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PLAYING WITH THE ODDS
INTRODUCTIONIf you seek long term success at the Bridge Table then when faced with a choice of plays you should always 'go with the odds', i.e., pick the line of play that is most likely to succeed. Of course, unless your chosen line is in fact a certainty then it will be the case that 'some you win, some you lose' - but if you always strive to go with the odds you will win more than you lose, and that situation can make the difference between achieving moderate success and good success.
The fundamental issue tends to revolve around how suits will 'break' and, for example, should you 'play for the drop' or finesse to pick up the missing queen? The table linked here gives it the way it is - for every conceivable number of missing cards from two upwards it provides the statistical odds of finding the various possible breaks. So, for example, if there are six cards out in a suit, the table says that the odds of a 4-2 break at 48.4% are better than the odds of a 3-3 break at 35.5%. My thanks to Dr Nigel Cundy for providing the original material on which the attachment is based.
AN EXAMPLEYou find yourself playing in an optimistic 4♠ contract. You spot two chances for making this contract, one depends on a finesse in diamonds to pick up the Queen, the other on a 4-3 break in hearts. It is better if you can COMBINE the options, i.e., try one line, and if that does not work, fall back on the other one. Often, though, you don't have that luxury - you have to pick one or other option, and if it works out, success, but if not, you are doomed!
In the absence of any other information, you should note that the chances of a successful finesse are 50%, given that the vital card is equally likely to be in either of the defenders' hands, so half the time you will guess right, and half you won't. The linked table tells you that the odds of a 4-3 break are 62.2%, so in the long run when faced with this particular dilemma, you would be slightly more successful if you always chose to play for a 4-3 break, rather than rely on the finesse. By playing for the finesse you would be successful 50% of the time, but by playing for the 4-3 break, you would be successful 62.2% of the time.All this analysis assumes that you have absolutely no clues about the defenders' holdings. and it is based purely on statistical chance. The situation could change dramatically if, for example, the opponents contributed to the bidding. As a simple illustration, suppose one of the opponents had opened the bidding with a 'Lucas 2' opening of 2♥. The Lucas style of opening bids promises five cards in the suit opened and at least four in an unspecified suit. Now you know - unless your opponent psyched the opening bid - that the hearts do not break 4-3: they are 5-2, so now playing for a 4-3 break in hearts has a zero chance of success, and you have to fall back on the 50% finesse. By taking note of the point requirements of the opening bids, and the cards actually played so far by the defenders, you may even change your mind about the chances of success for the finesse - possibly you will conclude that the chances are better than 50/50, in which case, anticipate success! On the other hand, it may become increasingly obvious that the 'wrong' opponent holds the missing key card, so you may do better to play for, say, the vital missing Queen of diamonds to fall doubleton and try to 'drop it' instead.
It is all about the odds, and about allowing your calculations to be modified if and when vital clues come to light. By inference, it is best to delay facing your critical decision as late as possible, to increase the chances of 'picking up' critical clues.