Join Bridge Winners
An instructive deal for the non-math types

The following deal comes from the final session of the mixed BAM. The contract is 7C on a spade lead. Clubs are 1-1.

North
x
xxx
AQ10x
KJxxx
South
Axx
AKJ
x
Axxxxx

Do you try to drop the HQ with the diamond finesse in reserve or do you try to ruff out the DK with the heart finesse backup? 

Here is a relatively math-free way to think about it at the table. There are 8 diamonds. If they are divided 5-3, the DK will be in the 3 card suit 3/8ths of the time. There are 7 hearts. If they are divided 5-2, the HQ will be doubleton 2/7th's of the time.

Your intuition should be that cards in a suit distribute such that the length in each hand will be apt to be closer to equal (e.g., 3-2 is more likely than 4-1 which is more likely than 5-0.) Accordingly, you should expect 5-3 to occur more often than 5-2 (in actuality 5-3 occurs 47% and 5-2 30%.)

Because 3/8ths is larger than 2/7ths and 5-3 occurs more frequently than 5-2, 3/8ths of a larger number is more than 2/7ths of a smaller number. (Similarly, the chance of 6-2 is greater than 6-1 and 7-1 is greater than 7-0.) So it is more likely that the DK will ruff out than it is that the HQ will drop. That is all you need to know. 

Bridge is a cruel game. We played the board against Justyna Zmuda. She correctly, IMO, played to ruff out the DK. The DK was in the west hand but did not ruff out. The west hand also held the HQ doubleton.

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