high-card point counting systems. Without introducing other point-count systems it is still possible to see where experts feel the present-day system fails. There appears to be two weaknesses that should be recognised. Firstly Aces are undervalued, with some experts introducing a bigger point gap between Kings and Aces. Secondly 10's are ignored, but many experts attribute a ½ or 1 point to a 10. Some but not all experts appear to down grade the Jack, and some give a ½ point to both the Jack and 10.
According to the experts the 'best bet' might be to give 5 points to an Ace, 3.5 points to a King, 2.3 to a Queen, 0.9 to a Jack, and 0.3 to a 10, but this would require a complete revision of the point-count system for partial and game contracts, etc.
The key message is that experts think that Aces and 10's are more valuable than the point-count suggests.
However computer simulations of 1,000's of hands tells us something even more interesting. One of the key messages is that if you are playing a particular suit contract the Ace, King, etc. in that suit are more valuable than the same cards in another suit. If we look at the simulations the Ace of trumps is still worth 4 points, but the King (3.3 points), Queen (2.7 points), Jack (2.2 points) and 10 (1.8 points) are all worth more than a simple high-card point-count would suggest. So the Ace of trumps is still worth 4 points, but the other Aces are worth only about 2.3 points. Other honours in the side suits are worth less than the same face-card in trumps or in the preferred side suit. We all know that the Jack in a short side suit is not likely to be useful, and in fact the simulation tells us that Queens, Jacks and 10's in short side suits are (on average) not worth much (unless Declarer need to exploit that particular side suit).
Clearly any specific hand might well need a good side suit and the Queen, Jack and 10 in that suit will be worth more, but on average they are worth much less. And Aces in side suits permits the declarer to 'control' the way the hand plays out, and can be far more valuable than having a couple of unproductive Queen-Jacks in side suits.
But what is really impressive is the value of small trump cards. The 10 is worth 1.8 points, the 9 is worth 1.6 points, the 6-7-and 8 are worth each about 1.4 points, and even the 5-4-3-and 2 of trumps are worth about 1.3 points each. This sounds reasonable because small trump cards will usually be correlated with longer trump suit holdings. Small cards in other suits are worth nothing, and what is surprising is that a simple 2 of trumps can be worth almost as much as a King (1.4 points) when 'exposed' in a difficult to exploit side suit.
In fact during the description of many bidding systems there are hints that 3-card support for Openers major can mean a lot more than just a 'fit'. Holding more trumps is worth more that holding honour cards in a 'useless' side suit. Holding a 5-4-3 in trumps is collectively worth about 4 points, and can be worth the same as an Ace and a badly placed King in side suits. We now understand better when experts say a partner holding x-x-x in trumps is nice but a partner holding K-x-x support in trumps is better (it can be worth 6 points).
We also now understand why an extra trump is worth its weight in gold because 9-x-x-x is worth as much as Q-x-x in trumps (and that means that those 2 high-card points can often be better used elsewhere). We can start to see why experts are willing to play game with a 10-card major and a 20-20 break in points. If a partnership has 10-cards headed by just A-K then having Q-J or x-x in trumps is the same, and the 3 HCP are probably more useful elsewhere.
The real difficulty in a trump contract is how to evaluate the hand during the bidding. The value of the honour cards will be different before and after the trump contract is decided. A 2 of ♠ could be quite valuable as the 9th card if ♠ are trumps, but worth less than nothing otherwise (holding a 2 in a side suit has a negative impact on the overall strength of the hand when playing in a different suit). Here we see the logic in re-evaluating the hand once a trump suit has been decided. But does that re-evaluation go far enough? Again we can now see the logic in a bidding sequence such as 1♠ - 2♠ - 3♦ - 4♠ which allows the partnership to upgrade the point-count for the second suit (♦) and downgrade 'wasted' honours such a Queen or Jack in a useless side suit.
If we turn to the computer simulation of No Trump contracts, we can see that having a nice 5-card suit can be worth more than having exposed high-point cards. In fact Aces are worth about 4 points and Jacks are worth about 1 point, but Kings and Queens are slightly over valued. We all know that a K-Q is worth just a bit more than an Ace, i.e. they are worth together only about 4.4 points and not 5 points (and as a doubleton they are only worth the same as an Ace). A 10-9 pair is worth about the same as a Jack, and smaller cards provide distributional support which we all know is useful in No Trumps despite the 'tradition' to only count high-card points for this type of contract.
Players should supplement the HCP with distributional points, either suit length or suit shortness. When playing in a suit I prefer to count ruffing potential, e.g. suit shortness. Initially I add 3 points for a void, 2 for a singleton, and 1 for a doubleton. However once a 'fit' (usually meaning 8 cards in a suit) has been found I will tend to count 5 points for a void, 3 for a singleton, but keep just 1 point for a doubleton. This type of distributional point count works well for 'three-suit' hands, but some players prefer to re-evaluate the distributional strength of their hand only when they are going to be dummy and only when they have the necessary trump support (avoiding both partners counting extra distributional points for the same suit).
An analysis of real world bridge hands shows that using HCP and distributional points correlates better with tricks won. It's not perfect, but it is better.
With 'two-suit' and 'one-suit' hands it is often better just to count 'playing tricks' rather than distributional points (or 'Losing Tricks' as we will see below). The problem here is to have a good partnership understanding on the definition of playing tricks and/or on using losing trick counts. Some experts define playing tricks as a number of expected tricks with no help from partner (e.g. a void in the suit). Others use it for strong hands and assume a reasonable distribution of cards and HCP around the table, including in partners hand. Most experts agree that it applies to hands with 16+ HCP.
