Card Play - Getting the Basics Right





Card play is about a declarer playing the cards with a dummy, i.e. after the auction has been bid and won the declarer must decide how to play the hand.

Here we will start by looking at some basic card playing techniques, without going into too much detail.

However before actually playing the hand the declarer should review the bidding, analyse the dummy and the lead, and plan the play of the tricks (decide how they can best win tricks and avoid losing tricks, and which
play techniques to adopt and in what order).

Review the bidding


What was the bidding (and
bidding system used by the opponents) and what does that say about the distribution of honour points (HCP) and cards in the opponents hands? A pass can be just as informative as a bid, and don’t forget to take into consideration the adversaries vulnerability in your assessment. Is there any information showing that the points or cards might not be regularly distributed, i.e. interventions, doubles, passes, etc.? Is one of the opponents likely to be more dangerous than the other?

Are you in the right contract?


Based upon the bidding system, did you and your partner arrive in the right contract? Have you the enough points and/or the right distribution for the contract? Do your opponents think/know you are in the right contract?

Everyone today uses some form of point counting system (
hand evaluation), and most books adopt the High Card Point (HCP) system and go on to suggest that a partnership needs 26 points minimum for a game in No Trumps (NT), Spades or Hearts, 29 points minimum for a game in Diamonds and Clubs, 33 points minimum for a small slam, and 36-37 points minimum for a grand slam. In addition it is necessary to account for the distribution of suits across the combined hands of the declarer and dummy (long suits, voids and singletons, exposed honours, etc.).

But this is just the beginning. Firstly, presuming an 8-card fit, 1 of a suit needs 16-18 points (honours + distribution), 2 of a suit needs 19-21, 3 of a suit needs 22-24, and game in a major 25-27 points. However, game in a minor needs 28-30 points. A small slam needs 31-33 points, with stoppers, and a grand slam at least 34-36 points with all the Aces. In NT the point requirements are the same, with 1 NT needing 19-21 points, 2 NT needing 22-24 points, and 3 NT needing 25-27 points. However, 5 NT needs 28-31 points, 6 NT needs 31-33 points, and a grand slam 7 NT needs 37-40 points.

These HCP estimates are subject to a number of constraints, such as holding stoppers, 'usual' distribution of remaining points and cards in the opponents hands, and developing the right plan for the play of the cards.



However there are different 'rules' for experts, i.e. those who can declare, plan and play the cards well. For example, most 'expert' systems will game-force with a combined 24 points, particularly if the point distribution in the two hands is 16 and 8, whereas they will settle for a part-score with a distribution in the two hands of 12 and 12 (although a partner holding KJ 9x or a 5-card suit might push to game).

Zar Points - an alternative way to assess hands


The reality is that such a “simple” approach to point counting can be incorrect or sub-optimal.
Zar Points is said to capture better the strength of a hand, as perceived by expert players. The points mix the systems of Milton Work and Charles Goren with Aces counting for 6 points, K for 4 points, Q for 2 points, and the J only 1 point.
Zar distribution points are the sum of the lengths of the two longest suits plus the difference between the longest suit and the shortest suit.
Assuming an 8-card fit, Zar add 2 points for every extra trump card, if the hand has a void. And Zar adds 1 points for every trump card over an 8-card fit, when holding a singleton. For a second 9-card suit Zar adds 1 point, and for a second 10-card suit Zar adds 2 points. There are additional modifications, such as the misfit adjustment, and adding a point if high-card honours are concentrated, etc. In addition Zar rightly points outs that in matchplay, partnerships should bid game or small slams if there is a 50% chance of success. Using this counting system, bid 8 tricks with 44 Zar Points, 9 tricks with 48 ZP, 10 tricks with 52 ZP, 11 tricks with 56 ZP, 12 tricks with 61 ZP, and 13 tricks with 67 ZP.

Other Ways to Assess Hands


Yet other systems suggest that high-value cards are 'more valuable' when a fit has been found, and equally long suits have more value than would normally be seen in conventional point-count systems. Examples include adding an extra points when holding Axxx, KJxx, QJ 10x, and xxxxx, and adding an extra point for holding an extra card, and 2 points for holding an another extra card, and even 3 additional points for holding a 7th card in a suit.

Double Dummy


Every point counting system is trying to 'code' the best way to represent hands that prove to have 50% (or higher) chance of being played successful for a given contract. Double dummy analysis is a way to find the best line of play when all hands are visible. This presumes that the declarer can find the best line of play, but that the opponents also can find the best line of defence. Double dummy looks at all the possible contracts that each of the four players could play if they could see all of the hands. Computer simulations can be run on 1,000’s of types of hands to search for the best contracts, best lines of play, and best defence. Statistical analysis can be performed on 'real world' results of many, many tournaments, yielding the actual probabilities of success and failure for different types of contracts. Some of these analyses yield surprising results.

Based upon a computer simulation of more than 700,000 bridge hands selected at random the following statements have been made. Game can (should) be made 47% of the time, part-scores 40% of the time, slams 10% of the time, and grand slams 3% of the time. This does not mean that in the real world, real players actually bid these games, part-scores, and slams. We must remember that for any particular hand one partnership might be able to make game, but the other partnership might also be able to make a part-score. And in the real world both declarers and opponents might also under-bid, or over-bid. In the case that one partnership can make game, there is only about a 1% chance that the other partnership can also make game! These simulations do not take into consideration sacrifice contracts, e.g. bidding 4 Spades over 4 Hearts. However, the statistics over the 700,000 hands showed that sacrifices did not change significantly the overall distribution of scoring hands. But in the real world, and for specific hands where both partnerships can make game or part-scores, each also may have a winning sacrifice option. In addition the vulnerability counts. Part-scores are slightly more frequent when both parties are vulnerable (3% more likely as compared to part-scores when both partnerships are not vulnerable). Game scores are significantly more frequent (2%) when both parties are not vulnerable.

Real World Players


But do the results of real bridge players follow these computer simulations? It is true that stronger players bid more games and fewer partial-scores. Inexperienced players bid far too many partial-scores. World-class players bid far more games and slams, about 10% more than very, very expert players (expert players underbid about 6% of the time). Interestingly world-class players also bid far more games and slams (9% more) that the computer simulations consider possible! In part because they exploit the weaknesses and inexperiences of their real world opponents. Expert players also make partial contracts about 65% of the time, game contracts about 65% of the time, and slams nearly 60% of the time (depending upon level of expertise).

What do the statistics tell us about assessing the strength (point-count) of a hand? Distribution points do not adequately reflect the strength of unbalanced hands. For 55% of game hands, 25 points is sufficient (the shift to 15-17 points for 1NT reflects this change, as does the opening bid with 12 points minimum, and the 2-level reply with 10+ points). 10’s are important (particularly playing NT), and should be included in point-counts (½ point for each useful 10). Aces and Kings in balanced hand are substantially over valued (by around 7%).
By adding 4 10’s with an additional 2 points, a hand would contain 42 points. This has the advantage of returning the game point count to 26, as originally envisage.

Another point-counting system used for balanced (NT) hands, introducing 10’s and 'under-valuing' Aces and Kings, leads to a point count of A=5, K=4, Q=3, J=2, 10=1, for a total of 60 points per hand. This approach (as compared to the “classical” point-count system) reduced the value of Aces by 7% and Kings by 3%. It gives 7% of the total value of a hand to 10’s, and adds 3% to the value to Jacks. Game would then be 39 points, and so on.

There are many different
alternative point-counting systems, but they are not likely to get much traction in the coming years. However this discussion helps understand the limit of the present approximations being used.

Double Dummy versus Real World Play


The comparison of the computer simulations of double dummy hands, versus the actual play by real world players is also interesting. On average there is a 14% difference between those who make the best leads versus those who make the worse leads. So learning to make the best leads could improve a players score by 14% (and hurt declarers scores at the same time). But what are the best cards for opponents to lead against different contracts? Generally a reasonable declarer will score slightly better than the computer simulation of double dummy hands, simply because the opponents do not always play the best defence. There are 3 leads that cause the most problems to declarers according to the computer simulations, the 4 Clubs, 7 Hearts, and the 9 Diamonds (just this lead can give the opponents the edge in 1 in every 30 hands). The worse leads for the opponents (best for declarer) are 5 Clubs, 7 Diamonds, 6 Spades, the Ace Spades, and the 10 Hearts (this can give the declarer the advantage in 1 in every 23 hands).

As we have said, the reality is that real world players do not do the same as the best options based upon the computer simulations. Tournament players actually do better than the double dummy computer simulation 29% of the time, and do worse than the computer 17% of the time (remember they are playing real world tournament opponents). What are the leads that limit declarers ability to do better than the computer simulations, i.e. stopping declarer from making over-tricks? The 4 leads are 9 Diamonds, Q Spades, K Spades, and the best is the 8 of Clubs.

