[bluecalm]

Bidding :
4S - pass - pass - pass

Dummy :

63 J7 AT873 KJT4

Hand :

AQJT9742 Q95 - 85

We receive fortunate lead of K of diamonds. What's the best plan ?
Some possibilities :
a)throw club, play small heart to the queen;
this wins if defenders are unable to play trumps two times without conceding heart trick we also need heart finesse; it fails every time RHO has 2 trumps and one top heart
b)throw heart, finesse spades;
this wins if we finesse works and we guess clubs. Clubs are guessable 50% of the time; 25% we win automatically, 25% lose automatically; let's say our guessing is a bit better than 50% but we lose with 3-0 spades break. The line wins about 25% of the time (depending on how well we guess)
c)throw club, finesse spade play heart to the jack; This wins if if finesse works and AK of hearts is on the same hand or in some miracle case when we will be able to ruff heart anyway due to defenders not being able to play 2nd spade;
d)throw club and finesse Th

In actual hand I threw the heart and finesse spades. Clubs were not guessable. Contract was played on two other tables; one declarer threw club and played heart to the nine. The other one threw heart and played for spade finesse (he won but oppontents either misclicked or lost on purpose).

Any ideas about the best line ? All comments are appreciated

[Fluffy]

if you trhow a club and play a heart to the 9 you are winning anytime ♥10 is onside and ♠ is onside (not third) since sooner or later you will be able to take the trump finese, but this needs also hearts not to break so badly

If you throw a heart and finese spades you are winning more or less the same (2 fineses), but you can guess clubs latter, and you don't need hearts breaking, so seems best.

However in practice if you play a heart to the 9, RHO will raise with ♥AK for sure. This evens the thing a bit more.

[Simplicity]

Fluffy, on Dec 3 2009, 07:13 PM, said:

However in practice if you play a heart to the 9, RHO will raise with ♥AK for sure. This evens the thing a bit more.

Add to that we can be fairly sure LHO isnt looking at ♥AK himself, i think playing to the 9 is infact the better theoretical line.

♥T onside or ♥AK onside looks about 66%, with a 5-3 break as well thats around 55%. Getting the clubs right is basically 50% without any info. However if you would expect yourself to get the guess correct when the club honours are split 60% of the time or more chucking the heart would be the best practical line.

[suokko]

Simplicity, on Dec 4 2009, 04:32 PM, said:

Fluffy, on Dec 3 2009, 07:13 PM, said:

However in practice if you play a heart to the 9, RHO will raise with ♥AK for sure. This evens the thing a bit more.

Add to that we can be fairly sure LHO isnt looking at ♥AK himself, i think playing to the 9 is infact the better theoretical line.

♥T onside or ♥AK onside looks about 66%, with a 5-3 break as well thats around 55%. Getting the clubs right is basically 50% without any info. However if you would expect yourself to get the guess correct when the club honours are split 60% of the time or more chucking the heart would be the best practical line.

Multiply all the odds by 0.78 when you lose 3-0 ♠ onside. This is quite large lose position here for guessing the ♥ when you add that ♥ has to be 5-3 (47) or 4-4(33) you end up with less than 50% for ♥ play (0.78*0.8*0.66=0.41).

[dellache]

I agree with Suokko's argument but not with the conclusion. There's yet another factor in favor of the Heart finesse : the case for the club finesse includes the cases where Clubs are always guessable : ♣AQx+ by West. OK but then those cases exclude hands like x Axxx KQ(J)x AQxx where West may have found a T/O double . This gets even more clear when West has got a Spade void.

All in all, in practice I would definitely finesse the ♥10.

[suokko]

dellache, on Dec 4 2009, 05:03 PM, said:

I agree with Suokko's argument but not with the conclusion. There's yet another factor in favor of the Heart finesse : the case for the club finesse includes the cases where Clubs are always guessable : ♣AQx+ by West. OK but then those cases exclude hands like x Axxx KQ(J)x AQxx where West may have found a T/O double . This gets even more clear when West has got a Spade void.

All in all, in practice I would definitely finesse the ♥10.

I agree

I also didn't mention that there is meaningful chance for ♣ to break 6-1 (- xxx KQxx Axxxxx) causing them to be guessable but still not making contract. Likewise there is distributions where finessing ♥ T would win but they are impossible on biding.

But important extra chance in playing with ♥ is that you maybe able to get the ruff in some layouts when defense can't lead the 2nd trump to stop you from ruffing. (x AKT KQxxx Axxx; ok. unlikely t still extra chance)

So good luck solving the odds and finding which line realy is the better. I think they are close.

[gnasher]

If you throw a club on the diamond and lead a heart up, and RHO has ♥AK and ♠K, he should clearly play low, and I don't think it's particularly hard. What hand can you have where it's right to play high?

[dellache]

AJT9xxxx Qxx --- xx.
The contract is unmakeable unless you play against an imaginative East who plays small when you lead a small Heart from dummy at trick 2.

(It doesn't prove that East should not duck the Heart anyway. The situation is not that clear, and the difficulty for East is to duck in tempo, when South specifically has Q9x).

[Fluffy]

Even if RHO is good enough to duck ♥AK you can add that he can have ♠K stiff and not the ♣A and you still ruff the heart in dummy

[dellache]

Fluffy, on Dec 4 2009, 07:04 PM, said:

Even if RHO is good enough to duck ♥AK you can add that he can have ♠K stiff and not the ♣A and you still ruff the heart in dummy

You mean : "... the stiff ♠K *AND* the ♣Ace" I guess...
That's true and it's very rare because now West needs to also have the ♣Q.