kenberg, on Aug 18 2005, 05:25 PM, said:
My thoughts on the restricted choice question:
For a moment, let's treat the 9,T,J as indistinguishable (I'll get back to this). Declarer plays towards the Q and one of these cards appears on his left. He can pick up the suit if that card is stiff by finessing, and pick up the suit by playing back to the Ace if it is not. The three holdings where he must finesse are stiff 9,T,J. The four holdings where he should not finesse are 9T,TJ,J9 and 9TJ. Roughly 4-3 odds in favor of declining the finesse. Clear-cut odds, but not so overwhelming that they cannot be overpowered by other evidence, as happened. For example if declarer is convinced there cannot be three cards on his left, the odds look pretty even.
Are 9,T,J indistinguishable? Obviously only the case of J9 needs discussion and in the case at hand I think the answer is yes. Declarer is in 6, he has lost a trick, and he is leading from his hand towards the Q. Declarer holds the AK or we needn't fret. The only hope is that he will guess wrong in the way he plays the suit. Throwing the J from J9 has good chances to be a successful falsecard in most games, at least if delarer has some other push towards the finnesse. At a high level the J and 9 should be randomly thrown from J9.
That's my opinion. This never would have occurred to me had you not brought it up.
Ken
I agree with this analysis, but:
1) I can promise you that, even at the highest levels, it is far from routine to play the J from J9 doubleton in this kind of situation. I agree with Kenberg that this is a play that a really good player should be able to figure out, but in practice there are few really good players who would even consider such a play (and it's not like you can spend a lot of time at the table considering this play or it will be completely ineffective when you eventually figure out it is a good play).
2) Kenberg implies this in his post, but does not say so explicitly: Not all cases are equally likely. In particular, J10, J9, 109, and J109 are equally likely as are J, 10, and 9, but each 3-2 break is a little more likely than each 4-1 break.
As a pure math problem Grue's play was definitely against the odds, but I do think he had enough information from the bidding and early defense to know that his choice of play was at least even money to succeed. Hats off to Grue for having the courage to make this play. Imagine how he would be feeling right now if he had gone down in his slam (and what his partner, his teammates, and all the spectators would have thought).
Fred Gitelman
Bridge Base Inc.
www.bridgebase.com
Hands rotated so Grue is south... he was sitting north really.