However, perhaps the better question is how to maximise match play scores, i.e. plays that are better than the other partnerships playing in the same tournament? In this case the worse leads (in order) for the declarer are Q Diamonds, J Clubs, 8 Spades, 10 Clubs, and the 9 Clubs (this lead gives a 6% edge to your opponents as compared to others playing in the same tournament). The reason for this could be the difficultly to interpret the significance of such a lead, and the fact that they are often associated with safe 'top-of-nothing' or 'top-of-sequence' leads.

The reality is that the most common leads are K Clubs, followed by Ace Diamonds, Ace Hearts, Ace Spades, 6 Spades, J Hearts, etc. Yet the reality is that most of these leads will score under 50% for those opponents. Despite the 9 Clubs being the most effective lead for the opponents, they actually lead the K Clubs 6 times more frequently.

Can this type of analysis tell us about the usefulness of opponents leading trumps? Again the reality is that a lead of a trump major gives the declarer a slight edge, 2% for Spades and 3.5% for Hearts. But leading a minor trump is effective, giving the opponents an edge of between of 1.7% for Diamonds and 2.6% for Clubs.

An understanding of the way scoring is made can also tell us something about when to bid games, slams, and grand slams (this is the so-called
expected value). All things being equal a partnership should bid a non-vulnerable game (major and minor) when it has a better than 46% chance of making the contract. This is even more marked with a vulnerable contract, a partnership should bid game (major and minor) when having more than a 38% chance of making the contact. Pairs should bid slams when they have a 50% chance of making it, but to move to a grand slam they must have at least a 56% chance of making it (and only if a small slam is certain). This is based upon Imperial Match Point gains and losses when one table bids the game, slam, or grand slam, and on the other table the opponents do not bid the same game, slam, or grand slam (each with the associated risk of 'going down' or of under-bidding). Example, bidding and making a vulnerable game could produce a gain of 10 IMP’s versus opponents who played the same hand but did not bid game, as compared to losing 6 IMP’s by bidding game and 'going down' by 1 trick when the opponents did not bid game and made just a partial-score. Therefore in the long-run partnerships should always try to bid vulnerable games if their chances of success are better than 38%. The odds are not as good for non-vulnerable games (46% versus 38%), but there is still an advantage for those who bid games versus those who do not. A practical example of this is to bid game if it just depends upon a simple finesse, but do not bid game if it depends upon a finesse and the outstanding trumps splitting 3-2. The combined probabilities of these two things happening is less that 38%. If you don’t believe this check it out here.

Back to basics, let us turn to the probabilities of having a particular honour (high-card) points count (i.e. counting 4/3/2/1)? You have a 56% probability of having at most 10 points, and a 65% probability of having at most 11 points, and a 73% probability of having at most 12 points. You have a probability of 33% of having a hand holding between 11 and 19 points. You have a probability of 6% of having a hand holding between 15 and 17 points. You have a probability of 36% of having a hand holding between 6 and 10 points. The probability of holding a hand with more that 18 points is about 2.5%, and the probability of holding more than 20 points is less than 1%.
Another way to think of these probabilities is as follows. You will probable hold more than 20 point in 1 hand in 100. If you play a 24-hand competition once per week, you are likely to see a hand with 20 points or more once per month. The probability of holding a hand with 24 or more points is 10 times less, i.e. you might see 1 hand like this per year! People spend far too much time learning how to bid improbable distributions and high-card point counts, when they should be learning how to pass. The probability of holding 6 or less high-card points is about 21%, or 1 in every 5 hands.

________



Changing the topic, players should remember that at their turn, during the auction and before the final pass, they can ask for an explanation of their opponents' prior auctions. They can not ask what future calls might mean. They are entitled to know about calls actually made, relevant alternative calls that were not made, and relevant inferences from the choice of actions where these are matters of partnership understanding.
Remember that the opponent (defender) on the declarer’s left may ask for a review of the bidding (it must be reviewed completely, and not partially, and the review can not be cut short), or for an explanation of the opponents auction. The defender must choose the lead and make it face down so that their partner can still ask questions (if the lead is made face up, the partner must wait their turn to ask questions). After the opening lead is made face down, declarer may also ask for a review of the auction and for an explanation of opponents‘ bids. The declarer’s right to a review and explanation expires with the play of the first card from dummy. The opponent on the right can still ask a question concerning the auction, but that right expires with the play of a card on the first trick. It is my understanding that when using bidding boxes the bids should be left on the table until the lead has been uncovered and the opponents have had the opportunity to review the auction and ask any questions. But even when the bidding cards have been returned to the box, players still have the opportunity, at their first turn of play, to require that previous calls be restated.

________


A few rules concerning
bidding boxes. Players must not deliberate while touching the bidding box cards. A call is made when the bidding card is removed from the box, and placed on (or near) the table (i.e. the bidding card has left the confines of the box). Corrections can be made if they are made without pause for thought, i.e. correcting an error.

________



Asking about the lead conventions used by the opponents is permitted. For example, is the 4 Hearts the 4th highest from an honour (or the 5th highest), or is it the 3rd highest from three cards with an honour? Is the 8 of Spades the 2nd highest from “nothing”, or is “MUD” from 3 small cards, or a “top-of-nothing”, or the top of a doubleton? The opponent (to the declarers right) must describe what lead conventions they use, but not what they might think that particular lead means. Remember the declarer should be precise in their question, and they should remember that lead conventions can be different against suited contracts and against NT.

Remember that understanding the significance of the lead can help declarer decide to apply the
Rule of 11 and the Rule of 12. The Rule of 11 is when the opening lead is the 4th best card of the defenders suit (often used against NT contracts). By subtracting the rank of the card from 11, this tells the declarer how many high cards are held by the declarer, dummy and the other opponent. Thus the declarer can deduce the number of higher ranking cards held in the other opponents hand. Naturally the opponent receiving the lead can also make the same deduction concerning the hand of the declarer. The Rule of 12 is based on a similar logic and is used when the lead is the third card of a 3 card suit including an honour (often used against suit contracts).

________



Analyse the dummy - it is a wonderful information resource to be used by both declarer and the opponents to find patterns, and plan the play of the cards. Does the contents of the dummy confirm the bidding? Is it better or worse than expected, and what does that tell you about the holdings of your opponents? The opponents will also be assessing the bidding and dummy, and what it tells them about the chances of declarer making the contract.

Strictly speaking the analyse of a dummy is in two parts. The first part is simply to confirm that the dummy corresponds to the bidding, or is better or worse than expected (or just different from that expected). Usually the opponents will do the same analysis, but they must factor in what they expect is the declarers point count and distribution. The second part comes slightly later when the declarer has to plan the actual play of the hand.

Before playing the first card from dummy the declarer must prepare the plan for playing the tricks. What to play first? Why? Which techniques to use, and in what order? Often declarer is uncertain about their chances of making the contract, and if there is a need to play damage limitation.

Dummy can be classified into 3 types. A “dead” dummy is one with a flat distribution and few entries. A “long” dummy is one with a long suit that must be “established” to create low-value winners. A “singleton” dummy is one which will be a source of tricks from ruffing. Declarer should immediately determine which type of dummy is in front of them.


The “
Law of Total Tricks” can help. It is a “law” that says that the total number of tricks available on a deal is equal to the total number of trump cards both sides hold in their respective best suits. What does that mean? This law is best when looking at competitive auctions, i.e. when both pairs have bid. Firstly declarer sees that they hold 9 trump cards, and that opponents also hold 9 cards in one of the minor suits (their longest suit). Holding 18-tricks (9+9) will occur 67% of the time, and thus playing a 3-level partial contact will be successful 67% of the time. This type of law can be used to justify bidding (say) 3 Hearts over a 3 Diamonds. It can also be used to (say) bid 4 Hearts (non-vulnerable) over 3 Spades, accepting to go down -1. It can also help understand that if opponents only possessed 8 tricks in (say) Spades, and the declarer appears to hold 10 Hearts, and is in a contract of 3 Hearts, then 67% of the time they will have underbid. In fact the author also noted that provided the trump lengths combine to 20 cards or fewer, the “Law of Total Tricks” will lead to the correct decisions about 70% of the time.
Declarer can use this law to help assess their chances of success, and the need or not for damage limitation.

________



Analyse the lead - does it conform to your expectations? In the lead unusual considering the auction? What does that lead mean to your opponents? What defensive agreements are used by the defense? What are their signalling (“carding”) conventions? Does the lead imply that the defending pair intend to adopt an active or passive defense? Active defense emphasises quickly setting up winners and/or taking tricks. Passive defense emphases waiting for tricks that declarer must eventually lose, making a safe lead, and avoiding plays that will set up tricks for the defender (and hoping to exploit errors and/or the inexperience of the declarer). The lead might place other high-card points, e.g. a lead of a K will usually imply that the opponent also has the Q. Opponent might lead trumps. Are they trying to reduce the ruff options in dummy, or was it a safety play?

