[KurtGodel]

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Playing duplicate last night, partner and I end up in 6♠, the bidding was slightly botched and if I'd remembered our convention a bit better we would have ended up in four.
The lead is K♥, opponents do not bid.
I won the first trick, won two clubs (north covered my jack), two diamonds and then I led Q♠ and lost the finesse, the heart continuation sets the contract.

The contract makes if you draw one round of trumps and then discard a heart on the last club. The question is, is that the best line of play with the hands concealed? What would you have done?

[KurtGodel]

If you're interested, the field is all in 4♠.
Most are +1, a couple are +2.
We came tied bottom, (someone was in 3NT-1).
Making that 6♠ would have been a top. Oh well...

[Phil]

Nice hand and welcome to the forums. This hand is much tougher than it looks because the ♣7 and 6 provide an interesting restricted choice position.

The field won't be in 6 with a balanced 12 opposite a balanced 14, so you shouldn't worry about overtricks. +980 will be fine.

You need the club finesse for starters. If its on, you will then need either the spade finesse to work, or to establish a fast heart pitch on the clubs. This can be done with a) clubs 3-3 or b) with 8x or 9x in the south hand. With b), South cannot have the long spade. These conditions present several lines, and I'll ignore the necessity of the club finesse:

A. As you did - club finesse, (return if covered) and finesse the spade. If it wins and spades are 2-1, you have a claim, and can even try three clubs for the overtrick. If North has ♠KT7, you still have a chance with 3-3 clubs. I am calculating this line as 45% for the non 3-0, plus 36% of the 3-0 with North, so 46.8% or so.

B. ♣J finesse, ♣T covered and won, and ♠A. If RHO drops a non-8/9, then try a 3rd round of clubs. If they split, you are home. I'll leave the 8/9 calculations aside. ♠K dropping is 12.5% 26%. Of the remaining 7/8 74%, 36% for the 3-3 split, so about another 31.5% about 27%, for a total of 44% 53%.

Can we do better when the 8/9 drops? There are adequate entries to pull this off - ♦ to the A, run ♣7, ♦ to K, ♣K ditching heart. The problem occurs because you also need the hand with the long club to hold the long spade. This *seems* better than 46.8, but I will leave this to others more qualified to finish.

[Cyberyeti]

I'd be half inclined to lead J♣ at trick 2, and if this goes off well (and particularly if N thinks declarer only has 4 spades), lead the Q♠ playing the ace if not covered and there's no hint of a twitch. If spades are 2-1, I'll play for clubs 3-3 as while there is a restricted choice situation, I need the third one not to be ruffed.

[perko90]

Phil's on to something with the chance of playing clubs for no losers is more than just a 3-3 split. Also, the chance of dropping the K is more than stated above. It happens 1 out of 3 times that spades break 2-1, which is (33%*78%) 26% of the time.

Nonetheless, I'll leave the mathematical heavy lifting for another time/person.

At the table, I would finesse the spade, knowing that even if the club finesse works, I'm a bit less than 50-50 for making.

[plaur]

Phil, on 2012-June-26, 09:29, said:

. ♠K dropping is 12.5%. Of the remaining 7/8 ...

♠K drop is 25%, 2/8 right ?
That would put line B a hair above 50%

[gnasher]

The chance of ♠K singleton is 26%. You can work this out without using odds tables. After you've dealt someone ♠K, the next spade has to go to the other hand, which is 13/(12 + 13). Then each hand has 12 vacant spaces, so it's evens where the remaining spade goes. Hence it's 13/50 = 26%.

[ArtK78]

plaur, on 2012-June-26, 12:08, said:

♠K drop is 25%, 2/8 right ?
That would put line B a hair above 50%

No. While there are 8 possible distributions of the three spades, they are not all equally likely. The chances of spades being 3-0 are 22% (11% each way).

So, spades are 2-1 78% of the time. There are six cases (2 for each singleton), and the singleton K is 2 of those cases. So 2/6 x 78% = 26%.

[Phil]

Yes sorry, 26%. I was thinking 2/8 of 50% instead of 2/6 of 78. Weird.

[nigel_k]

Someone named Kurt Godel should be able to do the mathematics himself.

[KurtGodel]

nigel_k, on 2012-June-26, 14:11, said:

Someone named Kurt Godel should be able to do the mathematics himself.

Godel is more famous for his work in metamathematics
I beat myself up quite a bit of time thinking that there must be a better line of play, it seems as though there was, but it's not a lot better.

It just seemed to me at the time that playing for a 3-3 club split wasn't the best line. I just know that that is 36% and a spade finesse is 50%, I forgot that I drop King singleton. Maybe I didn't do this because I was missing the ten of trumps (I know it doesn't change anything, but it had a psychological effect).