[han]

KQ98x
K86
9xx
KJ

AJ
QJ7x
A10x
108xx

3NT at IMPS. North has opened 1S in first seat, his shape and strength are known. South has only relayed.

LHO led the diamond jack, then the king, then the queen which I won with the ace. Not wanting to commit myself I played a heart to the king and ace. After some solid thought RHO returned a heart to my queen, the 10 and the 8. On the ace of spades both opponents played low (udca) and on the jack of spades LHO played small. How should I continue?

The opponents are a regular pair and better than I am, but not world class.

[gnasher]

Did RHO follow to the third diamond?

What do they normally lead from KQJx and KQJ ?

[bluecalm]

If RHO had 4th diamond then they could already defeat that game and they would as they could see that either partner has A♣ or A♠ so playing a club is safe and necessary.
So LHO has 4 diamonds almost surely without A♣ as it's hard to imagine they would let you make the contract in such case.
Sooo... assuming opponents are good I will work on hypothesis that they couldn't defeat the contract which leaves me with 2 choices:
a)finesse Q♣
b)overtake spades and try to take 5spades and 3 hearts.

a) looks like bigger chance so I play for it.

[gnasher]

With Bluecalm's assumptions (which I agree with): LHO has four diamonds and 2-3 small hearts; RHO has three diamonds, 2-3 small hearts, and two aces. That gives a vacant space ratio of 6:6 or 7:5.

Using Pavlicek's cheating device, the odds after we won the second heart were:

If it's 6:6: 3-3 is 43.3%, 4=10x is 8.1%, total for the drop = 51.4%; total for the finesse = 50%
If it's 7:5: 3-3 is 37.9%, 4=10x is 12.6%, total for the drop = 50.5%; total for the finesse = 58.3%

So I agree with the club finesse.

[cherdano]

 bluecalm, on 2012-January-24, 11:21, said:

If RHO had 4th diamond then they could already defeat that game and they would as they could see that either partner has A♣ or A♠ so playing a club is safe and necessary.
So LHO has 4 diamonds almost surely without A♣ as it's hard to imagine they would let you make the contract in such case.
Sooo... assuming opponents are good I will work on hypothesis that they couldn't defeat the contract which leaves me with 2 choices:
a)finesse Q♣
b)overtake spades and try to take 5spades and 3 hearts.

a) looks like bigger chance so I play for it.

But a) is also playing for a misdefense. If someone has ♠Txxx, RHO could have defeated the contract by playing a club when in with the ♥A.
Since RHO is better than Han he would obviously find that defense.

In fact, since RHO only needs to find this defense 20% of the time, I think it's enough to swing the balance in favor of playing for the drop.

[FrancesHinden]

I think hearts are 2-4. With South's hand unknown, LHO is unlikely to play the 10 of hearts unless forced to (why couldn't south have QJ9x and be wondering how to play the suit for 3 tricks? His shape and high card location is unknown). That means he either has 109x or 10x and the latter is much more likely.

I assume that makes the club finesse better odds?

[gnasher]

 FrancesHinden, on 2012-January-25, 14:25, said:

I think hearts are 2-4. With South's hand unknown, LHO is unlikely to play the 10 of hearts unless forced to (why couldn't south have QJ9x and be wondering how to play the suit for 3 tricks? His shape and high card location is unknown). That means he either has 109x or 10x and the latter is much more likely.

Shouldn't we weight it, half of hearts 3-3 and all of hearts 2-4?

Quote

I assume that makes the club finesse better odds?

Probably not. Cherdano's point seems more relevant than my analysis.

[han]

LHO started with 4 diamonds.

(1) If RHO has AQ of clubs LHO could have switched to a club at trick 2 or 3 and defeat the contract.

(2) If LHO has the ace of clubs RHO could have defeated the contact by switching to clubs.

(3) If LHO has Qxx(x) of clubs RHO could also defeat the contract by switching to clubs.

Does everybody agree that (1) is almost impossible to find for the defense, (3) is very hard to find but maybe possible, but (2) would always be found?

At the table I was not 100% convinced that RHO would find the club switch holding Qxx (I might have held J QJ87 A9x A10xxx?), although LHO would probably have played jack-queen of diamonds instead of jack-king. If RHO has 10x of spades it is not clear to them that the spades are running.