Some examples are the lead of the 4th best card in the opponents longest suit against a NT contract. Or the “top of nothing” lead, or the top of a sequence, or a low card that might promise an honour, ... A good example is the lead of an Ace. Normally the opponents should not lead an unsupported Ace, unless they do not have a better alternative (or if the suit was bid by their partner). Also opponents should not lead from under an Ace in a suit contract, but it is possible to lead from under an Ace in their longest suit against a NT contract. However, the lead of an Ace is a good start against a slam contact. If opponents do lead an unsupported Ace, then it could be a singleton or doubleton, or it could mean they intend to take their tricks as quickly as possible.

Players often think a lot about what to lead when playing in defense, but spend less time thinking about the meaning of a lead when faced with planning the play of a contact. One of the best uses of the time available to a declarer is to try to understand the significance of the first card lead. With the opening lead the opponents are trying to convey a lot of information to each other. Declarer should “listen in” to that information. Remember the traveller (the score slip) includes a space to note the first card led, i.e. it is that important. Opening leads are different against NT and suit contracts, and declarer must know what those differences mean. In NT’s opponents will look to establish a suit, whereas in a suit contract opponents will look to take the first two tricks in any particular suit (or look to promote their lower-value honours). Statistical analyses of 1,000’s of hands shows that opponents can easily make the wrong opening lead, so declarer should take time to understand the meaning of the lead, and how best to exploit the mistakes made by the opponents.

The below discussion on the opening lead may appear academic at times, and more oriented to helping the opponents make the best lead. But the reality is that declarer must read the maximum information from the lead, since it is the best place for opponents to make mistakes, and the best place to find extra tricks.

In a statistical analysis and simulation of real-life hands it was found that the lead that produced the best score for the opponents was the card that they actually led the least. The best lead produced a 56% success rate for the opponents, the worse card lead scored only 42%, and the worse card lead was picked more frequently than the best lead. That difference is there for declarer to exploit if they can interpret the meaning in the opponents first lead.

Purely on the statistical analysis it was the 9 diamonds that was the best lead (for the opponents, worse lead for declarer), and the worst lead for the opponents was the 10 Hearts, followed by Ace Spades. Such a statistical analysis has its limitations, because it depends on how well declarer plays the contract, which may or may not be dependent upon the lead itself. Also it is not clear how statistically significant some of the analysis results are, given that some of the suggested leads are actually not made that frequently. However, what is clear is that the lead of a 9 Diamonds confuses the declarer the most, and potentially reveals the least information about the distribution of points and cards in the opponents hands, i.e. a safety play.

Another type of analysis is to try to beat a “double dummy” analysis, i.e. for the opponents to beat the score of the computer simulation. This actually happens more frequently that people think, an expert player can beat the computer simulation around 25-30% of the time, but will do worse than the computer around 15-20% of the time. Based on this analysis the best lead for the opponents is 8 Clubs, followed by K Spades, Q Spades, and the 9 Diamonds. So the best “safety” lead for opponents is the 8 Clubs. If the actual “real world” scores are considered then the most effective leads (for opponents) are (in order) 9 Diamonds, 10 Clubs, 9 Spades, J Clubs, and the Queen Diamonds.
Strangely a cross competition analysis yields completely different results. The most common leads are Clubs, Spades, Hearts, then Diamonds. The most common leads are K Clubs, Ace Clubs, Ace Spades, Ace Diamonds, Ace Hearts, K Diamonds, 2 Hearts, King Spades, ....The least commonly lead cards are 9 Diamonds, 10 Spades, 9 Spades, 8 Hearts, and 8 Diamonds. The K Clubs is 6 time more likely to be led than the 9 Diamonds.

More generally, not leading a trump is better for the opponents than leading a trump, but it depends. Based upon both computer simulations and real world statistical analysis, leading trumps against game in a major suit is in fact a poor choice for opponents (only 48% success), but it is a good choice against game in a minor suit (53% success).

Statistics is great, but has its limitations. However remember, a lead of a black 9 has the most positive impact for the opponents, red 8’s are poor leads, and black 5’s are most unprofitable leads for opponents. A lead of a red Ace is more effective (for the opponents) than a lead of a black Ace. The safest lead to avoid over-tricks is the 8 Clubs.

The above statements are statistically correct, but possibly not significantly so, nor do they appear to be based upon any logic or rule system that players can adopt and use. However, statistically analysing many hands can be useful. Increasingly the rule “lead the 4th card of your longest suit” against a NT contract has come into question. The idea is that many NT contracts are a race between two partnerships to establish a long suit, so leading a long suit looks like a good first step. Leading from a 3-card honour sequence, KQJxx or QJ 10xx, looks a safe bet for opponents. But what about leading from a broken suit such as Q 10xxx, KJxxx or AQxxx? If the opponent with the opening lead is holding 10 points, against 3NT, then their partner may only be holding 2-5 points (short on high-value cards), so what is the chance that they are holding just the right honour card in your broken suit? If the opponent with the opening lead is holding Q 109xx, and no other points (so their partner is placed with 10-12 points), then the 10 might be a good lead. But the “down side” might be the promotion of a long suit but no possibility to enter the hand. Computer simulations show that finding a partner holding 2 honours in the same suit as an opening lead is very infrequent. It is perhaps more useful for a weak opponent to try to lead into length in their partner hand.
Again computer simulations show that leading from a 4-card suit is not a good choice. Even if the lead is “lucky” it is unlikely to create extra tricks. Leading a short suit might help partner establish their long suit. Computer simulations show that leading from a broken 4-card suit against 1NT is a very poor option (leading top of a 4-card suit with a 3 honour card sequence is fine). The best lead against 1NT is an honour from something like QJx, if this does not look attractive, lead “passive”. Leading from something like Q 10x, is not a good choice, but leading J from a major Jx might be just the kind of aggressive lead that is needed (provided there is a good chance that partner is holding 4-5 cards in that suit).
Computer simulations show that it is almost impossible to establish a 6-card suit in a weak hand.
Playing 2NT is usually a “close affair”, and a safe “passive” lead is probably the better choice. Passive leads are also highly recommended when declarer is placed with lots of points in front of a very weak dummy.
Passive leads against 1NT or 2NT (and 4NT and 5NT) can also be very effective in limiting the number of over-tricks with declarer.

There is a very nice expression “hope is not a strategy”. This is valid for opponents making the first lead, and it equally valuable for declarer.

Remember, exploiting a poor lead is the best place for declarer to make their contract, or even make over-tricks. Time spent understanding the implications of the opening lead is time well-spent.

________



Plan the play of the tricks - an important first impression is to decided, based upon the auction and lead, on the “style” of play to be adopted. Should the declarer be conservative or aggressive? Was the bidding “over-optimistic”? Is the declarer considering over-tricks? Is making the contract going to be a good result? Will the declarer have to try to “limit the damage”?

Sometimes the lead will condition how conservative or aggressive the declarer can be. The need to play conservatively or aggressively can be based upon the skill of the opponents, the quality of the declarer’s game so far, what the rest of the field is likely to have declared, and the overall probability of success.

Before anything else it is absolutely vital to plan the play of the contract before playing the first card from dummy.


________



It is very difficult to discuss the planning and play of a contract without first knowing the different techniques involved in playing the cards. However there are some basic questions that a declarer needs to considered before looking in more detail at different playing techniques.

In playing NT contract, it is important to count winners, and to understand how many additional tricks have to be developed. The most likely place to find additional tricks is by promoting low-value cards in the longest and strongest suit. Is there a suit that could be a problem, and how best to minimise that problem? Is there a communication problem in getting to and from the dummy?

In playing a suit contract, it is important to count the worse-case losers (i.e. if all finesses fail), and to determine how many of those losers can be avoided. Which are inevitable losers (Aces and Ace-King combinations) and which can be finessed, trumped or discarded? How to play the different suits in order to have the best chance of success? Should I draw trumps, or do I need to ruff some losers first? Do I need trumps to access the dummy?


It is perhaps useful here to simply remember the probability of different patterns of card holdings. Firstly we must remember that there are only 39 hand patterns. Around 35% of all hands will include a 4-card suit, 44% of all hands will have a 5-card suit, around 17% of all hands will have a 6-card suit, and only 4% of all hand will have a 7-card suit.
In order, the most probable hand patterns are:
4-4-3-2 occurs 22% of the time
5-3-3-2 occurs 16% of the time
5-4-3-1 13%
5-4-2-2 11%
4-3-3-3 11%
These 5 distributions account for 73% of all hands.
The probability of holding a NT style distribution (4-3-3-3, 4-4-3-2, or 5-3-3-2) is 48%.
The probability of holding a two-suiter (5-4 through to 7-6) is 29%.
The probability of holding a one-suiter (a 6-card suit or better) is 19%.
The probability of holding a three-suiter (4-4-4-1 or 5-4-4-0) is 4%.
The probability of holding a singleton is 33%, and of holding 2 singletons is 10%, and 3 singletons is 2.5%.
The probability of holding a void is 36%, and of 2 voids is 15%, and 3 voids is 2.5%.

