[helene_t]

I was discussing deep finesses with my p. She said that it is always right to play to the T when you have AQT(...) in dummy. Intuitively I would normally play to the queen. I have been thinking a bit about it. The answer appears to be a bit complicated.

Dummy shows up with AQT9x and declarer has shown four cards in the suit. The suit only poses a problem if declarer is missing the king so defenders will have to assume that, and declarer might as well play it with open cards.

Assuming that declarer needs four tricks, he should clearly play low to the ace: This way he will always make it when RHO has J, K or KJ. If he finesses (whether the Q or the T) and it loses (T to J or Q to K) he is left with the guess as to whether to drop or finesse against the other honour.

If he needs five tricks, finessing the T is right when LHO has KJx(x) while finessing the Q is right when he has Kx(x). The latter chance is slightly bigger.

What I found interesting was that if LHO holds Jxx he should play J if he suspects declarer if playing safe (if he plays low, declarer will play the ace and make five tricks) and low if he suspects declarer is playing for five tricks (declarer will now play the queen and when it loses he will play RHO for KJ, making only three tricks).

Can we construct a scenario in which declarer's choice depends on what he thinks that LHO thinks that he (declarer) plans to do? Suppose declarer plays low and the Jack shows up. Declarer might think: "It only matters if the Jack was played from KJ, KJx, KJxx or Jxx. From KJ he would always play the J unless he is 100% sure that I would play the Q on the J. From Jxx he would play the Jack if he thinks I am playing safe. From KJx(x) he might play the Jack if he thought that I might play the T over x but A over J". This latter scenario seems a bit weird but on the other hand, a priori KJx(x) is almost thrice as likely as Jxx.

So it seems that when LHO plays the J you should still play the Q. OTOH, the fact that he might play J from Jxx makes playing low to Q even more attractive (it was already the best play for five tricks if LHO could be assumed always to low).

I wondered if one could come up with a scenario in which Suitplay would be wrong because the objective is not simply to "make 4" or "make 5" or "maximize expected #tricks", but that declarer thinks he needs a different number of tricks than defenders think he needs, or defenders think he thinks he needs, etc. The example I studied does not seem to feed the bill AFAICS: If declarer needs five tricks, LHO plays low from Jxx, and declarer plays Q over x. If declarer needs four tricks, LHO play J from Jxx, and declarer plays A over x. In both cases, declarer plays Q over J.

[awm]

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On lead, West cashes the ♣AK with east following ♣9, ♣8 (UDCA) and declarer playing two small cards. Finding east with the heart ace seems the best chance to beat the hand, and east's high club at the second trick suggests a preference for hearts over diamonds. So west continues ♥3, ♥4, ♥Q, ♥A. Declarer leads a low trump towards dummy. Now what?

Dummy has 10 points and declarer 16 or 17. Combined with west's 8, east will have 5-6 of which we have seen 2. East has at most one useful card at this point (and west has none). East's one trick will not beat the contract. The only chance is to get east in with the ♠K!

South has seen all the high cards except the ♠KJ. To avoid losing two spade tricks, rising with the ace for the safety play is obvious at IMPs. However, once he sees the ♠J south just might get greedy and play for an overtrick, especially since the heart ruff to defeat the contract requires a 6-1 break (extremely unlikely a priori).

[Lorne50]

helene_t, on 2013-October-23, 03:43, said:

Assuming that declarer needs four tricks, he should clearly play low to the ace: This way he will always make it when RHO has J, K or KJ. If he finesses (whether the Q or the T) and it loses (T to J or Q to K) he is left with the guess as to whether to drop or finesse against the other honour.

Not sure this is correct. Assuming you have 3 small and the oppo have 5 cards including the KJ then playing low to the 10 and then the nine produces:
5 tricks: 22.04%
4 trick: 53.96%
3 tricks: 22.04%
2 tricks 1.96%

If you play the ace first you gain a fourth trick only for KJ offside but lose a second trick to either Kx or Jx offside (depending on whether you play the 10 or Q second time). There are 3 Kx combinations (or 3 Jx) but only one KJ. Obviously in a weak field they will rise from Kxx second time but assuming a strong player on your left you are better not to play the ace first. The best play changes when the oppo have fewer cards however, and I am assuming entries to pick up Kxxx or Jxxx on your left.

[cherdano]

Lorne50, on 2013-October-23, 09:54, said:

Not sure this is correct. Assuming you have 3 small and the oppo have 5 cards including the KJ

Maybe you should reread Helene's post.

[blackshoe]

Thanks for posting this, Helene. You've given me a reason to dig out Roudinesco's The Dictionary of Suit Combinations. Been a while since I've looked at it. Of this combination (AQT9x opposite xxxx) he says:

Wanting to maximize number of tricks from the suit, or needing 5, first finesse the queen, then cash the ace. This gives the following probabilities of success: 5 tricks - 26.57%, 4 tricks - 50.00%, 3 tricks - 18/65%, 2 tricks - 4.78%, with an average number of tricks of 3.98. If you need 4 tricks, first cash the ace, then lead to the queen. This has a probability of success of 56.22%. This is all absent any information about defenders' holdings. There is a variant: if declarer's LHO is likely or known to have 3 or 4 cards in the suit, first finesse against the jack, and then against the king.

[FrancesHinden]

This is a variant on the position when they bid, say, 1NT-3NT and dummy has

xx
xx
AKJxxxx
xx

while you hold Q1098 of diamonds sitting under dummy.

When declarer plays a diamond towards dummy, play the Queen

[GreenMan]

FrancesHinden, on 2013-October-24, 11:38, said:

This is a variant on the position when they bid, say, 1NT-3NT and dummy has

xx
xx
AKJxxxx
xx

while you hold Q1098 of diamonds sitting under dummy.

When declarer plays a diamond towards dummy, play the Queen

I'm having trouble understanding this position. Are we assuming declarer intends to duck the first round as a safety play, and we want to persuade him to play from the top? That's the only scenario I can come up with, but I may well be missing something.

Thanks.

[helene_t]

FrancesHinden, on 2013-October-24, 11:38, said:

This is a variant on the position when they bid, say, 1NT-3NT and dummy has

xx
xx
AKJxxxx
xx

while you hold Q1098 of diamonds sitting under dummy.

When declarer plays a diamond towards dummy, play the Queen

Would it work against a good declarer? When we play the Queen he knows he is safe for six tricks if he ducks. But of course it can do no harm trying.

He might think he needs seven tricks but in that case he wouldn't duck if we played low either.