I've seen some experts consider adding 'playing tricks' and 'losing tricks' together to make 13. The more you have one, the less of the other.
Yet other experts talk about 'clearcut tricks' when opposite a void in Partners hand, and others increase the DH value of the partnerships 2nd best suit.
And finally some experts appear to equate 'playing tricks' with 'controls' or 'quick tricks', and add value for every card from the 4th in their long suit.
Some players will add additional distributional points for long suits. e.g. 1 point for any 6-card major suit and 2 points for any 7-card major suit. With these declarations it is sensible to only add the points if the long suit also holds at least two of the top three honours, or three of the top five honours. This is the basis of most pre-emptive bids.
The addition of 3 points for a void, etc., and the negative point adjustment for unprotected honours, and the extra points for long suits, the 4 Aces and for 10's are together called the Pavlicek Point Count. An important point here is that 13 Pavicek (total) point count becomes the threshold for making an opening bid. Pavlicek also added a couple of additions. Firstly he adds a point for any suit in dummy that is Qxxxx or better. Equally he adds 1 point for a 5-card suit if partner raised the suit without knowing it was a 5-card suit. He adds 2 points for every trump card over five if they had not been 'shown' to partner. And finally he adds an additional point for each card over three in a side suit. Adding everything together he sets game firmly at 26 points.
There are many different ways to allocate distributional points, some players add points, some subtract points, and others mix the points up. We have honour trick counting with 2 points for an Ace, 1½ point for A-Q, and 1 point for KQ. There are playing tricks points with an extra point for a 5-card suit with honour cards, 2 extra points for a 6-card suit with honours, etc., and an extra point for the Ace and for the King in trumps, and the same for Q-J in trumps, but just a ½ point for a Q or J-10. The losing trick count counts the tricks to loose in the first 3 cards of each suit (we will look at this option below). The 'asset point system' adds points to the high-card point-count with 2 points for a void, 1 point for a singleton, and 1 point for a 5+ card suit. Another distribution point system added 1 point for the 5th card, 1 point for 6th card, etc. in trumps, and 1 point for the 4th card plus 1 additional point for the 5th card in one side suit. Another system added one point for a biddable 4-card suit, plus 1 point for the 5th card, plus 2 points for the 6th card, plus 3 points for the 7th card, etc. (this system required 28 DH for game).
One distribution point system subtracted 1 point for no Aces, 1 point less for suits with unprotect honour cards, ½ point less for suits holding less than the 3 top honours, and ½ less for no 10's. Another system added ¼ point for each Ace, ½ point for each 10, and ½ point for suits with 2 of the three top honours.
On these webpages I use the abbreviation DH to mean 'Distribution+HCP'.
Sometimes it is difficult to evaluate the game or slam potential of a hand, e.g. should you pass or bid game or even a slam? One way is to look at 'controls', e.g. the Aces and protected Kings that correspond to a particular HCP. If a player has 5 HCP then they should hold an Ace or King, if not the hand is 'weaker' than 'average'. Many experts attribute 2 control points to an Ace and 1 control point to a King. Hands with 5 HCP and only 1 control point, and hands with 7-8 HCP and only 2 control points are considered poorish hands.
Things start to look interesting with 10 HCP and 3 control points, with 12-13 HCP hands should have 4 controls, 15 HCP expect 5 controls, 17-18 HCP expect 6 controls, and with 20 HCP hands should have 7 controls. You might like a hand holding A-K-x and another K-x-x, but not a hand holding A-x, plus 2 Queens and 2 Jacks is different suits.
However the reality is that analysing 1,000's of real world bridge hands the correlation of controls and trick winning is not that good. The use of controls is probably more useful in specific situations rather than as a general principle.
Another equally useful approach for these 'boarder line' hands is to look at the presence or absence of specific negative features that would reduce the value of a particular HCP count. These are:-
Honour doubletons K-Q, K-J, Q-J. Q-x, J-x unless in partners suit - reduce by 1 point from the HCP count.
Honour singletons (exempt the singleton Ace).
Honours in opponents' suit when deciding to support partner's suit (these points could be useless), and in particular honours in suits shown by your Left Hand Opponent (they are sitting 'over' you).
There are also specific distributions that enhance hands and support a more 'aggressive' bid, namely:-
Two or three honours in long suits, or better still honour sequences in long suits - add 1 point to the HCP count.
Honours in partner's suit when deciding to support it.
Honours in own suit when deciding to overcall.
Two or three intermediate cards in a suit (8, 9, 10) especially if headed by honours.
Honours in suits shown by the right hand opponent (you are sitting 'over' them).
And many players like to open the ♠ suit whenever possible to make overcalling more difficult.
Assessing a 'boarder line' hand is also about the defensive strength of a hand. Good defensive values include:-
Honours in shortish side suits, e.g. K-x-x.
Honours and/or length in opponents suit.
Lack of honours in your own suit.
Players might find it better to play a contract rather than defend if they have an abundance of honours and length in their own suit, and a lack of defensive values. Again the decision will also be affected by the vulnerability.
There are some 'quick fixes' to assess the opening value of a hand, e.g. the 'rule of 20' or "open if the HCP plus the number of cards in the two longest suits add to 20 or more". Another way is to add the number of cards in the 5+ length and the number of honour cards in the same suit (Ace down to and including the 10). With 7 open at the 1-level, with 8 open at the 2-level, and with 9 open at the 3-level.
