Best line for 6D

[sieong]

I saw the following play problem from a JEC match this weekend. You are declarer in 6♦.

 

[hv=pc=n&s=sj4haq84dakj6ca42&n=sa5hjd98542ckq963]133|200[/hv]

 

The lead was ♠T.

 

If ♦ are 2-2 or ♦Q is singleton and clubs breaks no worse than 4-1, the contract is cold. Assuming ♦ break 3-1, is it better to

 

1. Hook a heart (♠A, ♦A, ♦K, ♣K, heart to the Q); or

2. Play for ♥K coming down in three rounds, or person with long diamonds have 3-4 clubs (♠A, ♦A, ♥A, ruff a heart, ♦K, ruff a heart, then if ♥K is still outstanding, play on ♣?)

 

In general, is there good way to determine the odds at the table (♥K coming down in 3 rounds is about 22%, but how to determine the conditional distribution of the person with long diamonds having long clubs? And how to factor in that hearts are breaking no worse than 5-3?)?

 

Thanks.

[winkle]

I'll reply to how to estimate the odds of long diamonds with long clubs.

 

A way to get a pretty good estimate is to look at empty spaces, and further simplify the problem by looking at 3-2 club breaks. So:

 

If long (3) diamonds are with long (3) clubs, one hand would have 7 major suit cards and the other hand 10. If long diamonds (3) are with short clubs (2), one hand would have 8 major suit cards and the other hand 9. The ratio of these two hand types are: 9!8! : 10!7! = 8:10. This gives you 44.4%.

 

If you do the same thing for 4-1 breaks, you get 7*8:10*11. This gives you 33.7%.

 

So the figure is somewhere in between, but closer to 44.4%. Call it 41%?

 

I used to spend a lot of time trying to figure out exact percentage of various lines but nowadays I don't do it because it doesn't help me at the table. At the table I'd just note that it's slightly (but not much) less than 50%... I would've expected around 45% but it appears 40% is a better guess.