Solution to the Hand of the Month 

ÍAQ63 
Ì 102 
Ë AQ872 
Ê A2 

Í J954           
Ì KJ86             
Ë J6543                      
Ê —-            

Í 82 
ÌAQ7 
Ë K 
Ê KQ109653 

This problem is a classic lesson in counting your tricks and playing safely to protect cashing them. I hope you noticed that ... barring the possibility of a 4-0 club break offside ...  the hand has 12 cold tricks when you play it in 6NT: the 4-0 club break is onside, and the bad diamond break won’t change the fact that you can cash 12 top tricks no matter what the lead is. However, your job was to make 6§, and we can argue about who should have bid 6NT over the dinner table. 

How should it be played after the spade lead? Here are some choices: 

(C player line) Put in the ªQ at Trick 1. This is the weakest possible way to handle the hand. (Bill’s calculations put it lower than 60%, since if it loses and a spade comes back, the dummy entry to the 12 top tricks is in jeopardy.) 

(B line) Rise ªA, come to ¨K, two rounds of trump ending in dummy, try to cash two diamonds to pitch a spade and heart, then take a heart finesse. (Bill makes this line much better, about 75%.) 

(A line) Rise ªA, cash ¨A and ¨Q pitching the spade, then take a heart finesse, intending to ruff a heart in dummy if the finesse loses. (This is much better still, and Bill makes this about 85%). 

(Expert line) Duck the spade! If this didn’t occur to you, it should have. This will protect your 12 top notrump tricks, and you will make the contract unless East can give West a ruff in some suit at Trick 2, or when clubs are 4-0 offside. 

(Bill thinks that is about 92%). 

Incidently, I unleashed John Strauch, one of the math gurus I keep chained in my dungeon to deal with math problems of this nature. In general he agreed with all of Bill’s figures, but his take on the expert line is that the pure figure should be slightly higher: The 4-0 offside club break occurs only 4.78% of the time, and the wildly improbable ruff situations do not increase the number of failing cases by much more than a small fraction of a percent. 

The figure he came up with on the bad clubs combined with a possible spade ruff was 94.97% probable success rate, so adding in the possibility instead of a red-suit ruff would still keep that figure over 94%. 

Thanks, John: you won’t have to return to your shackles for a while, as my reward for your stellar efforts!