Losing Trick Count
A technique which I personally like to use to assess 'boarder line' hands (and this can be when deciding to bid, over-bid, to support partner, to pass, ... as well as to bid game or even looking for slams) is the losing-trick count. This is used when a partnership has found a trump fit. The question is often, do I raise, bid game, stop, invite, ....?
The idea is to weigh shape and fit rather than just point counts. The player should look only at the top 3 cards in each suit. Then evaluate losers in each. If you have a void, you have 0 losing tricks. A singleton (other than an Ace) is 1 losing trick. An Ace and King doubleton is 0 losing trick, whereas A-x, K-x or K-Q is 1 losing trick, and naturally something like Q-x, J-x or x-x is 2 losing tricks. So clearly with 3 cards such as A-Q-x or K-Q-x you have 1 losing trick. This gives your losing trick count for the hand. If you open you are presumed to have 7 losing tricks, so this helps you decide to open or pass with certain boarder line hands. If you partner also has 7 losing tricks he knowns that 7+7=14, subtract from 18 leaves +4, so you can bid up to level 4 or game in a major. If your partner has 8 losers they would jump to the level of 3, e.g. 18-(7+8)=3. and with 9 losers you simply raise to 2, e.g. 18-(7+9)=2. And of course if you only have 5 losers then 18-(7+5)=6, a slam is certainly possible. Some people count to 18 and others to 24 but the result is the same, e.g. 24-(7+7)=10 total tricks.
Clearly as opener if your partner supports your suit you can then 'count' the number of losing tricks, and you can invite or even raise to game as required.
An analysis of 1,000's of real world bridge hands shows a good correlation between counting losers and winning tricks. It's good, but not that good.
There are more complex loser counting systems, but I find this one is simple and provides help in deciding about boarder line hands. Some experts think that this count system undervalues Aces and overvalues Q-x or singleton Kings.
Total Number of Tricks
In situations where partnerships have a fit but are competing with their opponents it is sometime difficult to decide to make an additional bid or just pass. A simple rule is that a partnership will make (more or less) the number of tricks corresponding to their combined holdings in trumps (this is the so-called T.N.T. or Total Number of Tricks). This is particularly useful when a partnership has made a weak-two or weak-three opening bid or overcall, indicating 6, 7 or even 8 cards in a particular suit. If the partner has a weak defensive hand they can bid to the level of the combined holdings in their suit, e.g. holding a total of 9 cards in their suit they bid to the 3-level. Clearly they need to be careful about the vulnerability at the table.
In a workshop in early 2019 hosted by Milan Macura there was a suggestion to use different hand assessment schemas for different types of hands.
You should use high-card points (HCP) for balanced hands which are mostly likely to be played in NT.
You should use high-card points (HCP) plus distributional points (my DH) for irregular or semi-balanced hands where the contract might be in a suit.
And you should use losing trick count for truly unbalanced hands.
This is just a marker for this hybrid approach, which is developed in more detail on a separate webpage.
Shape - hand evaluation in one word
A lot of players will stop once they have counted their high-card points (HCP) and adjusted for a long or short suit. But in fact it's just the start. With DH calculated the player is on the first rung of the ladder.
Hand evaluation is in reality all about shape. This last section is the longest on this webpage, and in many ways one of the most important. So take your time, read carefully, and maybe it will change the way you evaluate your bridge hands. But a word of warning is in order, you will need to know how to play your cards after you have won the auction.
Shape tells us that in a suit contract a doubleton is essential, and two is even better if it comes with a 6-card trump suit. In No Trump 4-4-3-2 is better than 4-3-3-3, and 5-3-3-2 is also an even better shape for No Trumps provided the 5-card suit is a minor (although most experts will also play No Trumps with a 5-2 in a major and semi-balanced distribution).
Shape tells us that honour combinations in the same suit are more powerful than the two honours sitting in two different suits. A simple Q-x-x-x will add almost nothing to a contract if it's not in trumps, and a King in a side suit might not be worth much more. But a K-Q-x-x is an entirely better story even opposite x-x-x with Partner. Honours in long suits are worth more than the same honours in short side suits, simply because it will be easier to establish the long suit. Stating the obvious, K-Q-x-x in front of x-x, is better than x-x-x-x in front of K-Q.
Shape tells us that intermediate cards, 10's and 9's, can change completely a hand, particularly if they are sitting under one or more honours, A-J-10-9 is great sitting in front of x-x-x, or would you prefer A-J-x-x in front of x-x-x?
Shape tells us that side suits are often essential to making a contract, in particular when playing weak hands. Shapes such as 7-3-3-0 or 7-4-2-0 are far superior to 7-2-2-2. Many experts prefer hands as unbalanced as possible, and average players don't play unbalanced hands very well.
Shape tells us that honours in your hand are more valuable if they are in a suit bid by Partner. They are also more valuable if they are in the suit bid by your right-hand opponent (RHO). Honours in unbid suits are less interesting, and honours in suits bid by your left-hand opponent (LHO) are also of less value. But think a bit more. If you are holding a singleton or doubleton in opponents suit, then what you want is for Partner to be void in honours in that suit as well.
Shape tells us that if your Partner has bid a side suit, then holding support in that suit is good, but equally being shorted in that suit can be useful if your trump holdings are sufficient. If you know that Partner is short in the opponents suit, the holding K-J-x-x in that suit is not likely to be useful, but holding x-x-x-(x) is a good thing. Firstly, points are not wasted on a weak suit, and secondly Partner will be able to ruff your losers. This is one reason why experts play Splinter bids, it shows immediately a fit with no wasted values.