The probability of holding an Ace-less hand is just over 30%.

The probability of finding a “fit” with partner is as follows: 8 card fit has a 46% probability, 9 card fit 28%, 10 card fit 9%.
If you are holding 4 cards is a specific suit, the probability that your partner is holding 3 cards in the same suit is 32%, 4 cards 21%, 5 cards 9%.
If you are holding 5 cards is a specific suit, the probability that your partner is holding 2 cards in the same suit is 29%, 3 cards 31%, and 4 cards 17%.
If you are holding 6 cards in a specific suit, the probability that your partner is holding only 1 card in the same suit is 19%, 2 cards 33%, and 3 cards 28%.
If you are holding 7 cards in a specific suit, the probability that your partner has a void in the same suit is 7%, 1 card 26%, and 2 cards 35%.

If you have two possible suits, what is the probability of find a “fit” with your partner?
If you have two suits 4-3 then you have a 49% probability of finding a “fit” on one or the other.
If you have two suits 4-4, then the probability of finding a “fit” is 60%.
If you have two suits 5-3, then it is 55%.
If you have two suits 5-4, then it is 74%.
And if you have two suits 5-5, then you have an 84% probability of finding a 8-card “fit” with partner.

Your chances of holding all 13 cards in a suit is around 6 parts in 10 billion. On the other hand you chances of holding a solid 7 NT hand is at least 10 time better. Good luck!

________



With this mind, below is a quick summary of the different techniques that can be adopted within a plan for playing a hand (starting with the simplest).

There are a multitude of different ways to play any specific bridge hand, however there are only 4 ways to win a trick.
Firstly, have high-value cards (lots of points) that the opponents can not better.
Secondly, trump an opponents winning card (have lots of trumps, singletons and voids).
Thirdly, to establish a long suit.
Lastly, find the opponents high cards in the right position, e.g. make winning finesses, or for example, find the opponents Ace is placed before the declarers K.

No matter how complex, bridge hands are all about planning the play of the tricks in order to exploit one or more of the above four ways to win tricks. This includes ruffing, cross-ruffing, establishing a long suit, the finesse, duck/holdup, managing communication/entries, when to draw trumps, and general suit management techniques. More complex variations are just different ways to exploit these four different trick winning techniques, and they include dummy reversals, end plays, and squeezes.

________


Exploit the longest, strongest suit. As necessary remove controlling honours in the suit held by the opponents. Do not hesitate to use honours to force out a controlling honour in the hand of the opponents. Ensure that communication with the dummy is possible.

In exploiting a long suit play the honours in the shorter hand first, ending with a play back to the hand holding the most cards in the suit.

This is a good moment to look at how the opponents cards in a suit might be distributed.

The most common situation is that declarer (with dummy) holds 8 cards in a suit and the opponents hold the remaining 5 cards. The 5 cards held by the opponents will be distributed 3-2 68% of the time, a distribution of 4-1 will occur 28% of the time, and a distribution of 5-0 4% of the time. Logic tells us that we should expect to finesse a K or Q, but not a J. The probability of dropping a singleton K is only 6%. The probability of dropping a Q doubleton with A and K is only 31%, so a finesse of the Q is a better choice. A play of A, K and Q will drop a J in the opponents hand 73% of the time, so do not finesse the J. Even with only 6 cards in a suit, the probability that A, K, and Q will drop the J in the opponents hand is still 54%.

What is the situation if declarer (with dummy) holds 9 cards in a suit? The remaining 4 cards with the opponents will be distributed 3-1 50% of the time, 2-2 40% of the time, and 4-0 10% of the time. Logic tells us that we should finesse the K but not the Q or J. The probability of dropping a singleton K is about 12%, but the probability of dropping a Q (i.e. the Q is not in the hand with 3 cards) is still 52%.

What is the situation if declarer (with dummy) holds 10 cards in a suit? The remaining 3 cards with the opponents will be distributed 2-1 78% of the time, and 3-0 22% of the time. Logic tells us that we should still finesse the K but not the Q or J. The probability of dropping a singleton K is 26%, the probability of dropping a Q with the play of A and K is 78%.

What is the situation if declarer (with dummy) holds 11 cards in a suit? The remaining 2 cards with the opponents will be distributed 1-1 52% of the time, and 2-0 48% of the time. Logic tells us that we should not take a finesse, the probability of dropping a singleton honour is 52%.

Another useful consideration is the following question. If you possess a distribution 5-3, with opponents holding 5 cards, the distribution can range from 3-2 to 5-0. If you play the A and both opponents follow suit, then you have eliminated the possible 5-0 distribution. Does this change the probability of the remaining card distributions. e.g. after eliminating the 5-0 distribution is the 3-3 distribution more or less probable? And as an extension is a 1-1 distribution more or less likely than a 3-3 after declarer has played two rounds, i.e. having demonstrating that opponents were not holding the 6-0 or 5-1 distributions? Remember, if your were holding 7 cards, the probability that the opponents were holding 4-2 was 48%, 3-3 36%, 5-1 15%, and 6-0 was about 1%. Taking only the 4-2 distribution as opposed to the 3-3 distribution shows a 57% chance of 4-2 against 3-3. If the 5-1 and 6-0 distributions are eliminated by playing (say) A and K, then the remaining chance of finding a 2-0 against a 1-1 for the remaining cards is still 57%.


If declarer is holding a long, strong suit, then usually declarer will also be holding a short suit with a limited number of controls. The lead is likely to be in this suit, which can be very damaging when playing NT. Do not hesitate to focus on ensuring the contract, and/or (only if needed) taking the best “percentage” chances. Remember other players on other tables will have the same problems and will be taking the same “percentage” chances.
This is often called a “
safety play”, i.e. making the contract, and not looking to take risks that might yield a higher score but might put the result in doubt if the distributions are unfavourable. Some experts have defined it as taking out an insurance premium. A “safety play” is a precautionary measure, sometimes associated with the loss of a trick, designed to guarantee a successful contract despite an adverse distribution. Deciding to take a “safety play” in matchplay is often a question of common sense. It will depend upon the declarer knowing what the outstanding cards are, what the possible adverse distributions are possible, and finding a acceptable plan. If a “safety plan” can not lose, it should always be employed. A “safety plan” that involves losing a trick but guaranteeing the contract might still produce a poor results in a match-point tournament. The “perfect safety play” is where a trick must be lost, but it is all about how to lose that trick in a way as to be protected against an adverse distribution. Take the example of a declarer holding AK54 with dummy holding 9876. If the outstanding cards split 3-2 declarer will lose one trick, but could lose two tricks if the QJ and 10 are badly distributed, i.e. 4-1. The best play is the Ace as a protection against a singleton Q, J or 10 (and with the hope that no opponent is holding QJ 10x). Then declarer should play the 9 from the dummy with the intention to finesse. If the finesse does not work, the K will clear the suit (one loser). If the 9 is covered then again declarer will lose only one trick even with a distribution of 4-1.


Associated with exploiting a long suit is the techniques for clearing a suit of winners held by the opponents (affranchissement in French). Once “cleared” the long suit provides some additional needed “winners” for the declarer, i.e. promoting some low-value cards as winners. For example the simplest way is to play the tricks until the opponents are forced to win (say with the Ace). Other simple ways to clear a suit are by trumping (
ruffing) and by finessing.

Generally the declarer will be looking to win his contract by using his honour cards, by clearing a long suit to create additional winners (which are not honour cards), and by trumping (in other than NT contracts).

________


Using trumps means creating additional tricks by trumping those tricks that otherwise would be won by the opponents. Ideally the declarer would like to use the hand holding the fewer number of trumps to win additional tricks. If trumps are distributed 4-4 then ruffs should be limited to one or other of the two hands. Ruffs should only be made in both hands if a so-called
cross-ruff is adopted. A ruff is also a valid way to ensure communication between hands.

As a general rule, declarer should avoid ruffing in the hand holding more trump cards, declarer should aim to ruff in the shorter, “poorer” hand.

As already suggested above, ruffing a long secondary suit can be a way to clear that suit and create additional winning tricks.

So ruffing can be used to win tricks that would otherwise be lost, to clear a suit creating more winners, and to regain control from the opponents.

One of the most important questions, is when to pull trumps? Everything depends upon the plan developed by the declarer, however a key element is the ruffing of high-value cards held by the opponents, and eventually with the idea to promote low-value cards held by the declarer (or dummy). In principle any five-card suit can be cleared, promoting one or more low-value cards as winners. However, communication between hands might be a problem and the winners created might be un-necessary when compared to alternative methods to create additional winners, e.g. finesses.

