Posted 2006-April-12, 05:16
All this discussion of avoidance plays is interesting in a theoretical sense, but to be honest it's nearly irrelevant to the hand in question.
Let's look at it as a single dummy problem.
When dummy hits we can count 3 spade tricks, 2 hearts, 1 diamond (at trick 1/2) and 1 club. That's only 7.
We play low from dummy at trick 1, in case RHO is going to play the ace (getting us up to 8), but RHO plays the 2. Assuming they play standard leads and signals (of course we check) the 2 is discouraging, from either singleton 2 or a low doubleton, and LHO has AJ109(x).
To get to 8 tricks we will need a second club trick.
To get to 9 tricks we either need a three club tricks, or an endplay, or a squeeze.
Let's think about the 3 club tricks approach. If we are going to do this, any avoidance play in diamonds is irrelevant. Either they are 5-1 and RHO can't play a second round of the suit, or they are 4-2 and they only make 3 diamonds and 1 club.
I believe that the best line for 3 club tricks is very close between ace then low to the queen, and low to the queen followed by low to the 10. Knowing the diamond break may change the odds slightly, but I don't think it does so enough to make low to the 10 right on the first round. The presence of the C7 in combination with the diamond break may make a difference.
What about two club tricks followed by an endplay on West, or a squeeze (hearts and clubs) on East?
For an endplay on West to succeed, we need West to be 2254 or 3154; or 3244 with East having no quick club entry. Any time West has a third heart he just hangs on to it grimly as an exit card. It's more likely that East has the club length than West. It's possible there is some sort of complex squeeze position but it doesn't feel right to play for it from trick 1.
A heart/club squeeze will need diamonds to be 4-2 and East to have the club menace; and even then it can probably be broken up if they don't cash the diamonds but instead attack hearts. Another layout that I'm not going to play for from trick 1.
So it seems to me that the best line is to play clubs for 3 tricks, with a back-up plan of end-playing West if possible. Win the diamond, club to the Queen, club to the 10. My extra chance is if West has KJxx or Kxxx in clubs and is 31 or 22 in the majors (club to the queen holding, club to the 10 and jack or jack and ace, win the return, ace of clubs East discards, cash majors exit in clubs. If he rises on the first club I can cash the Q and A next and find out they don't break).
On the actual layout I think I'll be two off. I will need a lot of convincing that the winning line is actually a significantly better line, and that will include some very detailed calculations on the club break conditional on the diamond break.
p.s. If East has KJx of clubs and manages to duck the first round I'll congratulate him (club to the queen, club jack ace, cash majors, exit in clubs.... ooops!)