We are closing this webpage with a discussion of shape, and a series of examples and test questions.
Example 1: ♠6-3 ♥K-8-3 ♦Q-J-8-4 ♣A-Q-J-5
Example 2: ♠Q-J ♥A-Q-J ♦K-8-4-3 ♣8-6-5-3
In these two hands the honour cards are the same, and the distribution is the same. However one is superior to the other. The first example has its honour cards better protected and they are in the 4-card suits which might make it easier to establish extra length tricks. The honours in the short suits in the second example may still win tricks, but they probably will not create extra length tricks.
Example 1: ♠9-8-6-4-3 ♥A-Q ♦K-Q ♣J-8-3-2
Example 2: ♠A-Q-9-8-6 ♥4-3 ♦3-2 ♣K-Q-J-8
Same HCP and distribution, but the 'quality' and playing shape are totally different, and example 2 is by far the better hand with all the honour 'pulling their weight'. In the example 1 the hand does not provide much support for Partner bidding a red suit, and even with a fit would require honours and length from Partner in the black suits. Some players would see more defensive strength in example 1, and would not open with this hand. In example 2 the hand is certainly worth opening because there could be a chance of game if Partner has support for ♠ and a decent 11-12 HCP.
Example 1: ♠K-Q-8 ♥Q-J-5 ♦K-Q-10-9-2 ♣8-5
Example 2: ♠A-Q-8 ♥Q-J-7 ♦10-7-6-4-3 ♣A-9
These two hands have same number of HCP and the same distribution, but does that make them the same? In a major or No Trumps its going to be difficult to establish additional tricks in the long ♦ in example 2, whereas in example 1 Declarer would have a fighting chance.
So what should we be looking for?
Positive features are:-
Holding several intermediate cards, 10, 9 and 8
Have intermediate cards in the long suits
Having a 5-card suit or two 4-card suits
Honours in the long suits
Length in the majors
Negative features are:-
Lack of intermediate cards
Suits with unsupported honours, or two honours not touching
The 4-3-3-3 distribution is the worst one you can be dealt
Honours 'lost' in short suits, e.g. Q-x
Too many Jacks that may not actually serve any useful purpose.
You will see many of these advantages and disadvantages mentions in the below section on controls.
Let's look a bit more at specific shapes, i.e. distributional patterns.
4-3-3-3 is disliked by many players because it provides no ruffing potential and no long suit potential in No Trumps.
4-4-3-2 is better than 4-3-3-3 in that it offers potential to find a 4-4 fit in a major, or a 9-card major suit if Partner opens.
5-4-2-2 is a semi-balanced distribution, but could be considered balanced if the honours are in the short suits, and in any case it permits the player to consider bidding in two different suits. With this type of distribution the hand is considered stronger if the honours are in the long suits.
5-4-3-1 is unbalanced and is better than 5-4-2-2. The unbalanced distribution offers 2 possible trump suits in the majors, support for a bid in a 3rd suit, and with ruffing potential. The semi-balanced shape 5-4-2-2 just offers two possible trump suits. Obviously 5-4-4-0 is even better.
6-5-3-0 is better than 6-3-3-1, which is better than 6-3-2-2.
7-3-3-0 or 7-4-2-0 is better than 7-3-2-1 and the worst is 7-2-2-2.
Example 1: ♠J-6-3 ♥A-K-Q-J-10-9 ♦Q-4 ♣8-3
Example 2: ♠K-J-3 ♥Q-J-10-9-6-3 ♦A-Q ♣8-4
One word of warning. It is possible to be too rich in a long suit. Which hand do you prefer? Example 1 will win you 6 tricks, but nothing else, and in game Partner will need to bring you 4 tricks. With 3-card support you don't need the Jack and the Queen is not really needed 50% of the time. It would be much better to have those 3 HCP somewhere else, better still as a King. In example 2 you have the same HCP and the same distribution but two of the side suits have useful honours. Yes, you might have given up the top honours in trumps but you should make that up because your trumps are solid and you will almost certainly find a good side suit with Partner. We should not go too far in this logic, the trump suit should be solid enough to play with 2 or 3 small cards with Partner, e.g. yes to ♥Q-J-10-9-6-3 and no to ♥Q-8-7-5-4-3.
Here are some tests about shape and hand evaluation:
Test 1: Your Partner opened 1NT, with ♠A-Q-4 ♥8-5-3 ♦A-J-10-9-7 ♣10-2 you bid what?
Test 2: With ♠A-J-10-8-6 ♥K-Q-10-7-4 ♦8-6 ♣3 do you pass or open?
Test 3: Your Partner has opened 1♠, holding ♠5 ♥Q-8-4-3 ♦K-8-5 ♣K-J-5-4-2 what do you bid?
Test 4: Your Partner has opened 1NT, holding ♠J-8-6-4 ♥K-8-3 ♦A-J-2 ♣Q-9-5 what do you bid?
Test 5: With ♠K-Q-J-8-7-6-5 ♥8-2 ♦J-10-9-8 ♣- what do you bid?
Test 6: With ♠K ♥Q-J-6-3 ♦A-J-8-7-5 ♣Q-8-2 what do you bid?
Test 1 - This is a good 11 HCP (8-losers) which could bring 5 or 6 tricks to Partner, bid 3NT.
Test 2 - With 10 HCP (6-losers) but great shape with honours in the long suits and including 10's, bid 1♠.
Test 3 - This hand has 9 HCP (7-losers) but has a lot of negative features, split honours in ♣ and an exposed K and Q, a bid of 1NT is the only option.