If ruffs are needed to win the contract, then drawing (“pulling”) trumps too early can be a mistake. Communication between hands can be lost, and the declarer can end up losing control.

________


The
finesse has multiple options, starting with the simple finesse of an isolated honour held by the opponents against a group of honour cards held either by the declarer or in the dummy. This is just playing a small card up to the hand holding for example AQJxx (the French call this an impasse simple through a fourchette). If it works, it can be repeated until the K emerges and is taken by the Ace (a double or triple finesse). The general assumption is that this is a 50-50 chance. This is often called a “direct finesse”.

Other simple finesses that essentially work on the same 50-50 chance are as follows. Playing a small card up to KQx, the Ace is either one side or the other, and the declarer will make either one or two tricks. Holding Axx and playing a small card to Qxx, essentially relies on the same 50-50 chance. This is often called an “indirect finesse”.

An often found combination is A 10x held in one hand and Qxx held the other. The question is how best to play this? The best way is to play x to the Q, i.e. a finesse against the K. If the K takes the Q, then a finesse back through A 10 has a 74% chance of winning two of the three tricks, i.e. you will lose 26% of the time when both the K and J are on the “wrong” sides (for the declarer that is), K sitting over declarers Q, and J sitting behind declarers A 10.

Another often found distribution is A 2 in one hand and J 10 5 4 3 in the other. How best to ensure that declarer wins 2 tricks? Play Ace, and x to the J 10. This will fail only against KQxxx sitting above the J 10. This play is successful 90%. How best to ensure that declarer wins 3 tricks? Play Ace, and duck the 2 with the 4. This works against a 3-3 distribution and a 4-2 distribution with a doubleton KQ. This play is successful 64.6%.

But we should not forget that many situations are far simpler. If declaring is holding 9 cards in a suit it is better to play A and K to “drop” the Q, rather than take a finesse (you have a 52% probability that the Q will drop under A and K and a 90% probability that a J will drop under A, K, and Q). If holding 11 cards in a suit, the Ace should be played, looking to drop the K (you have a 52% probability of finding a singleton K).

There are many combinations of cards that are open to finesses, however the finesse is often very valuable when used to develop additional winners in a long suit.

Another type of finesse is a so-called ruff-finesse (an expasse in French). This involves playing an honour through your void, but discarding (défausse in French) a loser if the opponents do not immediately cover it with a higher honour.

A “deep finesse” is one that involves finessing two (or even more cards). For example, declarer can see a loser in AK 10, but he can simply play up to the 10 in the hope that both QJ and held on the left and the opponents are inattentive. This situation is not that likely, but if the 10 is a loser anyway then there is nothing lost in trying. A “deep finesse” also can have another purpose. Playing to AQ 9, and playing the 9 over a low card played on the left is not likely to win. However, a finesse can also be used to keep the player on the left off the lead.

A “two-way finesse” is one that can be played in either direction, e.g. with declarer holding KJ x with A 10x in dummy. Selecting the best direction for the finesse must be based upon an analysis of the distribution of cards held in the opponents hands. It can also be based upon which opponent you prefer to give the lead to. Another reason to take a “two-way finesse” in one particular direction, is when the declarer needs the finesse to work to create an additional entry to the other hand.

The so-called “backward finesse” involves the following combination, A xx held in one hand and KJ 9 in the other. the “classical” finesse would be to go to the Ace, and run a small card through KJ. The “backward” finesse involves running the J up to the Ace (the so-called “high-leading finesse”) and playing low if the opponent plays low. If the Q covers the J then the Ace takes the trick, and the finesse of the 10 is run back to the K 9 combination. This type of play can be made if the declarer has a reason to suppose that the Q is sitting on one specific side, or if he wishes to avoid one player taking the lead. This is a typical play of some one who is “
shooting” or taking a play against the odds in the hope of scoring a “top”.

Finesses can be very simple through to very complex in that variations can be dependent upon the holdings of low-level cards. For example, playing properly with A 10xx and J xxx in dummy depends upon understanding the split of card and honours in the two opponents hands. The “normal” way to play this might be to lead the J up to the A 10. However if the left-hand opponent covers the J (say with the Q), then the 10 could later be in danger if the right-hand opponent is holding K 9. The assumption is always that the honours are split. If the declarer knows (suspects) that the left-hand opponent is holding only two cards, then the best play is to lead x towards the J, a so-called “indirect” finesse. If the left-hand player takes the trick then the finesse will later be made against the other honour held in the right-hand opponents hand. If the left-hand opponent ducks, and the J is taken by the right-hand opponent, the declarer will play the Ace to take the remaining honour in the left-hand opponents hand. But if declarer thinks that the left-hand opponent holds 3 card with an honour, then the best play is to finesse from the dummy to the A 10 in declarers hand, and then later to drop the remaining honour in the right-hand opponents hand with the Ace. If the right-hand opponent plays his honour then declarer can take it with the Ace and play through the left-hand opponents honour to the J in dummy. So we learn that the key here is to play a low card through the opponent holding only two cards (one of which is an honour)!

Another type of finesse is the so-called “
coup en passant” in which declarer plays a losing trick through the hand holding a winning trump. If the opponent ruffs, declarer discards. If the opponent discards, declarer ruffs.

What declarer really likes is the so-called “free finesse”, where the opponents play the winning finesse for them.

But “free” finesses are not always forthcoming, so declarer must study different
suit combinations (specific sets of cards held by declarer and dummy). Declarer knows which cards are out, but not the exact distribution. Suit combinations tell declarer how best to play each specific distribution of cards held by the opponents. For example, if the opponents are holding 5 cards in a particular suit, there are 32 possible combinations of those cards. Suit combinations will be dealt with on a page dedicated to more complex playing techniques.

But before moving on, we should look at some common suit combinations in which two honours are missing, and the best way to play them.
Holding KJ 10 and xxx, finesse the Q with a play of x to the J or 10.
Holding Kxx and J 10 9, finesse the Q with a play of the J past the K (same with Axx).
Holding AJ 10 and xxx, finesse twice through the AJ and then through A 10.
Holding AQ 10 and xxx, finesse twice through AQ and then through A 10.
Holding AQx and 10 9 8, finesse twice, first with the 10 then through AQ.
Holding AJ 9 and xxx, finesse the 9, then the AJ.
Holding Kxx and Q 10x, play x to the K, then x through the Q 10.

Remember the probability to find a particular card, e.g. a specific K, with one specific opponent is 50%. The probability to find both K and Q in the same suit, in the same opponents hand is about 25%. The probability to find the K and Q in the same suit split between the opponents two hand is 75%.

As a general rule with two missing non-touching honours, declarer should start with a finesse on the lower value honour.

Remember the declarations of the opponents can provide vital information about the distribution and position of missing honours.

________


Exploiting long suits - returning for a more relaxed review of the notion of shape (hand distribution or pattern). Exploiting long suits is particularly important in NT contracts. An often overlooked feature of a long suit is that tricks can be won with low-value cards.

One of the simplest techniques to exploit a long suit is the “
coup a blanc” (I am not sure what this is called in English - but it is like shooting a blank). If declarer holds Axx and Kxxxx, there will remain a protected honour with the opponents, e.g. Jxx with the Qx dropping (assuming the most probably 3-2 distribution). To avoid this, play a “coup a blanc”, simply a low-value card on a low-value card, i.e. ducking or not playing an honour. When declarer gains control again the A and K will (should) free up 2 more low-value winners.

This “coup a blanc” is designed to counter a poor distribution in a suit, and it has the added advantage of conserving an entry into what might be a weak dummy. It also forces the opponents to win a trick early in the play of the hand, making it harder for them to retain control and make the right plays. They might have preferred to take control later in the hand when they have developed other winners (it might also remove a communication between the opponents). Another advantage is that it creates low-value winners that can be used to squeeze the opponents into discarding important or winning cards. Finally it is also a way to create an opportunity to ruff when playing a suit contract.

It is perfectly acceptable to play a double “coup a blanc” if the declarer wishes to create (say) 3 winners from Axx and xxxxx, and has appropriate entries to exploit the remaining low-value cards.

Shape or distribution can be valuable even with a hand such as a singleton x sitting across from xxxxx. Given that the most likely distribution is 4-3 in the opponents hand, you can take 3 ruffs, and promote your 5th x as a winner (presuming that you have 4 entries into the hand with xxxxx). Often slam contracts in a suit depend upon exploiting length in a second suit.

________


Communication between the hand of the declarer and dummy is an essential part of playing bridge. Planning the play of the cards is usually dependent upon the ability to move back and forth across the table to dummy, and otherwise secure contracts can go down because of a lack of entries into the dummy. The techniques are simple but they can not be improvised.

