What was the best line?

[Fluffy]

[hv=d=e&n=saqjxxhkq10xxdjcxx&s=s109xxxhajxdxxxcax]133|200|Scoring: MP

W - N - E - S

--------1♣-1♠

ps-2♥-3♦-ps

5♦-5♠-X -ps

ps-ps[/hv]

 

The lead is a diamond to the ♦Q, and ♣K comes back.....

[awm]

Seems like there are two lines. I'd take the one in bold.

 

(1) Take the spade finesse. You make six if it's on, go down if it's off.

(2) Play the spade ace. You make six if the king is singleton, and also make if spades are 2-1 with the doubleton hand having three-plus hearts, or spades are 3-0 with the three hand having four-plus hearts.

 

In isolation, line (1) is 50% whereas line (2) is roughly 1/4 (king singleton) + 1/4 (2-1 break with the king doubleton plus longer hearts with the spade king) + something very small to account for spades 3-0 with four hearts with the long spades. So line (2) very slightly better.

 

But the bidding implies that RHO has a huge number of minor suit cards. It's quite likely he's 5-6 in the minors. In this case, if RHO has Kx spades both lines fail and if RHO has xx spades both lines succeed. If RHO is 1-1 in the majors, then line (2) always wins whereas line (1) wins 2/3 of the time. If RHO is 0-2 in the majors, then line (1) always wins and line (2) always fails.

 

The odds (assuming RHO has exactly 11 minor suit cards):

 

2♠+0♥: 3/28

1♠+1♥: 15/28

0♠+2♥: 10/28

 

So line (1) succeeds with probability 1/28 + 10/28 + 10/28 = 21/28 = 3/4.

Line (2) succeeds with probability 1/28 + 15/28 = 16/28 = 4/7.

 

If RHO has twelve minor suit cards, then line (1) is 7/8 and line (2) is guaranteed to succeed. However, even if RHO is 50% to have twelve minor suit cards (otherwise having eleven):

 

Line (1): 3/8 + 7/16 = 13/16

Line (2): 4/14 + 1/2 = 11/14

 

So line (1) is better, on the auction.

[kfay]

My initial reaction is to play a spade to the ace and play on hearts if the king doesn't fall. but this seems unlikely to work since i'll believe that if RHO is doubling with the king of spades that he has Kx which gives him at absolute most xx of hearts. so i'd take the spade finesse T3.

[Fluffy]

so Basically Adam you say that given the minor 2 suiter, a 3-0 distribution is twice as likelly as bare king offside (10/28 vs 5/28). I didn't come to anything 28 fractional, just counted the sole cases.

[awm]

so Basically Adam you say that given the minor 2 suiter, a 3-0 distribution is twice as likelly as bare king offside (10/28 vs 5/28). I didn't come to anything 28 fractional, just counted the sole cases.

Yes.

 

There are five hearts out, so ten possible pairs of hearts. There are five possible pairings of singleton ♠K with one heart.

[Fluffy]

I am still a bit confused hehe.

 

there are 9 missing major cards

 

chaces of giving spade king to east = 2/9

chances of giving him 2 hearts = 20/81

 

Ok, now I see, spade K only works combined with another heart, so only 2/9*5/8 works wich is 10/72, more or less the same.

[awm]

There are eight missing major suit cards, five hearts and three spades.

 

The odds RHO has the spade king and a heart are (1/8)(5/7) for the "first card" to be spade king and the "second card" to be a heart, doubled because the cards could be dealt in the opposide order. This gives 10/56 = 5/28.

 

The odds of two hearts are (5/8)(4/7) = 20/56 = 10/28.

 

Alternately, there are 8 choose 2 = 8*7/2 = 28 possibilities, of which 5 are the spade king and a heart versus 5 choose 2 = 5*4/2 = 10 are two hearts.

[ArtK78]

It seems to me that playing a spade to the Ace is the right line on this auction.

 

As was previously stated, RHO has a large number of minor suit cards, meaning that LHO has more major suit cards. So, even if the ♠K does not fall under the Ace, the odds that LHO has to follow to 3 rounds of hearts are very good.

 

Of course, if RHO has Kx of spades and less than 3 hearts, there is nothing that you can do.

 

If LHO has all 3 spades, you will be left with hoping to find him with 4 hearts, meaning that RHO has doubled 5♠ on 0-1-5-7 distribution. However, I find it hard to believe that RHO would double 5♠ on this auction with a spade void.

[keylime]

I wrestled with this trying to determine if playing the AS off was the correct line, but I don't believe it is.

 

The auction said a lot about what the partner of opener has. They can't have four hearts unless weak; they did not raise clubs, and when given the choice they opted back into clubs instead of raising diamonds. I'd take LHO to be on 3 clubs once I saw the dummy, and on 3-4 diamonds. There's a lot of room leftover then for the spade king.

 

I would infer that RHO was doubling on a high club honor and AK of diamonds, and got a shock when they saw the dummy. It would make zero sense to double on something like high club honor, AD, and the KS because they don't know where the spade Ace is. Furthermore, RHO has to have 11 minor cards for their auction - with ten and equal length and strength it would have started with a diamond bid. So, I'd picture something like x-x-5-6.

 

Thusly, a lot of reason to go for the spade finesse. We already have some inferential count and me thinks LHO is trying to in the bidding muddy the waters into a losing play.

 

(edit: misread the auction; thought clubs and not diamonds were trumps. Sentiment tho remains unchanged).