Test 4 - This hand has 11 HCP (9-losers) but has lots of negatives, a flat distribution 4-3-3-3, exposed honours, no intermediate cards, it could bring 3-4 tricks to Partner or just 1 trick. Some players might bid 3NT, other might pass, and others might bid 2NT. Expert opinion is to pass.
Test 5 - With 6 HCP (6-losers) and a 7-2-4-0 shape, this is ideal for a pre-empt, but at what level? Let's say that both pairs are vulnerable, does that help? This hand is too strong and yet still weak. Ideally you want to bid, take the contract and not be doubled. The only bid that has that chance is 4♠. If Partner has 0 points you have 6 winners in ♠ and a winner in ♦, so down 3, against opponents who have 34 HCP.
Test 6 - You have 13 HCP (7-losers), but it is a poor opening hand, and should be downgraded because of the singleton King. Downgrading this hand means 'Pass'. If you open 1♦ you have nowhere to go except 2♦. This hand has a good shape and a lot of bidding options should Partner open or intervene.
Above we saw that shape is important in deciding to bid or pass. But it is equally important in understand if you should bid game or accept a part-score.
Here Opener bid and Partner responded, 1♥ - 2♥, what does Opener do now?
Test 1: ♠J-3 ♥A-Q-J-7-4 ♦A-Q-10-8-6 ♣5
Test 2: ♠5 ♥A-Q-J-8-6 ♦10-9-6 ♣A-K-Q-3
Test 3: ♠Q-J-6 ♥A-K-J-9-2 ♦K-3 ♣Q-8-4
Test 4: ♠Q-8-4 ♥A-Q-8-3-2 ♦A-7-4 ♣K-5
Test 5: ♠K-5 ♥A-Q-J-10-8-6 ♦J-10-2 ♣9-7
There is a nice rule that was mentioned in the article I'm using for this last part on shape. The attribution is to Tony Forrester, and is often called the 'Two Card Rule'. Sit back and think, Partner is promising 3-card support and 6-9 or 6-10 HCP. What can we expect from Partner in an ideal world? Let's say 2 good cards, maybe an Ace and Queen, or two Kings. Some players might pump that up to 7 HCP and expect an Ace and King. Clearly Partner could be supporting Opener with rubbish, but good shape, who knows.
In any case if those two good cards are not enough for a chance of game, then Opener should 'Pass'. Let's face it you might want to 'invite' but if you can't 'see' game even with those two ideal cards, then what's the point of inviting? This is an important concept, if under ideal circumstances Partner can't be holding what you need why continue? Even if you have 'extras' your Partner can't perform miracles, they just can't have more than the ideal.
Now if Opener has a good shape, then it might be worthwhile telling Partner. What Opener will want is that the honours in Partners hand fit well with a long side suit, and if they are opposite a singleton or doubleton they will be less valuable. The standard approach is to bid a long (4-card) side suit to help Partner judge how much waste they have.
How to judge 'waste'? Three of more cards with no top honours in a suit is a bad holding, and Partner should downgrade their hand. Partner will upgrade their hand with less than three losers in that suit. This could be with an honour heading 4 cards in the side suit. Or it could be with ruffing potential on that side suit, provided Partner has a 4-card support in trumps.
So let's have a look at our test hands. Answers:-
Test 1: With a hand of 15 DH and only 5-losers, a game is certainly worth a try. A bid of 3♦ will enable Partner to upgrade their hand. Support in ♦ would be great, and since Opener is short in black cards an Ace or King in ♠ or ♣ could be very valuable, but minor honours in black suits will be worth little or nothing.
Test 2: With 19 DH and only 5-losers, again game looks a good option. Some players might say a bid of 3♣ is a good idea (like in Test 1 above). But let's face it, Partner will have bad cards in ♣'s and could even be discouraged and not bid game, but a bid of 3♦ might do the job since you are going to need a winner there. Of course in a simple bidding model, Opener will just bid game on the basis that there is a good chance that opponents will not be able to run 3♦ winners and the ♠Ace. And Opener bidding 3♦ might just stop a lead in that suit.
Test 3: This hand has 16 HCP (6-losers) and with the ♦K-x could be considered a balanced hand. The recommended bid is 2NT. Despite finding a fit in ♥'s this tells Partner that all high cards will be valuable. Partner can 'Pass', or bid 3♥, 3NT, or 4♥. Remember Partner could have supported Opener with an unbalanced 5 HCP, and now has the possibility to mention a poor 6-card side suit (e.g. 1♥ - 2♥ - 2NT - 3♦). With the sequence 1♥ - 2♥ there is no risk of Opener misinterpreting a very weak distributional 3♦. Remember Partner would have bid game if they were holding anything more than 8+ HCP and 3+ useful cards.
Test 4: This is easy, there is no combination of 'two good cards' with Partner that would offer suggest anything but a 'Pass'.
Test 5: Opener bid with only 11 HCP (13 DH) but 7-losers. Even attributing 2 Aces to Partner (Two Card Rule) there is no possibility of game. So opener might consider to 'Pass'. However the partnership might have only 16-18 HCP, and if so there is a chance that one of the opponent is holding 10-12 HCP and could find a part-score with 2♠ or even a competitive 3♠. So the recommended re-bid of Opener is a non-invitational 3♥. For beginners the sequence 1♥ - 2♥ - 3♥ is invitational. However, we have seen that 2NT (1♥ - 2♥ - 2NT) or a change of suit (1♥ - 2♥ - 3♦) is invitational, so this sequence is not invitational and for experienced players it is a kind of mini-pre-empt (blocking a potential competitive intervention from the opponents).
