Free, on Apr 6 2006, 07:38 AM, said:
East having AJx = 12.4348% (1)
East having AJ = 6.7826% (2)
East having Ax = 13.5652% (3)
East having A = 6.2174% (4)
(other distributions aren't possible anymore)
So basicly cashing works in situation 2 and 3 which adds up to 20.3478%, while finessing only works in situation 4 which is only 6.2174%. In situation 1 you always lose 2 tricks.
These percentages are from Suitplay. It's a clear advantage to play for the drop. You don't even need this program to know that, but since you wanted percentages, here they are.
First, this not analogous to AKJ missing Q (as a problem) because until you touch the suit, you have almost a 70% chance to make simply by leading towards the KQ. One easy way to show the difference is to compare the key card off side long. Here the key card is the J or Q.
With AKJ, Qxx of side is 18.7% of the time. But with "Jxx" can be AJx in which case no play works (only 12.4%) or Jxx for 6.2% so you can't go wrong.
But ok, the problem states you lead to the king which loses to the ACE and WEST follows low. Now the problem is analogous to the AKJ situation.
All the possible holdings for EW have been eliminated except:
West held initally, Jxx ,or west held initially xx. This is "almost" the 11:10 ratio that was mentioned above. Actually it is 12:11 (the correct ratio here). So the "correct" percentage is not the 52.38 Limey_p gave (11:10) but rather 52.174 if you want to be more precise (After west play xx, he has 11 unknown cards, after east play A he has 12 unknown cards, this is the 12:11. 12+11 = 23 cases, the missing jack will be with the 12 card 12/23 times or 52.174% of the time).
Free used a program called suit play. Google suitplay.exe to find it. Even using suit play, he made a mistake. He had palying for the drop way too good (drop 24.35 finesse 6.2%). His mistake in his calculations is his situation 3 (East with Ax) has been elimianted when WEST follows with x on second round (there is no "x" for East to hold). Also, situation 1 has been eliminated for the same reason, that is once WEST follows to the second round, EAST can't have AJx.. So the two endings are:
East having AJ = 6.7826% (2)
East having A = 6.2174% (4)
IF you add the %'s (6.7826+6.27174 = 13) and then divide the drop by the total, you get, 6.7.826/13 = 52.1739... tada...
Of course here, you don't need suit play, you just need to know the JACK is more likely to be in the hand with more "space" for it.
Help
You are playing the following card combination in the trump suit with no bidding from the opponents & the rest of your hands are fairly balanced.