Often the dummy is weaker than the declarers hand, but it may contain a long second suit that must be exploited. The simplest technique is to simply remember to unblock controlling cards in the declarers hand so as to enter and remain in the dummy (thus exploiting the length in a second suit). Inattention concerning lower value cards is a major mistake, and can be very costly. Unblocking controlling cards in the declarers hand can mean throwing winners under winners from the dummy, e.g. declarer must throw the 10 9 8 (from 10 9 8 x) under the AKQ in dummy (thus unblocking AKQxx against an opponent holding Jxx).

Another way to unblock a hand with KQ and AJxxxx, is simply to play the K, then to take the Q with the A and continue with the J hoping to unblock the remaining low-value cards. A similar situation might occur with Q and AJ 10 9 xx, where declarer will take the Q with the A and continue with the J forcing out the K and promoting the remaining cards as winners (provided an alternative entry in the hand is available).

Exploiting length in the dummy requires entries, and this means from the very first card to have a plan to retain the necessary entries. Often declarer is faced with a first lead against Ax and Kx, and must remember to develop the plan for playing the hand before playing the first card. Often it is wise to retain entries into the weaker hand. Another situation often found is opponents leading into QJx and Axx, or Q 10x and AJx, and a finesse looks interesting. Declarer takes the finesse and then thinks about the plan for playing the contract. It is sometime better to play to take the Ace in order to ensure an entry.

With an opening lead against Axx and Kxxxx it may be important to take an immediate “coup a blanc”, retaining both the A and K in order to exploit the length later during the play.

Sometimes the declarer decides to exploit a length that is in fact a waste of effort given the lack of communication between the hands. It is vital that the plan for playing the hand takes into consideration the communication between the hands.

Some contracts depend upon a simple winning technique (e.g. taking a finesse twice) and that depends upon retaining entries into the dummy. Declarer might play the “obvious” first card without preparing the plan for playing the hand, and then find that the entries to dummy are not there. Declarer might decided rapidly to draw trumps and then plan the play of the cards, and find too late that Qxx of trumps was a needed entry into dummy.

Understanding the communication between hands (e.g. entries) may not be spectacular but it is a founding principle of good bridge play.

________


So the basic techniques needed in order to develop a plan to play a bridge hand are:
Analyse the coherence of bidding, the lead, and the dummy
Exploit a long strong suit
The ruff
The finesse
Understanding (and exploit) the distribution of cards
Understand the need for communication between hands.

________


Playing a NT hand - before playing the first card, count direct winners, identify potential winners, select the most likely winners from those potential winners, examine what are the risks, and determine the order in which the tricks must be played.

“Timing” is perhaps the most important element in playing a bridge hand, and with the lead the opponents have the edge. Determining the order in which to play the tricks is perhaps the most difficult part, and that often means understanding from the outset how to communicate between the hands.

One important element is to determine which of the opponents is the most dangerous, and how best to play to avoid that particular opponent. This can mean taking less likely options that place the lead in the “safe” or less dangerous hand.

Rule 1 - plan before playing the first card
Rule 2 - keep communication open between the hands for as long as possible
Rule 3 - keep entries intact for as long as possible to allow for changes to the plan
Rule 4 - Develop your winners (length, extract tricks), before taking your top cards
Rule 5 - Pick the best options (finesses, distribution, controls, squeeze, ...)

Remember a hand should take 7 minutes to bid and play. Take time to develop the plan for playing the hand. Play the hand quickly as long as tricks fall as predicted (i.e. the honours and cards are distributed as expected). If the distribution of honours and cards is not as expected, take time to assess the plan and if necessary make modifications. This can include a plan to limit the “down”.

________


Take or
Duck? - a question that declarer often asks on the opening lead (and is particularly important playing NT hands).

The easiest decision to make is to win the lead when declarer gains an additional control in the suit, i.e. a lead against Jx (play low from dummy) and A 10x (declarer) will always create an additional control.
Win the lead if there is a risk that the opponents shift the next lead to an even more exposed suit.
Win the lead if there is a good chance that the opponents will not be able to fully exploit the suit, i.e. declarer or dummy are holding something like J 10xxx or 10 9xxx.

Duck if you have only the Ace blocking the suit. How often should declarer duck? There is the so called Rule of Seven. When declarer's only high card in the suit led by the opponents is the Ace, count the number of cards in that suit held by declarer and dummy, subtract from seven and duck that many times (e.g. if declarer-dummy holds 5 cards in that suit, then 7-5=2, duck twice and take the third trick).
Duck if there is a chance to create a second control. The lead of a K (from KQ) to a declarer’s AJx should be ducked in order to create an additional control. This specific play is called the
Bath coup. Declarer should watch for the opponents to signal to not continue to play that suit (possibly a low card to discourage).

There is also the famous Rule of Eleven, already mentioned. Against NT it is often possible to assume that the opening lead was the fourth highest card in that suit. By subtracting the value of the card led from 11, the result is the number of cards in the other three hands that are higher than the one led. Declarer can make inferences about what the right-hand opponent is holding in that suit. Likewise, the right-hand opponent can then make inferences about declarer's holding in the suit by examining his own and dummy's holdings. The rule can be modified to subtract from 12 if the lead is thought to be third best, and from 10 if the lead is thought to be fifth best.


Duck a lead can be used to block communication between opponents in a suit that is dangerous to the declarer. As an example, the opponents lead a 9, which can be presumed to be the fourth highest card in that suit. Declarer holds Axx and dummy holds Kxx, so the rule of eleven tells us that the right-hand opponent only holds 2 or 3 cards, all lower than the 9. Logic tells declarer to duck the lead, ensuring that the AK holding will cut communication between the opponents. Taken too early, the lead might allow the right-hand opponent to continue to communicate with the partner allowing them to finally exploit the suit of the opening lead, and even to defeat the contract.

Duck a lead can have a psychological effect, particularly if the right-hand opponent does not have an easy signalling option, and the declarer can enhance that confusion with false carding. This can often incite the opponents to continue in that suit, to the benefit of the declarer.

________


Identify the more dangerous opponent - the lead on the first trick often tells the declarer which of the opponents is the more dangerous. Declarer will want to leave the lead in the hand of the weaker or less dangerous opponent. This is often easier said than done!

It is easiest to see this technique with an example. Declarer plays 3NT after the left-hand opponent had opened a pre-empt 3 Diamonds. The lead is the 3 of Diamonds, and declarer holds Kx in Diamonds with xxx in the dummy. Firstly, we should assume that the left-hand opponent holds 7 Diamond cards (so the lead of the 3 of Diamonds is a signal that the left-hand opponent probably holds an entry in clubs), and the right-hand opponent only holds one card in Diamonds. Therefore the right-hand opponent can not lead back Diamonds, therefore the dangerous opponent in on the left, and declarer should aim to play into the right-hand opponent. What does this mean in practice? Let us assume that declarer holds J 10 9 x in Clubs, with Axxxx in the dummy (and needs the Club tricks to make the contract). After taking the K of Diamonds, declarer should lead J of Clubs. If covered by the dangerous left-hand opponent, declarer will use dummies Ace, and play back Clubs hoping that the right-hand opponent has the outstanding honour. If the left-hand opponent plays low, dummy plays low and the right-hand opponent wins. The dummies A should (hopefully) drop the remaining Clubs honour with the right-hand opponent.
But what if the left-hand opponent after making the pre-empt bid, actually leads a small Spade? We know the distribution of Diamonds, and this is a clear message that the left-hand opponent is holding at least AQxxxxx. The Spade lead can not be showing a 4-card of better Spade suit, so it is probably a play to what opponents hope is a control or length with the right-hand player. In any case the aim of the opponents is for the right-hand player to eventually take control and to lead Diamonds through declarer’s Kx in Diamonds. Now the danger is with the right-hand opponent. How now to play Clubs? Declarer should lead the J and if covered by the left-hand opponent, play low from dummy. If the left-hand opponent plays low, dummy plays the Ace, and declarer hopes that the left-hand opponent is holding Kx must win the second round of Clubs. This is not a perfect play, but it is the only sensible way to play the hand.
Here we see that the dangerous hand can be either, depending upon the lead on the first trick. The good point about this situation is that the plan to play the cards is simple once the danger is identified.
But that does not mean all such situations are simple. Take a hand where declarer in playing 3NT against an opponent who opened with a weak 2 Hearts, and leads K of Heart. Declarer is holding Ax in Hearts with xxx in dummy. So the right-hand opponent has two Hearts, and declarer will win the second round lead of Hearts, to cut communications between opponents. Declarer needs to play correctly the Clubs, holding Qxxxx and with Axx in dummy. The “classical” play would be to play up to the Ace, and back to the Q, but this would certainly allow the left-hand opponent to gain control and play the remaining Heart winners. A “normal” finesse does not work because declarer is not holding the J 10 and 9 of Clubs. Playing up to the Ace, would allow a skilled opponent to unblock the hand by playing the K under the dummies Ace, leaving his partner with an entry with J 9x in Clubs. The only correct play is to lead from under the Ace in dummy towards the Q, assuming that the right-hand opponent is holding Kx or Kxx. The right-hand opponent can win with the K of Clubs but can not play to the partners Hearts. If the right-hand opponent plays low, the Q wins. The next play is a small Club back towards the Ace in dummy. But dummy must play low to allow (force) the right-hand opponent to win the trick. The Ace will draw the last Club and promote the remaining xx Clubs in declarer’s hand. This again is not a perfect play, but it is the only winning play when the honours in Clubs are split.