With the sequence 1♥ - 2♥ - 2NT we must now look at what Partner does after Opener bids 2NT? Opener is telling Partner that they have a fairly balanced hand (15-18 HCP), and that they are interested in all Partners HCP. This is easy. Partner has promised something between 5-10 HCP, and Opener is already expecting (hoping) for a couple of good honour cards. So if Partner replied 2♥ with a minimum (say 5-7 HCP) then they should 'Pass', but if Partner replied with a maximum 9 HCP (even if it's counting Queens and Jacks) then they should bid game.
With ♠J-5 ♥Q-J-8-4 ♦A-7-6-5 ♣10-8-3 bid 4♥
With ♠K-9-8 ♥K-10-4 ♦6-3 ♣Q-9-7-6-5 bid 3NT (maximum points but only 3-card support), Opener can correct to 4♥
With ♠Q-7-6 ♥K-9-8-3 ♦J-7 ♣9-8-7-4 bid 3♥ (with a poor 6 HCP this is a minimum expression of a preference for ♥ with a 4-card ♥, with a 3-card ♥ a 'Pass' would be justified)
With ♠6-4 ♥K-8-3 ♦J-9-7-5 ♣Q-8-6-4 'Pass' with a balanced hand and only 3-card support
With ♠9 ♥Q-8-6 ♦Q-J-9-6-4-3 ♣10-4-2 bid 3♦. This not a forcing bid, remember this follows from a weak 2♥. It is an expression of distribution with poor HCP, a 3-card ♥ and a 6-card ♦. Opener would normally 'Pass' but could prefer a 3♥ with a 5-3 split, or a gamble 3NT, but in any case Partner will 'Pass' on whatever Opener bids.
What to do if Opener bids a second suit (e.g. 1♥ - 2♥ - 3♣)? Just as with the 1♥ - 2♥ - 2NT, this usually promises 15-18 HCP and an useful 4-card minor, and is asking Partner to re-evaluate their hand in both ♥'s and ♣'s. Taking as an example the sequence 1♥ - 2♥ - 3♣:-
With ♠10-7-6 ♥Q-8-6-3 ♦J-9-4-3 ♣A-8 bid 4♥. This hand has a 4-card support with an honour, and the Ace doubleton in Openers second suit.
With ♠Q-5-3 ♥Q-9-8-6 ♦Q-8-6-5 ♣8-3 bid 3♥. This hand has a 4-card support with an honour, and a useful doubleton in Openers second suit (ruffing potential). But the two unprotected side Queens make it a weak hand, thus the bid of 3♥.
With ♠9-7-5-3 ♥Q-10-6-4 ♦K-10-9-4 ♣7 bid 4♥. With 4-card trumps with a honour, a side King and a singleton in Opener's second suit, this 5 HCP becomes 9 DH, and worth a game try. If Partners hand was ♠9-7-5-3 ♥Q-10-6 ♦K-10-9-6-4 ♣7 it would be a sign-off in 3♥ because of the 3-card ♥, but with ♠9-7-5-3 ♥Q-10-6 ♦A-10-9-6-4 ♣7 it would be (again) a 4♥ game bid.
With ♠8-7-5 ♥Q-9-6 ♦K-Q-10-9-7 ♣J-2 bid 3♦. This hand is maximum with 9 DH and a good 5-card ♦. Only 3-card support for ♥ but with a honour, and poor ♣'s. This suggests a game try in NT, but Opener must decide.
Responder makes a game try
The above hands were about Opener receiving support from Partner, and then deciding on the opportunity to make a game try.
However, it is perfectly possible that the suit of Responder or Partner is agreed, and thus it is the Partners decision concerning a game try, e.g. 1♣ - 1♥ - 2♥. Now its Partners suit that is agreed, and it is Partner who must decide. This situation is potentially more complex, the simple raise by Opener suggests a near minimum opening hand 11-14 HCP (13+ DH) but can hide quite a variety of distributions (see below).
Distribution 1: ♠K-5-3 ♥Q-8-6-4 ♦8 ♣A-Q-10-8-6 with 13 DH and only 6-losers, open 1♣ and support Partner in ♥'s.
Distribution 2: ♠8 ♥K-5-3 ♦Q-8-6-4 ♣A-Q-10-8-6 again with 13 DH and only 6-losers, open 1♣ but then Opener has to decide between either 1NT with a un-balanced hand or support Partner with 3-cards.
Distribution 3: ♠K-Q-6 ♥J-10-7-3 ♦K-9-4 ♣K-10-9 is a sterile 4-3-3-3 with 12 HCP. The only option is to open 1♣ and support Partners ♥'s, but perhaps Opener should not have opened.
These three distributions are typical for someone playing 5-card majors and a strong No Trump. The rebid of Partners ♥'s can mean different things, e.g. honest support but bidding with a singleton, or only a 3-card support but still bidding additional value, or a hand that is probably not really worth an opening bid.
Try these tests where Opener started with 1♣, you bid 1♥, and Opener supports you with 2♥, now what do you bid?
Test 1: ♠Q-8-3 ♥A-10-7-6-4 ♦Q-9-7 ♣K-4
Test 2: ♠10-3 ♥A-J-10-8-6 ♦Q-8-6-4 ♣K-2
Test 3: ♠K-2 ♥Q-7-6-3-2 ♦Q-5-3-2 ♣Q-8
Test 4: ♠A-Q-4-3 ♥Q-9-8-7-6-3 ♦10 ♣5-4
Test 5: ♠A-6 ♥K-J-9-7-5 ♦10-4 ♣Q-8-7-6
Test 1: Responder has 11 HCP but with a 5-card ♥ (their 1♥ promised a 4-card suit), and a doubleton. The ♣K could be useful with Openers 1♣ bid, but at least one of the Queens will drop, and both could be useless if Opener has 5-4 in ♣'s and ♥'s. Experts suggest a Responder bid of a game invite 2NT but asking for Opener to consider their whole hand, and not one particular suit.
