[sieong]

aj64

---

*♦K - ♦5 - ♦A - ♦6
? - ? - *♣8 - ?

Do you play E for the ♣K or not?

Spoiler

Raw odds favor finesse, since the odds of 3 discards with the spade suit is only about 27%. Does it matter that E did not double any of the artificial club bids? How automatic is the club shift given that E does not see the CJ, and he knows you know the odds of bringing in the spade suit?

[c_corgi]

East knows the whole hand apart from the Jack of clubs, so if he is confident that you will analyse that his club switch will not be from the King (unless the spades were coming in), he will expect you to go up with the ace of clubs whether or not you hold the Jack. That would put him in a position to switch to clubs from the king, assuming that with Axxx you would rely on the legitimate chance of the spades coming in rather than the "gift" of the club finesse. In reality I doubt East would risk a club switch from the King when the spades weren't coming in, so I go up with the ace.

[jallerton]

Who is East?

[sieong]

Yadlin Doron

[jallerton]

This is an interesting situation, unusual in the sense that (assuming RHO trusts our bidding) he is close to double dummy (apart from knowing the location of the jack of clubs). He knows that (if we hold the jack of clubs) we would play to combine our chances in the black suits on any other defence.

There are four possibles scenarios.

A The club finesse works but no-one holds ♠Qxx
B The club finesse works and someone holds ♠Qxx
C The club finesse does not work and non-one holds ♠Qxx
D The club finesse does not work but someone does hold ♠Qxx

In doesn't matter what you do in case B (can't go wrong) or case C (can't get it right), so we are comparing case A with case D

A priori, I make the chance of case A about 36% and the chance of case D about 14%.

In case D, an alert East player ahould always find this defence.
So the crucial question is: in case A, with what probability will East switch to a club?

I disagree with c_corgi's assessment of East never switch to a club from this holding, because that strategy would gift you the contract when you do hold ♣J. It will depend on East's own number of clubs, but on average from his point of view you'll hold ♣J about half the time.

Let's say that he uses this basis for his strategy and switches to a club about half the time he hold the K. Now when he has switched to a club, I'm comparing:

Case A 50% of 36% = 18%; with
Case D: 100% of 14% = 14%.

So I finesse.

[sieong]

Thanks for your reply and analysis.

So here is where the game theoretic aspects got me confused. I followed a very similar line of reasoning at the table, andI drew the conclusion that the percentage play is to hook the club (I was assuming that East would return a club most of the time, like 80%, since the position of breaking up combined chances seems standard). But then if East knows that I know the percentages, and that he believes I will follow the percentage play, then would he not lose the cases when spades are not coming in and his partner has the CJ?

Or perhaps I am over-thinking this? I think Kit Woolsey once wrote something about follow only the percentage play and ignore the game-theoretic aspects (or may be I am mis-attributing something wrote by someone else to him). Is that a universal principle?

[c_corgi]

jallerton, on 2013-October-25, 15:25, said:

I disagree with c_corgi's assessment of East never switch to a club from this holding, because that strategy would gift you the contract when you do hold ♣J. It will depend on East's own number of clubs, but on average from his point of view you'll hold ♣J about half the time.

Let's say that he uses this basis for his strategy and switches to a club about half the time he hold the K. Now when he has switched to a club, I'm comparing:

Case A 50% of 36% = 18%; with
Case D: 100% of 14% = 14%.
...

"Never" is going a bit far, but 50% of the time seems a lot. It seems to me quite a leap of faith [from East] to expect the result of South's number crunching to protect you from the horrible occasion when you have the K♣, you do switch from it and partner had the J♣ and the Spades were not coming in.

When declarer does not have the J♣, (from East's POV, just as likely as the true layout, and once he has switched to a club, the Jack) he will see:

Case A: East's club switch was from the King and no-one holds ♠Qxx
Case D: East's club switch was not from the King and a defender holds ♠Qxx

Case A = East holds K♣ x He doesn't have J♣ x He switches to a Club x Spades not coming in
= 50% x 50% x 50% x 72%
= 9%
Case D = 14%


So when you add in the times when Declarer doesn't have the Jack you get:

Play East for KC: (18%+9%)/2 = 13.5%
Play for Spades: (14%+14%)/2= 14%

Which, admittedly is rather closer than I estimated before my first post. In fact I suspect I have demonstrated that in this case the defender is still conveying the impression that playing on Spades is an option, rather than it being right to do so. That is not what I thought I was doing when I began this post! In fact it looks like it is right to finesse in clubs when you do have the Jack and play on Spades when you don't.

sieong, on 2013-October-26, 18:12, said:

...
So here is where the game theoretic aspects got me confused. I followed a very similar line of reasoning at the table, and I drew the conclusion that the percentage play is to hook the club (I was assuming that East would return a club most of the time, like 80%, since the position of breaking up combined chances seems standard). But then if East knows that I know the percentages, and that he believes I will follow the percentage play, then would he not lose the cases when spades are not coming in and his partner has the CJ?
...

Confusing is right: the defender has to guess whether declarer thinks like jallerton, c_corgi, or like neither. Then declarer has to guess what the defender concluded! In any case, all East has to do is adjust his frequency of switching to a Club from the King away from 50% (or 80%) and suddenly the analysis gives a different answer.