Another example will drive this point home. Declarer plays 3NT and the lead is the J of Spades. This suggests that the left-opponent is holding J 10 xx, or J 10 xxx, or J 10 9 x, or (since it is perfectly acceptable to lead from under an Ace), A J 10 xx. Declarer holds Kxx and dummy Qx in Spades. The only proper way to play this is to use the honour in the short hand, and play the Q. If the right-hand opponent has the Ace, the right play is to take it and play back Spades. In this case the Q holds, and so the danger is with the right-hand opponent, who can win a trick and then play Spades through declarer’s Kx.
Declarer needs to develop Diamonds to win the contract, and holds xxx in Diamond’s with AKxxx in the dummy. How to play this? Firstly declarer must assume a 3-2 distribution. Declarer must lead a small Diamond to the dummy, and if the left-hand opponent plays the Q of Diamonds, declarer should play low from dummy (otherwise declarer plays the Ace). Returning to declarers hand another small Diamond is lead with the same strategy. If the left-hand opponent again plays low dummy wins with the K, and plays a small Diamond hoping that the left-hand opponent holds the outstanding honour. Again this is not a perfect play, but it is the best option to win the contract.
A variation on this could be a lead of x Spade, with declarer holding KJ 10 and dummy with xx in Spades. Declarer might think that holding KJ 10 in Spades is strong, but after winning the first trick with the 10, declarer is still open to a play through KJ to the left-hand opponents AQxxx.

Remember in the above examples the bidding of the opponents often helps identify the distribution of points and cards, and is used to identify the more dangerous of the two.

The dangerous opponent is the opponent who can defeat the contract. In NT this is usually because that opponent holds an unblocked suit, or one of declarer’s suits holds an unprotected honour (e.g. Kxx or Qxx) that can be finessed by the opponents.

In the case where the opponent (often the opponent making the first lead) wants to unblock a long suit, the most powerful technique for the declarer is to “play-low”. That opponent may have an entry (e.g. Ace) and be able to run an unblocked suit and defeat the contract, but declarer must develop a plan that assumes that the dangerous opponent does not have a direct entry. The plan is thus to block communication between the weaker opponent and the dangerous opponent.

So, declarer should try to remove the dangerous suit from the weaker opponent. “Play low” and wait (if possible) is the key technique. An inexperienced declarer might prefer to take a lead of a K with their Ace, but it is more effective to take the last low-value card out of the hand of the less dangerous partner, in the hope of cutting communications between the opponents. Less expert opponents might not “see” the option to finesse the declarer, and might just play back the same suit (miracle’s happen occasionally).

A slightly less obvious situation is where the left-hand opponent leads from a 5 card Spades suit and declarer, playing in 3NT, holds AKx with xxx in dummy. Declarer might correctly place the right-hand opponent with only xx in Spades, and might think that they can take the first lead with the Ace, and even taken the second lead with the K (since the “weaker” opponent only holds xx). Declarer might think to take the first lead with the Ace, but duck the second lead of Spades. Consider that declarer is holding xxxx in Clubs and with QJ 10xx in the dummy (and needs to create 3 winners in Clubs). Declarer will assume that the remaining cards are distributed Ax and Kx. So declarer takes the first lead with the Ace, and plays x of Clubs to the Q, the left-hand opponent will (should) duck, and the trick will be won by the “weaker” opponent, who will play Spades. Now it does not matter if declarer takes it or not, the left-hand opponent still has the control of Clubs and can play out the winning Spades. Contract down! Now let us assume that declarer played low on the first lead, and took the second lead of Spades. Now playing Clubs the weaker hand on the right can not force our the remaining Spade control with declarer. Only the left-hand opponent can do so, but only using the one remaining entry, the Club honour. Contract made! If Spades were distributed 4-3, and not 5-2, then the opponents have an additional entry, at the cost of one less winning Spade. So contract made!

The second type of danger is when the opponents can try to finesse an unprotected honour with the declarer or in dummy. Here the objective is to ensure that the lead is only given to the opponent who can not finesse the unprotected honour. Often in NT there is more than one finesse option available to declarer. The key is to take the finesse (or finesses) that leave the lead in the “safe” place, even if that finesse is “deeper” or less likely to be successful. Remember the key is to find a safe way to successfully make the contract.

A good example is a lead of Hearts against 3NT. Declarer holds KJx with xx in dummy. The right-hand opponent plays the Q. If declarer plays low, the return Heart will (should) be ducked by the left-hand opponent (later the Ace will drop the remaining honour with declarer and free two additional winners). If the right-hand opponents gets in, they still have a Heart to lead. Contract down! Declarer can see AKQ of Spades, Ace of Clubs and holds RJxx in Diamonds with A 10 9xx in dummy. An inexperienced declarer will see 3 Spade winners, 1 Club winner, 5 Diamonds winners (assuming a 2-2 split), and 1 Heart. So, an “easy” 3NT+1. But assume that Diamonds brake 2-3 with the Q protected. The opponents win 1 Heart, then 1 Diamond, then 3 Hearts. So and “easy” 3NT-1.
The “safe” play is to win the Q of Hearts with declarers K, and to protect the Jx from a lead by the right-hand opponent. How to do this? Assume Diamonds will break 3-1 with the Q protected, but with the left-hand opponent. A simple Diamond finesse through the right-hand opponent will protect declarers Hearts Jx, and in the worse case produce 3 Spades, 1 Club, 4 Diamonds, and 1 Heart. Contract made without any risk.
In a competition, some less experienced teams may score more because of a favourable distribution (or poor defense), but the more expert team had a better plan. This example is interesting because declarer must identify the real problem at the outset, and not pick a “play-low” strategy. Expert opponents, after winning with the Heart Q, might well shift the lead to Clubs to remove declarers only control. This strategy could well produce 3NT-2 (Ace and Q of Hearts, 3 Clubs, and the Q Diamond if the distribution is 3-1). Taking the Heart Q stops experienced opponents from exploiting their control.

________


More about communicating with dummy - in particular when declarer is strong and dummy weak. A declaration such as 1 Club - 1 Diamond - 2 NT - 3 NT, implies that a strong declarer needed partners suit controls for a 3 NT contract. Often declarer-dummy will have one of these combinations Kxx - AJxxx, Jx - AK 10xx, xx - KQJxx, xx - ADxxxx, ..., with no other honour cards in dummy (i.e. no other entries to exploit dummies long suit). Counting the winners, declarer often does not need to win all the tricks in dummies long suit. An inexperienced declarer will hope for a favourable distribution, and will go down in the contract when the “wrong” opponent is holding Q 10 9x, Qxxx, A 10xx, or Jxx. The answer in each case is to accept to lose one trick by ducking a first-time lead:
Kxx - AJxxx, play K then x and duck in dummy (i.e. do not play the J for a finesse)
Jx - AK 10xx, finesse with the J but if covered duck
xx - KQJxx, the best defense against a opponent holding A 10xx, is to play x and duck (but any play to KQJxx presumes that opponents will hold up the Ace and dummy must have another entry - this play is an extended protection against opponents being able to block twice the suit by holding the A 10xx)
xx - ADxxxx, the intention is to finesse the K, but in the case that dummy has no other entries the safe play is to duck the first lead, and finesse only on the second lead.

There are situations where there is a need to overtake a winner in the declarers hand with a winner in the dummy, in order to create another entry to dummy. The example is a declarer holding Kx in Spades with AQxx in dummy, and R9876 in Clubs with J 10x in dummy. A small Spade to Q in dummy will allow the J Clubs to be played to finesse the Q Clubs. If this works and the Ace Clubs is forced out, then declarer should later over-take the K Spades with the Ace in dummy to create another opportunity to play the 10 Clubs and again finesse the Q Clubs.
The above example sees a winning K being over-taken by a winning Ace, but communication can be created with the smallest of cards, e.g. a 5 can be used to over-take a 4 and provide another entry to a dummy.
An entry can be created by ducking the lead. If declarer is holding AKxx Spades and dummy Jxx, and the Jxx is the only entry possible to dummy to exploit a long suit (imagine declarer holding AK with QJxxxx in dummy). With the first lead of a small Spade, it would be attractive to play the J from dummy, but this would destroy the only entry into dummy to exploit a long secondary suit. The lead suggest that the opponent is holding Qxx or Qxxx, so duck in dummy and take the lead with the Ace Spades. After clearing the doubleton AK, declarer can play back to the Jx in Spade to create the entry to dummy.
It is not always the longest suit that can provide the solution to a contract. Imagine that declarer is holding AJ9x in Hearts and 10 8x in dummy, and K 10 in Diamonds and AJ98x in dummy (declarer controls the other suits, and dummy has no other entries). The chances of the opponents allowing the Diamonds to break nicely and allow access to the dummy through the Hearts in slim to non-existent. So Diamonds can not be exploited, but Hearts can be exploited with a double finesses. For a double finesses, a double entry to dummy is needed. The 10 Diamonds is played to the J in dummy, if the Q Diamonds appears all the better. If not, a small Heart is played back to the J Hearts. The K Diamonds is then used as a second entry to dummy, and this time the 10 Hearts is run past declarer’s A9x. If this holds the dummy’s 8 can be run past declarers remaining A9. Note that the way the Hearts are played is one way to ensures that a Qxxx can not hold up the winning of 3 tricks by the declarer, playing the 10 from dummy and x from declarer will potentially block declarers hand.

