[lamford]

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Teams. IMPs converted to VPs. Lead J♣.

How would you play? This is based on a suit combination on bridgewinners, but this time the opponents know that South is off a key card.

If you lead a heart towards dummy, West plays the ten.

[alok c]

♥J & win or lose,finesse next time with ♥8.It wins against West KQ10x , K/Q 10x & KQ10.It loses against West 10x.

[Tramticket]

alok c, on 2016-December-05, 10:55, said:

♥J & win or lose,finesse next time with ♥8.It wins against West KQ10x , K/Q 10x & KQ10.It loses against West 10x.

Does west play the 10 with all of those? I'm not convinced.

But I still think that finessing twice has the edge.

[billw55]

alok c, on 2016-December-05, 10:55, said:

♥J & win or lose,finesse next time with ♥8.It wins against West KQ10x , K/Q 10x & KQ10.It loses against West 10x.

Tramticket, on 2016-December-05, 12:14, said:

Does west play the 10 with all of those? I'm not convinced.

The key does seem to lie in interpretation of the ten. Otherwise this is just a straight double hook position.

My first thought actually was to lead the 9 and run it if the 6 appears. Would we think anything different of T on the 9, versus on a low card?

[Winstonm]

The issue is the 10-spot, is it not? The holdings are limited to 10, 106, Q106, K106, KQ10, KQ106. Isn't this simply an extended restricted choice position? The only holdings that matter from a restricted choice basis are KQ10, K10, Q10, and 10.

If LHO had no choice, we should play the Jack.

The more difficult decision occurs IMO when the Jack loses to the K or Q, we win the return and play a second heart and LHO follows with the 6. Then what?

[nige1]

Lamford writes: Teams. IMPs converted to VPs. Lead J♣.
Teams. IMPs converted to VPs. Lead J♣.
How would you play? This is based on a suit combination on bridgewinners, but this time the opponents know that South is off a key card.
If you lead a heart towards dummy, West plays the ten."

From first principles:
If LHO knows that South's ♥s are 9 high, then it seems that ♥T is a compulsory false-card.
If LHO has ♥void or ♥T singleton, then you are doomed (at single-dummy).
If LHO has ♥HT doubleton, then you can't go wrong (2 cases).
A. If you rise with ♥A, you succeed when LHO has ♥HT6 or ♥T6 (3 more cases. So A succeeds in 5 cases).
B. If you finesse ♥J, then you succeed immediately when LHO has ♥KQT6 or ♥KQT (2 cases).
When ♥J loses to an honour, and, on the next round, you rise with the ♥A, then you succeed when LHO has ♥T6 (another case, so B succeeds in 5 cases).
C. When ♥J loses to an honour, and, on the next round, you finesse ♥9, then you succeed when LHO has ♥HT6 (another 2 cases. So C succeeds in 6 cases).
Hence, IMO, plan C is best.
KQT6 (B C) KQT (B C) KT6 (A C) QT6 (A C) KT (A B C) QT (A B C) T6 (A B) T (None).

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[Tramticket]

Ok, I don't get it. From LHO's point of view, this is only failing if RHO has both the KQ♥. He knows that RHO has the K and he assumes that RHO has the Q.

Nige1 states: "If LHO knows that South's ♥s are 9 high, then it seems that ♥T is a compulsory false-card."

But Nige1 also concludes the best strategy is: "When ♥J loses to an honour, and, on the next round, you finesse ♥9"

So it seems that the compulsory false card is not deflecting declarer at all. What am I missing?

[lamford]

I think this is a mixed strategy position for declarer and defender. West does not know whether declarer has the queen of hearts, but playing the ten from KTx can only cost the overtrick. With Tx, he needs to play the ten some of the time as well.

So, South and West should play in such a way that both sides achieve what is known as a Nash equilibrium. At a rough guess that is playing the ten half the time from Tx and KTx, and always playing low from KQx and KQTx. Declarer puts in the eight half the time West plays small, and the other half he puts in the jack. If West plays the ten, then half the time declarer plays the jack and half the ace. I think these "halves" are not quite right, and optimal game theory strategy might adjust for the likelihood of each distribution with 2-2 more likely than a specific 3-1.

Complicated!

[Cyberyeti]

I think K106 is different from Q106 in LHO's hand.

Q106, you know partner has the K.

K106 you'd feel sick if partner's card was small/9 rather than the Q if you played the 10 and declarer made an easy overtrick.

So not sure about the compulsory false card