[Stephen Tu]

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matchpoints
LHO leads a low diamond, appears to be from 3 or 4 (or stiff).

What's the best line?

[johnu]

I would make further inquiries about the opening lead. What do they lead from 3 small, 4 small? What spot cards get played at trick 1.

Spoiler

Taking the spade finesse requires 2-2 spades with finesse working, successful 1/2 x 40.7% ~= 20%. If it loses, you lose lose 2 clubs, a heart, and a spade. Pretty bad odds. There are some chances of a defensive error if the defense doesn't cash 2 clubs.

If I'm confident diamonds are 4-3, or at worst 5-2,

If diamonds are 4-3 (~62.2%), or 5-2 is (~30.5%), you can cash 2nd round of diamonds, ♠A. If spade king is singleton, 1/4 x 49.7% ~= 12.5%, you can draw trump, cross to South with a trump, and cash 2 more diamonds pitching 2 clubs, making 5. Success is about 11 1/2%

You also make if spades are 2-2 and the hand with ♠K has 3 diamonds (~6%), or spades are 3-1 and the hand with 3 spades has 4 or 5 diamonds (~17%, not adjusted for spade split)).

It looks like the combination play of ♠A and 4 rounds of diamonds is the best percentage play.

[Stephen Tu]

4th best leads, so the length is ambiguous.

[heart76]

You have 4 losers if spades don't behave, so I don't think there is much else than: win with the K and finesse the SK.
Suppose it doesn't work. You're home if opps don't attack clubs.
Unless you prefer to cash KJ of D and the SA and play the remaining D, hoping that D are 4-3 with Kx of S beside 3 D.
Or do I miss something?

[KingCovert]

This really requires more information about the opponents leads. This is a principle of restricted choice situation. Why did they lead a diamond? What is the situation in the round suits for a diamond lead to be right? My partner and I consider the 10 to be an honour, and will lead small from a suit headed by the 10. Is this their agreement? This really matters, because, this really screams of a singleton lead. If it's a singleton lead, what honours can West hold here that wouldn't preclude the singleton lead? Surely not AK of clubs for example.

After considering this, do we really think it's alright to take the spade finesse? Maybe we can get opponents to crash their club honours? A♠ and out a spade could be right! If the spade finesse loses, the hand that might have diamond shortness is on lead again, and can't give themselves the ruff, but they can cross in either round suit potentially for a ruff. So, I'm tempted to play East for the singleton K♠. This would be a very different situation if I had any intermediates in spades at all.... but... I don't.

And then... sometimes... Spades break 2-2, and the diamond lead was from TXXX.

I'm probably not taking the finesse, and playing small to the A♠. It gives me some hope of shockingly poor defense in the event of a 4-0 spade break.

[rmnka447]

I think you have to play for some good breaks.

Spoiler

The master hand is the dummy.

So, I'm winning ♦ K, and finessing ♠ Q hoping for ♠ Kx onside. Defense should cover ♠ Q, so that you have to go back to dummy to remove remaining trump with the ♠ J. Then cash ♦ J, and follow with low spot ♠ from dummy overtaken by higher spot in declarer's hand. Cash remaining high ♦s
pitching ♣ from dummy.

[FelicityR]

Stephen Tu, on 2019-October-20, 01:47, said:

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matchpoints
LHO leads a low diamond, appears to be from 3 or 4 (or stiff).

What's the best line?

It's an interesting problem. +1

The 'greed' (for want of a better word) of wanting to make 11 tricks at MPs as opposed to actually making the contract at IMPs (and MPs too) may get in the way here.

Given that many still play Acol with a weak NT in the UK may mean that the contract could have played by North if this hand was played on this side of the Atlantic, and different bidding and a different lead would have occurred. That's a consideration too.

I used to play club bridge with a lovely man (a long-time deceased sadly) who's philosophy was to play to always make the contract first, at IMPs and MPs, and worry about overtricks after.

I guess he might have looked at this problem philosophically that (perhaps) on another lead there were only 9 or 10 tricks available (depending on your line of play) so it was paramount to make the contract at whatever cost. Just because you have been presented with a 'fortunate' lead of a ♦ that gives you a chance of making 11 shouldn't mean that you should do so, even though at MPs it could give you a top or shared top.

So I agree with johnu's line of play.

[nige1]

Stephen Tu ' matchpoints. LHO leads a low diamond, appears to be from 3 or 4 (or stiff)
++++++++++++++++++++++++++++++++
3 possible lines...
1. JohnU's line: ♦KJ, ♠A, ♦Q, ♦A
2. Rmnka447's line: ♦K, run ♠Q.
3. Cash ♦KJ. Advance ♠Q to ♠A.

Line 1 wins when
- ♠K is singleton (declarer makes an overtrick).
- Defender has ♠Kx doubleton and 3 ♦s.
- Defender with ♠Kxx tripleton has 4+ ♦s.

Line 2 wins when
- RHO has doubleton ♠Kx.

Line 3 wins when
- RHO, with doubleton ♠Kx, covers (as he should).
- LHO has doubleton ♠Kx and 3 ♦s.
- LHO has ♠Kxx and 4+ ♦s.

If RHO has ♠Kx doubleton (3 cases), then Rmnka447's line 2 makes an overtrick, so might be best at pairs.

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[Stephen Tu]

"Wins" shouldn't be calculated in terms of "making the contract" at pairs. Rather, the candidate lines should be calculated relative to each other in terms of taking same or more or fewer tricks over all the possible combinations. E.g. line 1 beats line 2 on combos (set A), line 2 beats line 1 on combos (set B), set A has more combos than set B therefore line 1 > line 2.

There is also the question as to if taking the finesse line, if RHO covers, whether one plays for spades 2-2, or just plays off the diamonds. This gives up the overtrick in the Kx onside case, but might be necessary to make if RHO had stiff K or covered holding K??. One also has to calculate how often RHO should be covering the K (perhaps supposed to cover with KT? but not with K98, partner could have stiff A?)

I believe johnu's calculation is correct, unless someone can spot an error.