[Antrax]

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LHO leads a heart to the jack, king and ace. You draw trumps in two rounds, with RHO having Jx. What is your plan?

If/when you play a club from hand,

Spoiler

LHO plays the ♣2 in tempo.

If you check the diamond situation, you find out that

Spoiler

they're split 4-3

[Flameous]

Spoiler

We have two ways to handle clubs. We could duck the first round, if it wins, we take care of the 4-0 break.
If it loses to ten, we need it to be HT. If it loses to H, we finesse again due restricted choice.

Other choice is just banging down the ace and if honor falls from behind, playing small towards J.

First line handles 4-0. However we lose to KQ offside. Second one doesn't.

It's not maybe too intuitive, but the first one is somewhat better. For specific 2-2 sit we have 6,78% chance while for 4-0 we have 4,78%.
However due restricted choice we can essentially half the chance for KQ offside, thus dropping it to 3,39% which is smaller than that for the 4-0 break.

Better google for restricted choice if you want to know the math better.

[Zelandakh]

@Flameous

Spoiler

Take another look - when East wins the ducked club with bare KQ what is he leading back? Restricted choice appears to have nothing to do with this problem - remember it is a problem for beginners!

[BunnyGo]

@Zelandakh

Spoiler

He'll return a heart. You only get one ruff-sluff, which isn't enough. You'll still need to hook again.

[G_R__E_G]

Does anyone really think that West has 5 hearts? What are East's probable distributions?

[Cyberyeti]

G_R__E_G, on 2011-November-23, 14:39, said:

Does anyone really think that West has 5 hearts? What are East's probable distributions?

E is 2731 most of the time, with possibility of 2740, stiff K or Q is twice as likely as stiff 10, so small to 9 looks best and handles the 4-0 too.

This is unless I'm playing LoLs who only single raise with Qxxxx and out.

[Antrax]

You're certainly playing LOLs. There's no trick here, I'm not very good at posting things as problems yet. The simple play is what wins -- the reason I posted it is as a problem is that I was the only declarer to make 12 tricks in spades. I got one freebie from the defense but it only made me sure the "correct" line is going to win.

I'll post the account of my play below:

Spoiler

The first play already gives us a clue. E probably doesn't have the Q. Draw trumps in two rounds, E started with two spades and also had the J.
Now play three rounds of diamonds, ending in hand, since there's no reason not to. We might learn something about the diamond distribution, and might get to see a discard.
Diamonds are 4-3, so E has at most two clubs. Now we have to play clubs. We want to lose the club trick to E - if we're lucky, he'll fear a ruff and sluff (we all learned it's bad) and might return a club, since he has no way of knowing I don't hold the fourth diamond.

So at trick 7, play the club 7, to make it more difficult for the defense to count (if I play the 3 to the 4 and E wins something high, W can be pretty sure I have all the middle ones). If W will play K or Q, we play the ace, return to hand and play another club towards the J. E can't have three club, so this will bring the contract home.
W produces the 2. This is interesting. We all play second hand low, but if she had KQ she might be tempted to split (even though on this layout it loses), and by being able to produce the only "low" club (notice the sequence of spots between my hand an dummy) reduces the chance she only has two. So we duck. If clubs are 2-2 nothing bad happened yet. If they're 4-0, we just got on the road to winning the hand. If they're 3-1, then if the singleton is the remaining K or Q it's good for us and if it's the T we lose since W will score one of her K or Q of clubs. E wins the club king. This means he doesn't have the T, most likely. Now we wait for his return.

Trick 8. He thinks for a while and returns a heart. What is he thinking about? Assuming he's not thinking about what heart to return (he doesn't have the Q so he can't think it matters, really), he couldn't be thinking about returning his club Q if he has since he sees AJ in dummy. Could it be that he has the last diamond?
In any case, discard a club on his heart, W produces another heart, and ruff (high) in dummy.

Trick 9. Now return to hand with a trump. We know we're going to play a club towards dummy at some point, but the opponents might not have paid attention. They should know we have no hearts left, and if we have the fourth diamond it doesn't matter since it's high so my contract is made. They also know that unless I'm crazy, I have all the remaining trumps in my hand. Theoretically, they should know exactly what I hold -- but we still lose nothing by trying to see if they're still awake. Now we'll play trumps from hand before playing the other club, just to see what happens. It's unlikely we'll get a club pitch, of course, but let's see if both of them discard hearts confidently all the time. On the trump return to hand, both discard hearts. That's 8 out, E still has at least three of the remaining five. No surprises yet.