Test 2: Responder has 10 HCP but with a 5-card ♥ (their 1♥ promised a 4-card suit), and a doubleton with a useful ♣K. There is another rule from Forrester called the 'Rule of Nineteen' which added the HCP to the number of cards held in the two longest suits, and if the total comes to 19 or more then a game try is justified, otherwise stop. So the expert advice is bid 3♦.
Test 3: Responder has 10 HCP a 5-card ♥ and a 4-card ♦, and the 'rule of nineteen' holds as well. But the suits are weak and K-J and Q-8 are exposed. Experts suggest a 'Pass'.
Test 4: Responder has 8 HCP but with a 6-card ♥, a 4-card ♠ and a singleton and doubleton. This hand has only 18 points for the 'rule of nineteen' but is worth a bid anyway (so it looks as if the 'rule of nineteen' is not fixed in stone). Change the ♥Q to a ♥A and a 4♥ bid is more than justified, but the experts prefer an invitation bid of 2♠.
Test 5: Responder has 10 HCP but a 5-card ♥, a 4-card ♣ and two doubletons, one with an Ace. Now that ♥ is decided, a bid of 3♣ is a game-try with a 4-card ♣. It just like bidding a new suit and is not a non-forcing reply to Openers 1♣ bid.
Remember the sequence 1♣ - 1♥ - 2♥ - (2NT, 2♠, 3….) are game-try bids and are forcing for one round. In this sense 1♣ - 1♥ - 2♥ - 3♥ is not a game-try invitation.
And what does Opener do now?
But what does Opener do now in front of a sequence 1♣ - 1♥ - 2♥ - (2NT, 2♠, 3….)? Opener is forced to bid. If Responder bids a new suit it promises 10-11 HCP and a 5-4 distribution (note the 5-4 and not a 4-4). If Responder bids 2NT it promises about 11 HCP and a balanced hand (could still have a 5-card ♥ but normally Opener would expect 4-3-3-3 or 4-4-3-2).
If Responder bids 2NT Openers options are 3♥ with minimum and poor HCP and a 4-card ♥, bid 4♥ with a useful 13-14 DH and a 4-card ♥, bid a new 4-card suit below 3♥ or 3NT showing maximum 14 HCP and only 3-card support ♥, or bid 3NT showing a balanced 14 HCP.
On the second round if Responder bids 2♠, 3♣ or 3♦, Openers options are 3♥ with minimum and poor HCP a 4-card ♥ and little help in Responders second suit. Opener can bid a game 4♥ with 13-14 DH and help in Responders second suit (minimum would be a K-x help). Opener should be helpful with a 12-13 HCP with good controls, but cautious even with 13-14 HCP with few controls (e.g. no Aces) and exposed honours and honour sequences.
Special cases, or not so special after all
Let's look at this sequence 1♥ - 1♠ - 2♣ - 2♥. Opener has a 12-19 DH and a 5-4 distribution, and Responder has a 4-card ♠, max. 9 HCP and prefers ♥'s to ♣'s, but is probably only holding a 2-card ♥ (and could easily be holding only a 3-card ♣).
With ♠6 ♥A-J-9-7-6 ♦K-Q-4 ♣A-J-8-6 Opener has shown 16+ DH and a 5-4 distribution, and in front of a weak Partner with only a 2-card ♥, there is little or no possibility of game. The experts suggest a 'Pass'.
With ♠7 ♥K-Q-10-8-4 ♦A-Q-6 ♣K-Q-J-3 Opener has 17 HCP (the singleton in ♠ is worth nothing since Partner bid 1♠). In addition Partner has only a 2-card ♥, so an Opener rebid of 2NT will show 16-17 HCP and an interest in the strength of the Partner (who can pass in 2NT, or close in 3♥ or 3NT or 4♥).
With ♠Q-5 ♥A-K-J-6-4 ♦9 ♣A-Q-8-3-2 Opener has 16 HCP but a 5-5 distribution, so the expert advice is to bid again 3♣. Partner can 'Pass' or correct to 3♥, or bid game.
Now we get to the really hard part. Both Opener and Partner have bid twice, e.g. 1♣ - 1♥ - 2♥ - 2NT - ?, then what? Franky by now both parties should have a good idea if they should or should not be bidding game. The only question is in what? If Opener has a balanced 14 HCP, they should bid 3NT. With 14-15 HCP but a semi-balanced hand with a weak 4-card support and protected short suits, bid 3NT ('protected' could just mean Q-J through to A-Q). With a minimum 12-13 HCP and a flat distribution 4-3-3-3, even with 4-card support, 'Pass'. With a 12-13 HCP but a singleton in an unbid suit, insist on playing 3♥. With 15-17 DH and good quality support for Partner bid 4♥.
With bidding that goes 1♣ - 1♥ - 2♥ - 2♠ - ?, the situation is very similar to the above, except Partner is asking about strength (honours or ruffing potential) in ♠ (could just as easily be asking for ♣'s or ♦'s). By now the reader should be fairly clear about the options, if not go back and read everything again.