Communication with dummy can be achieved by a simple process of unblocking the declarers hand. Imagine that declarer holds Qx and dummy A9x. The opponents lead small, dummy plays small, and the K takes the trick. What does declarer play? If declarer plays low, the Q is a later winner, but the remaining Ace in dummy might not be reachable. Knowing that the lead of a J implies the holding also of the 10, declarer can “unload” the Q under the opponents K, and then finesse the 10 through dummy’s A 9, making 2 tricks instead of 1.

Declarer unblocking a suit can be even more dramatic. An extreme example might be declarer holding K9x with Jxx in dummy. Against a lead and the appearance of the Ace, declarer can drop the K under the Ace to unblock the J as an entry to dummy.

Communication with dummy is an essential feature of card play, but whilst unblocking honours and winners by declarer in order to access dummy is not difficult to understand, nevertheless it is difficult to commit to in practice. The key is to visualise the need well in advance, and this is all about planning the play of the cards and tricks before playing the first card!

________



Timing (
Tempo) is about deciding when to do what. Declarer will usually be obliged, during the play of a hand, to give the lead back to the opponents. The question is then, can declarer execute their plan before the opponents execute theirs? Timing is about when to return the lead to the opponents, how many times can the lead be given to them, and how often can declarer take back the lead. If declarer holds one more entry than the opponents, then declarer has the time to play finesses and/or develop winners in a long suit. If declarer does not hold sufficient controlling cards, then the plan for the playing the hand might need to changed.

An example might be with declare holding QJxxx in Clubs and 10xx in dummy, and xxx in Diamonds with dummy holding AKQx. With limited controls in the majors, declarer must decided if they possess sufficient controls to allow the Clubs to be promoted. Or, in order to make the contract before the opponents exploit their length in a major suit, should declarer aim for a 3-3 split in Diamonds in order to find the 9th trick in 3NT. If declarer is holding just two controls in each of the majors, then they do not have enough time to exploit the length in Clubs, the only option is to hope for a 3-3 split in Diamonds. The same situation can arise where declarer does not have the time (control) to develop a long suit, but can make the contract with one successful finesse. The question is then the balance a sure “down” against a possible “down”, and we can all guess what the better choice is.

Controlling the “tempo” can allow declarer to dump losers, to take fast-winners, to develop low-value winners, to develop ruffing options, to promote trumps, and to stop opponents drawing trumps.

Timing (controls) can be also important when deciding which of two long suits to exploit. In this case it is often better to exploit a long suit with just one finesse than hope to exploit another long suit by losing two top honours. Declarer might not have the time (controls) to do the second, but could make one finesse.

Timing, or keeping control of the lead, can force declarer to make unusual plays. For example declarer may hold KQ of Clubs with A98xx in dummy, but only have one entry in dummy (and only one remaining control on the opponents suits). Declarer can hope that Clubs split 3-3, play out KQ and go to dummy with its single entry. Or declarer can play K, and over-take the Q with the Ace of Clubs. This ensures 4 winners with a 3-3 split, and with a 4-2 split provided the J and 10 are split and not sitting J 10xx.

A common type of problem is a lead to declarer holding Axx with QJx in dummy. No matter how declarer plays these cards, they have two winners and one loser. However, the question may be how to ensure an entry to dummy. In this case play low from dummy and always take the trick with the Ace, now the QJ will ensure an entry. If declarer played the Q and it wins the trick, the opponents are still holding a K which will block the entry to dummy with the J. Declarer always wins two tricks, but has lost the entry to dummy. This kind of problem can occur with the first trick, and amply justifies the need for declarer to prepare the plan for playing the hand, before playing the first card from dummy.

Remember opponents do not always find the best lead. Declarer must be ready to exploit all opportunities. Remember a double finesses of AJ 10 9x has a 76% chance of success, and opposed to a 50% chance of success with a simple finesse of AKJ. A good lead might have forced declarer to take the 50-50 option, but a poor lead might give declarer the control to take the double finesse.

________


So far we have looked at techniques that declarer can use to try to make their contract. The techniques are about creating opportunities in the declarer-dummy hands. But there are also some basic techniques that can be used to block the opponents from developing a suit.

The Barricade Coup is played when opponents lead into K 10x in dummy and Qxx with declarer. The presumption is that the opening lead is towards a partner (on declarer’s right) who holds AJxxx. If declarer does not play the K from dummy, then opponents will play to force declarer to win with the Q. Now the K in dummy is compromised. If declarer plays K to force out the Ace, then declarer is holding Qx with 10x in dummy, the Q is the “barricade”, and in addition the opponent on declarers right can not lead back that suit.

The Bath Coup is played when the lead is the K (implying the holding also of the Q), and declarer holds AJx. By playing low on the lead of the K, declarer blocks a continuation in that suit.

The Belladonna Coup is a most complex example, and the last one on this page. Declarer holds AQJxx in Spades (trumps) with xxx in dummy, and Jxx in Hearts with Kx in dummy. Declarer is faced with a finesse in trumps, and the need to ruff the third round of Hearts. To make life difficult the lead is a small Spade from Kxx to J in declarers hand. Declarer must presume that the Ace of Hearts is sitting over the K in dummy, and the opponents will play Spades, removing the ruff option. So playing up to the K Hearts will produce 3 losers, plus the K Spade. Declarer (Belladonna) crossed to dummy with a Club, and played a small Heart away from the K. Now the opponent on the right has a problem. If they play low the opponent on the right can take the trick with the Q Hearts, but can not play Spades again from under the K. Opponents can now only win 2 Hearts (Ace and Q) and the K Spades (since declarer can now ruff the 3rd Heart). What if the right-hand opponent goes up with the Ace and plays Spades? Declarer takes the trick with the Ace, refusing the finesse. Declarer then plays to the K Hearts, and back into their hand with a minor suit control, to play the third Heart for a ruff. Opponents win the Ace Hearts and the K Spades.

Here is a description of different coups, including some even more complex than the one outlined above.

________



If there is one key message that summaries this whole page, it is to plan the play of the cards, before playing the first card from dummy.


Some hints for the road
When declarer has no information about the holdings of the opponents a finesse is a 50-50 proposition. Declarer should always try to understand the bidding, leads, etc. in order to increase the odds. Individual finesses should only be taken if there are no better alternatives.

If opponents are holding an odd number of cards, (e.g. 5 cards) then the cards will most probably been split evenly about 65% of the time (i.e. 3-2). If the opponents are holding an even number of cards (e.g. 4 cards) then they will most probably split unevenly about 65% of the time (i.e. 3-1). One implied conclusion from this is that it is better to play a contract with a 5-2 split in trumps than a 4-3 split.

Playing NT declarer should develop additional tricks (promote low-value winners, finesses, etc.) before cashing in winners. Declarer should lose the lead as early as possible, while they still possess stoppers.

Declarer should draw trumps first unless they need to ruff in dummy. Declarer should only draw opponents losing trumps, then force opponents to ruff with their trump honours.

In playing finesses always try to lead a low card to a higher one. Only finesse with a high card to a higher card when declarer-dummy holds 4 or the 5 honours. Remember a double finesse has about a 75% chance of gaining finding the honours split.

If declarer only holds 2 of the top 4 honours in a suit, wait until opponents are forced to play that suit.


There is one last “principle” not fully treated on this page, but of great use to declarer in playing a contract. It is the so-called “
Principle of Restricted Choice”. This is the basis for the assumption that honours will be split between the opponents hands.

________


https://cs.brown.edu/research/pubs/theses/ugrad/2008/winograd-cort.pdf
https://www.stat.berkeley.edu/~aldous/Research/Ugrad/Z_Zhang_project.pdf
http://www.occasionalenthusiast.com/bridge-hand-probability-analysis/
http://bridge-tips.co.il/wp-content/uploads/2015/08/When-is-it-best-to-Bid-Pass-or-Double.pdf