Trick 10. Let's play another trump and discard a low club from dummy. Now W thinks a bit and discards a heart. I discard a club, and E thinks and finally produces the last diamond. So that's what he's been thinking about after winning his ♣, and it also gives a complete count of his hand. He can't have any more clubs left, unless he felt like bidding 2♥ on a five-card suit with a single honor. We gave him a chance to err and he took it, hurray for us.
Let's say he doesn't make this mistake, and instead discards a heart. If we play another trump, we might learn something interesting, but we risk going two down instead of one down if we misguess the clubs.

In our theoretical trick 11, there are still ♣QT, a diamond and three hearts out there between the defenders' hands, with E having at least two of those three hearts, and either the last diamond, or the Q of clubs as his third card (we ruled out the T before). You will notice he can't just three hearts left - the defenders made another mistake in their discards, W didn't discard her Q of hearts, so I know the remaining hearts are 2-1. We play the club, W produces the club T we knew she had, and we play the J. If E had KQ tight all along and played the K, good for the opponents. But finessing now should have been our plan from trick 7. We know based on the bidding and the first six tricks that E doesn't have 3 or 4 clubs, so clubs are 2-2, 3-1 or 4-0. If they're 2-2, covering what W plays twice wins against anything that's not KQ tight with E, which is only one possible holding out of the six he could have. If they're 3-1, only the singleton T in E (1/4) defeats us. Everything we've learned so far still keeps us within those odds. After trick 7, it's given that clubs are 3-1 or 2-2, and the odds for 3-1 are much higher, both mathematically and based on the bidding. W only raised to 3 ♥, so she might not know they have an 11-card fit.

So, those were my thoughts. I'd be happy to hear if A/Es see a problem in my thinking - remember this is a club game, so you can allow yourself to pay off deception by the opponents. And if some beginner thinks this is interesting, all the better.

[Phil]

Seems like a reasonable line from what I can see, however, its unlikely clubs are 4-0 onside since RHO didn't x.

[Antrax]

Interesting. Hadn't thought of that, though I don't think that pair plays lightner doubles.

[FrancesHinden]

East doubled 4H, which surely (s)he wouldn't do with a club void, whether or not they play lightner doubles of slams.
I realise people do misdefend, but I don't think anyone would split with KQx club when you lead towards dummy.

As you say it looks as if RHO is 2731/2641 or just possibly 2632. When LHO plays the C2 he has KQ2, K102, Q102, K2, Q2 or 102. Playing the ace works on 5/6 of these.

[G_R__E_G]

FrancesHinden, on 2011-November-24, 14:18, said:

East doubled 4H, which surely (s)he wouldn't do with a club void, whether or not they play lightner doubles of slams.
I realise people do misdefend, but I don't think anyone would split with KQx club when you lead towards dummy.

As you say it looks as if RHO is 2731/2641 or just possibly 2632. When LHO plays the C2 he has KQ2, K102, Q102, K2, Q2 or 102. Playing the ace works on 5/6 of these.

And playing the 9 works on how many of the 6?

[Antrax]

Could anyone explain a bit about east's X? At the table I guessed it's some sort of "stolen bid", i.e. "I would have raised to 4 but now I can't". Is the assumption that with a club void he would've raised to 5?
Also, Frances, don't be so sure. One of the reasons I don't like playing in that club is that the defense gives away too many freebies so my hand evaluation is completely skewed. I always guess right with nine-card fits with two-way finesses by playing J to K, for instance, because many of those people never ever fail to cover an honor with an honor. I guess if they don't and it somehow backfires, their partner won't let it go.
Of course, I'm not sure how useful it is as a problem. I thought the problem was "how to play the club suit", and the points I was trying to make is that you always want to play diamonds first because diamonds are exactly three tricks no matter what, so it can't hurt to find out who started with how many diamonds, and that the right play is to finesse W twice unless new information comes to light. Does that make sense?