This final section of shape provided an excellent outline of bidding practices, and is (in my humble opinion) one of the most important topics to be studied and assimilated. The original article is well worth a read since I'm not sure I did it full justice.
A few additional definitions
This is a rather pedantic section that just looks at a few descriptions of words and phrases often encountered in bridge books, etc., but rarely defined in detail. For example, what is a 'robust' suit or a 'guarded' honour?
What is 'playing strength'? It is just the addition of the honour or high-card points (HCP) and the addition or subtraction of distributional points. The playing strength can change as the bidding progresses.
What is a 'guarded honour'? It is an honour card (e.g. King) that is 'protected' by a sufficient number of smaller card x-x-x…. in the same suit. For example, a K-x is guarded, but a Q-x is unguarded, however the Queen is guarded in Q-x-x and in a A-Q doubleton. A higher honour card can also guard a lower honour card, so the Jack in J-x-x-x is guarded as is the Jack in K-J-x. To guard a 10 you need 10-x-x-x-x or Q-10-x-x.
What is an 'artificial' bid? A 'natural' bid implies that the contract should be played in the suit that is bid, all other declarations are 'artificial'.
What is a 'forcing' bid? It is a bid that forces partner to bid if their Right-Hand Opponent (RHO) passes. In many systems forcing bids promise only strength, not distribution (this should be an explicit agreement in a partnership). A specific type of forcing bid is 'game forcing', which is mutually forcing on the partnership to reach a game contract.
What is a 'free' bid? This is any bid made where there was no longer an obligation on partner to bid.
What is a 'solid' or 'robust' suit? A solid 5-card suit is A-K-Q-J-x or A-K-Q-10-x, a solid 6-card suit is A-K-Q-10-x-x. So a solid suit is always headed by A-K-Q. A robust suit is one that hold 2 of the top 3 honours, or 3 of the top 5 honours. Weak-two's and pre-empts are made with robust suits.
What are 'honour-tricks'? Honour-tricks depend upon the honours held, A-K or A-Q-J are 2 honour-tricks, A-Q, K-Q-J or A-J-10 are 1½ honour-tricks, an A or K-Q or K-J-10 is 1 honour-trick, and K-x and Q-J-x is ½ an honour-trick.
What is a 'stopper'? A stopper is a suit containing 1 honour-trick (see above), and a potential stopper is a suit containing a ½ honour-trick. A 'double stopper' in a suit bid by the Right-Hand Opponent (RHO) should be where length+HCP equal to 8, e.g. A-x-x-x or K-Q-x. A double stopper held in the suit bid by the Left-Hand Opponent (LHO) should include A-K, or A-J-10, or K-Q-J.
What is a 'biddable' or 're-biddable' suit? Different systems have different definitions of a biddable suit. One definition is a 4-card suit containing 4+ HCP, or any 5-card suit. A re-biddable suit is one where the suit could still be bid if the two lowest cards were removed, e.g. A-Q-x-x-x-x is re-biddable, but K-J-x-x-x is not re-biddable. These definitions must be the subject of a partnership agreement.
What is a 'balanced' hand or an 'unbalanced' hand? A balanced hand is one containing no more than 1 doubleton. A semi-balanced hand is the distribution 5-4-2-2, containing no singletons or voids. An unbalanced hand starts with 6-3-2-2 or 7-2-2-2, or a hand containing a singleton or void (starting with 4-4-4-1). Some definitions include 6-3-2-2 and 7-2-2-2 as semi-balanced, and this must be decided by the partnership.
What does 'support' or 'fit' mean? Support starts with 2-cards in Partners suit. Support is when it is evident that the partnership hold 8+ cards in a suit or 7-cards containing 6+ HCP. Good support means that if the lowest card is removed Partner still has support, e.g. so J-10-x or x-x-x-x or better. Very good support means holding a biddable hand in the suit proposed by Partner. A fit is when the partnership holds sufficient cards and HCP for an agreed trump suit.
What are a 'raise', a 'preference bid' and a 'take-out' bid? If Partner has a free bid or if Partner supports Openers suit above the minimum level of reply, it is a raise (e.g. 1♥ - Pass - 2♥ is a raise as is 1♥ - 1♠ - 3♥). A preference bid is 1♥ - 1♠ - 2♥ means "I prefer to play 2♥ rather than Pass". A preference bid is also where a player expresses a preference for one of two suits bid by Partner. A take-out is a natural bid that is neither a raise nor a preference bid.
What is a 'limit' bid? These are bids that define an upper limit, or a small range of points, to a bid. Raises, rebids, and No Trump bids are limit bids, as are the weak-two opening bids. Some players using strong 2♣ and 2♦ will have a limit bid on 2♣. Some players consider pre-empts a limit bid as well.
What is 'offensive' and 'defensive' potential? Offensive potential is the trick potential of the suit added to the honour tricks held in the other suits, and trick potential depends upon the strength and length of the suit. An opening bid promises an offensive hand of 7 tricks assuming that partner delivers a 'fit' and about 8-10 DH (i.e. together 20-22 DH). A partnership bidding to a 2-level would expect to have an offensive potential of 8 tricks. An opening weak-two is made with a decent offensive hand but where a 1-level bid would overstate its defensive potential. A pre-empt promises an offensive potential of 7 tricks (assuming minimum support from partner), and poor defensive potential (usually max. 1½ defensive tricks in total). If the different between offensive and defensive potential is 5 tricks or more the hands are offensively oriented, otherwise much depends upon the evolution of the bidding.
These additional definitions were inspired by those provided for the original Computer Oriented Bridge Analysis program from the 80's.