Classic Rewind Rock-Scissors-Paper by Marshall Miles

   Declarer play requires entirely different fundamental modes of thought at matchpoints than it does at rubber bridge or IMPs.

S 6 5 2
H 8 7 5
D A J 10 8 4
S A 7 3
D Q 9 2
C A J 10 5 3

1 C Pass 1 D Pass
2 NT Pass 3 NT (All Pass)

   At matchpoints, with East-West vulnerable, West leads the king of spades. You need not be concerned with what can be made at another contract, because everyone should arrive at three notrump. In all probability, the king of spades is a normal lead. The question is when you should take the ace of spades. If you take the first trick, you might take all thirteen tricks, or you might be set if you take the diamond finesse. If you win the second spade trick, the diamond finesse can "safely" be taken, because if East has a third spade to return, spades must split four-three. If you had a hunch that the diamond finesse was not going to work, you would probably hold up till the third round to be sure of making ten tricks. Let's assume there are just three declarers playing the contract, No. 1 winning the first trick, No. 2 winning the second trick, and No. 3 holding off until the third round. Let's see how each team will fare. Fifty percent of the time the diamond finesse works, and No. 1 gets a top (two matchpoints) by taking all the tricks. About five percent* of the time, the diamond finesse will be off, but East will have no spade to return because West started with six. Again No. 1 gets a top. Perhaps, twenty percent* of the time the diamond finesse will be off and the spades will be split five-two, in which case No. 1 will get a bottom. Some twenty-five percent* of the time, the diamond finesse will fail, but spades will be split four-three, and No. 1 will tie with No. 2 for half a point. Fifty-five percent times 2 plus twenty-five per cent times 0.5 equals 1.225 matchpoints, or 61.25 per cent, which is No. 1's expectation. (*: These numbers include estimates of how often West would lead something else when he had only four spades.)

   No. 2 wins the second trick. Fifty-five percent of the time (when the diamond finesse works or when East has a singleton), No. 2 beats No. 3 and loses to No. 1 for one matchpoint. Twenty percent of the time, when the diamond finesse is off and spades are five-two, No. 2 gets a top. The other 25 percent of the time, No. 2 ties with No. 1 for half a point. Total expectation: 1.075 points out of 2, or 53.75 per cent.

   No. 3 gets a zero whenever the diamond finesse works or when East has a singleton spade. When spades split five-two, No. 3 loses to No. 2 and beats No. 1. The only time No. 3 gets a top is when the diamond finesse is off and the spades split four-three. No. 3's expectation is only 35 percent.

   Actually, the problem is even more complicated than this description implies. I conveniently had the same number of teams (one) adopting each line of play.

   As a child, did you ever play the game where, at the same instant, two people make a sign with their hands to indicate rock, scissors, or paper? Rock smashes scissors; scissors cut paper; paper covers rock. If you knew what the other person was going to do, you could always win. Similarly, if you knew what line of play most of the other declarers would adopt, you could make the play that would give you the best percentage. If a majority of the other Souths would hold up two rounds, you would hold up one round. Your play would beat the field whenever the diamond finesse worked or whenever spades were split five-two. Winning the first trick would be like bidding a grand slam when everyone else was in game. It would be better to try to beat the field by 30 points than to risk more to beat the field by 60. In contrast, if you believe most declarers would hold up one round, you should win immediately. Then, you would get a cold top about 55 percent of the time, and you would tie with the field whenever spades split four-three. My preference, not knowing what the field will do, is to win immediately. It is strange that such a bad play at IMPs can be a good play at matchpoints.

   Perhaps you got lost during this long discussion. Don't worry about it; no harm is done. The figures I used for percentages were only approximate anyway. I did not want to complicate the discussion by considering the possibility that East was long in spades or that the suit might block. The main point is this: There were two distinct types of play available. You could win the first spade trick, hoping that the diamond finesse would work; or you could hold off, hoping that the diamond finesse would fail. But if you were to hold off, how long should you hold off? Taking the first spade trick would be the best play at least half the time, and it might get you a few points even if it failed because spades might be blocked, or because some declarers would not hold off long enough. It is better to adopt a play that clearly gives you at least a 50 percent chance for a top, plus a chance for a few more points, than to adopt a line of play that will clearly be inferior 50 percent of the time and that may be no better some of the rest of the time. I would rather bet that a finesse will work than bet that it will not work and have to guess the distribution of a suit.

   In this example, the king was led, which prevented you from counting the suit. You should be able to learn the opponents' carding agreements, for example by turning to West and asking, "Does your partner generally high-low with three small cards?" or "Does East play a compulsory next-to-highest card whenever you lead the king?" But even if get this information, you must still guess about the distribution.

   What if West goes into a long huddle before leading, and finally lays down the deuce of spades? Although you presumably know the spade distribution, you should definitely win the first trick. If West had a problem (in this situation, it is usually a problem whether, with a weak hand, to lead his own suit or to try to find partner's strength), you can assume you have been fixed if the diamond finesse is off. Without a spade lead, twelve tricks are cold. If you win immediately, and the diamond finesse works, West's good guess on the opening lead will not hurt you.