[bftboy]

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P (1♣) 1♥ (1♠)
P (2♠) P, (4♠) all pass
at MP, P leads ♥ 8. You win the A as declarer plays the 5. What now and why?

[JLOGIC]

I assume that 1S showed 5+ spades?

You didn't ask, but I would not duck at trick 1 (often an option in this type of problem to avoid giving away a third heart trick) since the additional pitch will never help them. Even if they're 5224, pitching 2 clubs won't help since all their clubs are high. Better to win and either play a heart, or play the ace of diamonds.

Assume there are the cases:

-Partner has the SA
-Partner has the SK
-Partner has the DK
-Partner has no relevant card

I don't think he can have 2 of these.

I would guess that partner having the DK is the 2nd most likely, and partner having no relevant card is the most likely, followed by the spade honors.

When partner has the DK, playing the DA;
-Wins when he has a doubleton heart
-Breaks even when he has a stiff heart (note, partner will discourage, we will continue the HT, partner will underlead his DK).

When partner has no relevant card, playing the DA;

-Wins on some shapes for declarer that have a doubleton heart (5224, 6223, 6232 with CQ), breaks even otherwise ([/b]notably, if declarer is 5233 with everything, winning and playing a heart breaks even regardless of the CQ[/b]).
-Loses when partner has a stiff heart

When partner has the SK, playing the DA;
-Breaks even unless partner has a stiff heart and declarer later misguesses spades (should be a low percentage)

When partner has the SA, playing the DA;
-Breaks even when partner has a doubleton heart
-Loses when partner has a stiff heart

So basically the DA wins when partner has the DK and 2 hearts, and wins sometimes when partner has no card and 2 hearts (but not on the most likely shape, 5233).

A heart back wins when partner has no card and a stiff heart, or the SA and a stiff heart, and gives a guess when he has the SK and a stiff heart.

Obviously partner having the SA is less likely than the DK or no card.

Are there any clues from the bidding? Declarer MIGHT with AKxxx Kxx Kxx Qx have tried to get to 3N via 3H, but that seems like a minor clue.

Another clue is with 3262 or 2263 and the DK, would partner have opened a weak 2? Do we play them, is that his style? That is another minor clue. Lets say these cancel each other out.

What about the play? Well, declarer played the H5. Even if he is a perfect declarer, this is restricted choice. Excluding bidding clues, he is at least 2 to 1 to have Kx than Kxx. And 95 % of people go through their life always playing the H3. So if declarer is bad I wouldn't have even gone through all of this (this is a big thing to remember, in fact I take note every time someone does NOT play the lowest spot and try to remember them). But even with declarer being good, the DA seems like the winner here, even though more cases exist where playing a heart back is necessary, I don't think those cases are 2 times as likely.

[nige1]

bftboy, on 2011-January-06, 11:06, said:

P (1♣) 1♥ (1♠)
P (2♠) P, (4♠)
all pass at MP,
P leads ♥ 8. You win the A as declarer plays the 5. What now and why?

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Awed though I am by JLOGIC, I would always win ♥A and return ♥T because

• it makes the fewest assumptions about partner's holdings/expertise,
• if it works, I can compliment partner on his lead,
• I hope to have company, so that If declarer wraps up an extra overtrick or two, I don't expect a bottom.

[JLOGIC]

Winning the heart and playing a heart because you think partner is not good enough to not blow a trick when he has the DK and a stiff heart is certainly valid, it changes the odds of one play working vs another in a major way.

But I don't understand making fewer assumptions about his holdings, isn't that what this hand and more generally bridge is about, making educated assumptions about everyone's holdings and playing accordingly to maximize your score?

I also don't understand wanting to compliment partner on his lead, is that a real bridge reason or a joke? I guess I am making another implicit assumption that partner will lead from 2 small and a stiff heart equally as we overcalled the suit!

[nige1]

JLOGIC, on 2011-January-06, 14:17, said:

Winning the heart and playing a heart because you think partner is not good enough to not blow a trick when he has the DK and a stiff heart is certainly valid, it changes the odds of one play working vs another in a major way.

Good. With JLOGIC, one out of three ain't bad

JLOGIC, on 2011-January-06, 14:17, said:

But I don't understand making fewer assumptions about his holdings, isn't that what this hand and more generally bridge is about, making educated assumptions about everyone's holdings and playing accordingly to maximize your score?

The least material assumption -- and JLOGIC doesn't expect much in that department. If partner has a singleton heart, a heart-return earns a good score no matter what high cards he has. If partner doesn't have a singleton heart, we might still get our ♦A later.

JLOGIC, on 2011-January-06, 14:17, said:

I also don't understand wanting to compliment partner on his lead, is that a real bridge reason or a joke? I guess I am making another implicit assumption that partner will lead from 2 small and a stiff heart equally as we overcalled the suit!

A real bridge reason not a joke: You should be on the look-out for anything that partner does right, so that you have an excuse to compliment him. Here, if partner has led a singleton ♥, then his lead defeats a contract that might make on any other lead.

If partner's simple defence would succeed but your sophisticated plan fails then partner may be hard to persuade that your alternative is the better bet. Anyway, you want to encourage partner to lead your suit.

Incidentally, if partner has led a doubleton and declarer has say, ♠ KJ732 ♥ K5 ♦ K6 ♣ QJT2,
then you will still be able to compliment partner on his lead as the only way to set the contract, provided that you that return his lead

[Fluffy]

I love the way JLOGIC wrote 250 words to come to the conclusion that playing a heart is better when partner has singleton heart and bad when he doesn't (just joking, I recall doing lenghty analisys for more (and real) obvious conclusions in the past)

[awm]

I'd return a heart.

Playing a diamond will usually be better if partner has the diamond king (there is a position where declarer has ♠AKJxx ♥Kx ♦xxxx ♣Jx where it actually doesn't matter). I don't think the scenario where the ♦A goes away when declarer has the king is really that likely (for that to happen, declarer needs to be 5224 or 6223 with a strong spade suit, both red kings, and in the latter case also the club queen or JT -- those hands might actually make slam tries over 2♠).

It basically comes down to the relative odds of partner having singleton heart versus the diamond king. There are three possible heart holdings partner could have (singleton 8, or either of two doubleton 8s). Restricted choice applies here (i.e. if declarer had Kxx he could play either small card), which leaves the odds that partner has singleton heart a little less than 1/3. Partner could have any one of ♠K, ♠A, ♦K but could also easily have none of the above. It's this last possibility which I believe will push the odds that partner has diamond king down fairly substantially below 1/3.