AlexJonson, on 2011-November-24, 17:00, said:
Yes, of course, but the question is how exploitable LHO is on a club play. That's why the difficulty in attaching numbers. Does LHO play the club King when he has it?
Clubs is definitely better, in %, even before taking into account the >50% chance to guess it.
If you guess clubs you will make if either red suit is 3-3 or if either the diamond guard or the final club honour is with the long hearts. I.e. basically 50*(1-0.65*0.65*0.5*0.5)= 45%
If you guess clubs wrong you will still make
(1) When hearts are 3-3 = 0.5*0.355= 18%
(2) When hearts are not 3-3, but diamonds are 3-3, and the hearts are with the club honour 0.5*0.65*0.35*0.5=6%
(3) When hearts are not 3-3, diamonds are not 3-3, but clubs diamonds and hearts are together = 0.5*0.65*0.65*0.5*0.5=5%
I.e we are basically up to 75%.
If you play hearts at once you will make
(1) when hearts are 3-3 - 35%
(2) when hearts are 4-2 and either diamonds are 3-3 or 4 diamonds and the club K with LHO. - 48*(0.35+0.65*0.25)=25%
(3) when hearts are worse, and both the clubs and diamonds work, - 0.15*0.35*0.5=3%
(4) when the hearts are worse, and the clubs work, and the long diamond is with the long clubs with LHO. 0.15*0.65*0.5*0.25=1%
(5) when the hearts are worse, the clubs work, and the long diamond is with the long heart. 0.15*0.65*0.5*0.5= 2%
for a total line of 66%.
So its better to play clubs even if you dont guess better than 50%. The main reason being because playing hearts first destroys lots of your best squeeze options.
Obvio there are composite lines, but I dont have endless time...
EDIT to include the possibility of a heart-diamond squeeze, case B5 above. Also, note that I didnt take account of the fact that two long suits in one hand is appreciably less likely than split, just used half for the chance of a given guard being in a given hand.
The physics is theoretical, but the fun is real. - Sheldon Cooper