Wednesday, September 12, 2007

Odds and Ends of Bridge (Part 4)




The above hand is from Frank Stewart’s Bridge Column on Sunday, September 9. Let me digress a moment to discuss probabilities before I get to the play of the hand. The probability of the division of the 8 card diamond suit prior to the play of any card in the deal is:

5-0 or 0-5 = 3.91%
4-1 or 1-4 = 26.26%
3-2 or 2-3 = 67.83%

The Queen of Clubs is led and East discards the spade 2. We now have completely discovered the division of the opponent’s holding in the club suit as West 6- East 0. We learned in Odds and Ends of Bridge (Part 1) about the Law of Attraction, that a long suit in one hand tends to attract another short suit and that a long suit tends to reject another long suit. The probable distribution of the 8 card diamond can now be recalculated to:

5-0 or 0-5 = 8.44%
4-1 or 1-4 = 35.22%
3-2 or 2-3 = 46.34%

This simply drives home the point that the initial table odds that you so frequently see and hear about can change rapidly once the complete division of any second suit is known. In this case the odds of a 3-2 spit in the diamond suit have been reduced from 68% to 46% by reason of the club division. While ordinarily the probability of an 8 card suit dividing 3-2 is far superior to taking a simple finesse in another suit, the aberrant division of the clubs has now made the 3-2 split in diamonds a decided underdog to a finesse. The point is not the arithmetic or memorizing probability tables, but when the cards around the table in one suit start to do funny things, don’t expect everything else to be normal – make a disaster plan.

The bid contract as published was 3NT. Assume the scoring is matchpoints. You are on the board with the King of Clubs. If the diamonds split 3-2 you can make 12 tricks by playing a small diamond to the queen and then back to the board with the spade, running the rest of the diamonds from the top. If you decide to “Pig-out” and go for 12 tricks, you actually can make only 8 tricks since the diamonds split 1-4 and you now do not now have enough board entries to try the “split honors” finesse in the heart suit.

At matchpoints we take the line of play that will both fulfill our contract and, at the same time, present us with the greatest probability to net us the maximum number of overtricks without jeopardizing the contract.

In Frank Stewart’s analysis he did not put all his eggs in the “3-2 diamond split basket,” since he knew that the 6-0 split in clubs was bad news. He played the diamond Ace from the board (Queen from his hand), then the King of diamonds hoping for a 3-2 diamond split and 5 diamond tricks. When East showed out on the second round he put Plan B in motion leading a small heart losing to West’s Queen. He won the club return in his hand, used his spade entry to get back to the dummy, led is 9 of hearts and let it ride, ultimately winning 2 spades, 3 hearts, 2 diamonds and 2 clubs.

Frank’s line of play was a heavy favorite to make 9 tricks, and at the same time he preserved his long shot of finding the diamonds 3-2 and making 5 diamond tricks for a total of 11 tricks. There is a superior line of play to the one chosen by Frank that will preserve the same opportunities, introduce no further risk and at the same time make an overtrick for top board. Did you find it? Hint: You don’t need to smother your own Queen of diamonds!


Anonymous said...

After 6-card club discovery, the probable distribution of 8 card diamond is:
5-0 or 0-5 = 8.44%
4-1 or 1-4 = 35.22%
3-2 or 2-3 = 46.34% should be 56.34%

The 3-2 split is still above 50% but not as high as 68%.

Your blog is very helpful. Keep up with your great work.

Tommy Solberg said...

A typographical error. OK at math, bad at typing.My numbers only total 90%, so 46 should be 56.It is encouraging to know that somebody is reading this. Thanks a lot for your comment. tommy

Tommy said...

Bad at typing, OK at math. A keyboard error since my numbers only totoal
90%. Thanks very much for reading and your excellent editing eye. It nice to know that somebody is coming behind me to pick up the pieces