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February 12, 2002
Its All in the Percentages

Its All in the Percentages

When you develop a line of play you are often faced with a choice. If the situation is such that all possibilities can be attempted then that is clearly best. But often you must choose only one. In those cases you must choose the single line of play that affords you the best chance of success.

Look at the following hands and decide on your line of play.

The correct choices are provided at the end.

No. 1 North (dummy)
spade.gif (842 bytes)8652
heart.gif (841 bytes)K654
diamond.gif (837 bytes)A10
West club.gif (841 bytes)K108 East
spade.gif (842 bytes)??? spade.gif (842 bytes)???
heart.gif (841 bytes)??? heart.gif (841 bytes)???
diamond.gif (837 bytes)??? diamond.gif (837 bytes)???
club.gif (841 bytes)??? South (you) club.gif (841 bytes)???
spade.gif (842 bytes)743
heart.gif (841 bytes)A2
diamond.gif (837 bytes)KQ432
club.gif (841 bytes)AQJ
West North East South
Pass Pass Pass 1NT
Pass 2club.gif (841 bytes) Pass 2diamond.gif (837 bytes)
Pass 3NT Pass Pass
Pass      

The opening lead is the spade.gif (842 bytes)K. The defense cashes four spade tricks (West started with spade.gif (842 bytes)KQJ10 and East with spade.gif (842 bytes)A9). At trick five West leads the heart.gif (841 bytes)10. Thank goodness they could only cash four spade tricks. You only have eight top tricks and the ninth must come from diamonds. What is your plan?

No. 2

No. 2 North (dummy)
spade.gif (842 bytes)743
heart.gif (841 bytes)A6543
diamond.gif (837 bytes)A7
West club.gif (841 bytes)J108 East
spade.gif (842 bytes)??? spade.gif (842 bytes)???
heart.gif (841 bytes)??? heart.gif (841 bytes)???
diamond.gif (837 bytes)??? diamond.gif (837 bytes)???
club.gif (841 bytes)??? South (you) club.gif (841 bytes)???
spade.gif (842 bytes)AKQJ
heart.gif (841 bytes)KQ
diamond.gif (837 bytes)KQ3
club.gif (841 bytes)A976
West North East South
Pass Pass Pass 2NT
Pass 3heart.gif (841 bytes) Pass 3NT
Pass 6NT Pass Pass
Pass      

The opening lead is the diamond.gif (837 bytes)J. Plan the play.

Answers:

No. 1

No. 1 North (dummy)
spade.gif (842 bytes)8652
heart.gif (841 bytes)K654
diamond.gif (837 bytes)A10
West club.gif (841 bytes)K108 East
spade.gif (842 bytes)KQJ10 spade.gif (842 bytes)A9
heart.gif (841 bytes)108 heart.gif (841 bytes)QJ973
diamond.gif (837 bytes)J965 diamond.gif (837 bytes)87
club.gif (841 bytes)952 South (you) club.gif (841 bytes)7643
spade.gif (842 bytes)743
heart.gif (841 bytes)A2
diamond.gif (837 bytes)KQ432
club.gif (841 bytes)AQJ

The obvious choices are:

(1) Cash the three top diamonds. This is successful whenever the missing diamonds divide 3-3.

(2) Finesse the diamond.gif (837 bytes)10 (low to the ten) and then cash the top three diamonds. This is successful whenever the diamond.gif (837 bytes)J is in the West hand.

(1) will be successful 36% of the time.
(2) will be successful 50% of the time.

The correct play is to finesse the diamond.gif (837 bytes)10.

No. 2

No. 2 North (dummy)
spade.gif (842 bytes)743
heart.gif (841 bytes)A6543
diamond.gif (837 bytes)A7
West club.gif (841 bytes)J108 East
spade.gif (842 bytes)9652 spade.gif (842 bytes)108
heart.gif (841 bytes)J8 heart.gif (841 bytes)10972
diamond.gif (837 bytes)J1098 diamond.gif (837 bytes)6542
club.gif (841 bytes)Q52 South (you) club.gif (841 bytes)K43
spade.gif (842 bytes)AKQJ
heart.gif (841 bytes)KQ
diamond.gif (837 bytes)KQ3
club.gif (841 bytes)A976

You have 11 top tricks (4 spades, 3 hearts, 3 diamonds, and 1 club). To play for hearts to be 3-3 will win 36% of the time. However, if you give up one of your heart tricks you have two entries to dummy and you can take a repeated finesse in clubs. This will be successful anytime the club honors are split (one in each hand) or both with East. That equates to 75% of the time. A successful repeated club finesse will give you three tricks and enough to make the hand (4 spades, 2 hearts, 3 diamonds, and 3 clubs).

Win the diamond.gif (837 bytes)A and take a club finesse (losing to the club.gif (841 bytes)Q). Win any return and play a heart from the South overtaking with the heart.gif (841 bytes)A and repeat the club finesse.

-Gary King
 

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