[ArtK78]

The auction said a lot about what the partner of opener has. They can't have four hearts unless weak; they did not raise clubs, and when given the choice they opted back into clubs instead of raising diamonds. I'd take LHO to be on 3 clubs once I saw the dummy, and on 3-4 diamonds. There's a lot of room leftover then for the spade king.

No, opener's partner opted to support diamonds, not clubs. It appears that West has many more diamonds than clubs - probably 5-2. This leaves 6 major suit cards. So, as long as East did not double with a spade void, West has at least 4 hearts.

 

Quite frankly, even if East did double with a spade void, West could be 3-4-4-2 on this auction (East would be 0-1-5-7 - certainly consistent with the auction). In that case, a spade to the Ace will not be fatal.

 

This is by no means a sure thing. West could be 3-3-5-2 (and East 0-2-4-7). I still find the double with a spade void to be strange, but it is possible.

 

By the way, given that NS has 22 HCP and East opened and bid freely into a live auction opposite a passing partner, it is pretty clear that West is very weak. So there is a good chance that West has 4 hearts and not enough to make a negative double.

 

By the way, I know that this is a play problem, and since no one has mentioned it so far, I might as well be the first. I find North's 2♥ call to be absolutely terrible at matchpoints. Even if it is forcing, a 4♠ call stands out. Are the chances for slam really that good? As it was, the 2♥ call let East in to bid 3♦ at a relatively low level and pushed the auction to the 5 level. That is not to say that East might not have bid anyway - especially if it turns out that he is 5-7 in the minors. But at least you would learn something about his hand if he did bid over 4♠.

[awm]

If we add the possibility that RHO could be 4-6 in the minors, then:

 

Line (1) wins if RHO does not have the spade king, which is 5/8.

 

Line (2) wins if anyone has ♠K singleton (15 positions of 56) or if LHO has ♠K doubleton (20 positions of 56). If RHO has ♠K doubleton he also has singleton heart and can set you, and if LHO has ♠K third he has only two hearts and can set. The total of 35/56 is exactly the same.

 

So basically:

 

RHO 4-6: the two lines are equal

RHO 5-6: finesse is substantially better

RHO 5-7: play for drop is slightly better

RHO 6-7: both lines always work, and opponents cold for 6m anyway

 

So unless you think that 5-7 is somehow much more likely than 5-6 (which I don't really see, since the bidding makes sense either way and a priori 5-7 is much rarer) you should stick with the finesse.

[Fluffy]

also this is MP, the overtrick could be important

[ArtK78]

The contract is 5♠x, so I don't think the overtrick is a consideration.

 

Even if RHO is 5-6, which is possible, the question then becomes is RHO 0-2-5-6 or 1-1-5-6. 2-0-5-6 is not important, since you cannot make 5♠x if that is the case.

 

I go back to my original thought that I find it hard to believe that RHO would double 5♠ with a spade void. Clearly, if RHO is 0-2-5-6, then you have to finesse against LHO's ♠K to make. If RHO is 1-1-5-6, then either line works as long as the singleton spade is not the King.

 

Given all of the possible distributions that are consistent with the auction (LHO has at least 4 diamonds, RHO has at least 4 diamonds, more clubs than diamonds and a strong hand) I think that the chances of RHO having a singleton spade (as opposed to a void) and LHO having at least 3 hearts, or LHO having all three spades and at least 4 hearts is quite good. Good enough to warrant guarding against RHO having a singleton ♠K.

 

But, as I said before, there are certainly no guarantees.

[ArtK78]

So, what was the winning line? We could discuss the pros and cons endlessly. I have played a spade to the Ace. What does RHO play? And, if RHO shows out, does LHO follow to 4 rounds of hearts?

[Fluffy]

sorry, LHO was 3343. RHO 0256.

[ArtK78]

In that case, I take the spade finesse. Absolutely clear cut.

 

:)

[benlessard]

If east has 11 m cards.

 

1s, 1H Not finessing work 100% finesse fail when ks is stiff

 

2S, 0H always failed

 

0S 2H finesse= success, playing A♠ =failure

 

 

If east has 10 m cards.

 

 

3S 0H always failed

 

2s 1H always failed

 

1S 2H always succed

 

0S 3H finesse worked playing A first round failed

 

 

If east has 12 m cards

 

1S, 0H both line succed unless stiff king

 

1H, 0S both line succeed

 

 

 

I thikn its more likely East made a ligthner X or that hes got stiff Ks then made a X with a S void, so i play the A♠ but i don't expect to succed.

 

 

Knowing the opposition will help on this deal.

[ceeb]

Adam's elegant analysis shows the gain for the finesse occurs when RHO is 02 in the majors. But that gives LHO Kxx,xxx,10xxx,Jxx at most. I do not understand bidding 5♦ with that (notwithstanding Fluffy's comment that it was the case). Even 4♦ seems strange.

 

No, LHO must have at least 5 diamonds, and I would think a singleton as well. With ♦AKQ and ♣KQJ, RHO doesn't need to be 56; even 45 is possible. The closest I can find to a believable layout is

 

[hv=d=e&n=saqjxxhkq10xxdjcxx&w=skxxhxdxxxxxcxxxx&e=shxxxxdakqxckqjxx&s=s109xxxhajxdxxxcax]399|300|Scoring: MP[/hv]

 

Anyway, I'm a believer in the spade finesse.

 

Charles Brenner

[Fluffy]

I was west and I had 3343, actually I bid 5♣, but it made the hand a no brainer since 6-5 must be there, so switched to 5♦ for the problem.