[plaur]

Scoring: IMP

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Local teams. You have the flu, and probably should have called in a substitute but here you are declaring 3NT! Lead is a small spade to the Ace and a spade back. Plan the play.

[inquiry]

This is a classic type of problem, I am surprized no beginners/intermediates are taking a shot at it. I will provide a little something to think about.

1) If they get in before you get your 9th trick, they will be able to take enough spades to defeat you (they have at least 4♠ plus the suit they get in with)

2) You have 1♠, 2♥, 3♦ and 1♣ in top tricks (7 tricks)

3) You need 9 tricks (two more than your top tricks), and this is imps, so let's not worry about making MORE than 9.

4) No extra trick in clubs

5) If diamonds are dividing 3-2 or if someone has the singleton Jack, you have 2 extra diamond tricks

6) If you can find someone (east?) with a singleton diamond, you can hook the jack and still make 9 tricks

7) Hearts also provide some chances for two extra tricks (in fact, three extra tricks).

So the problem is how best (percentage wise) to combine your chances in hearts and diamonds, and keeping transportation issues in mind, as always?

[G_R__E_G]

I'll give it a try. ♦ offer the best chance, but if you try them first it is too late to try hearts as you will no longer be able to take the third heart trick with N's J after the Q drops doubleton and then get back to S to take your long ♥'s. So take your ♥AK first, if the Q doesn't fall then take the ♦A followed by small ♦ to the Q. If ♦'s break you're fine, if W has J 4th you can still finesse him on the way back.

[plaur]

If you start with the ♦Q you can pickup diamonds 5-0. If both follow then play ♦A, but now you cannot get back to hearts if you cash AK and the queen falls, so I think im with Greg's plan.

[civill]

I'm with GREG here.

[Limey_p]

My first thought was to try diamonds first, then fall back on hearts if necessary. This would mean this order of play:

♦A
♦Q
♦K
♥J for a finesse. Without any other late hand entry, you have to take first round finesse.

But Greg's line is good too - so which is better? We start using a priori probabilities.

My line needs ♥3-2 with the queen onside; half of 68% is 34%.

Greg's wins when the ♥Q is singleton or doubleton. Thats one fifth of 28% plus two fifths of 68%. Thats (er) 5.6 plus 27.2 which is 33%. That's close!

But my line is not that good - when diamonds are sour, East has them, so he has less room in his hand for hearts. So instead of half of 68% it'll be more like (adding up open spaces in each hand) 9/21 or three sevenths. That's only 28%, I think. So I say Greg has it.

BTW I've set out the numbers this way because it represents about the limit that I would be able to accomplish at the table without pencil and paper, and I'd probably not manage that with the flu, either. But my line isn't ridiculous, and if that's the worst I do in a session, I'll have done pretty well.

Andy