Percentages on Defense?

[awm]

[hv=pc=n&n=skqt63ha2d7543c83&e=s75hk987daj82ckq7&d=w&v=b&b=4&a=pp1d1sp4sppp]266|200[/hv]

 

Matchpoint scoring. Partner leads the ♦9. Dummy plays low, you contribute the ♦A and declarer plays the ♦6.

 

Partner's possible diamond holdings given your lead agreements and the visible cards to trick one are ♦QT9, ♦KT9, or ♦9 singleton.

 

If it matters, your bidding agreements are pretty standard here. What's your play to trick two?

 

In case it might be unclear, SOUTH is declarer and NORTH is dummy. You are sitting EAST.

[mohitz]

It seems right to play a club back. We might be able to defeat the contract if declarer is AJxxx Qxx Qx Axx for example. If we don't shift to a club, declarer can remove trumps and discard a club on the Q of hearts.

 

As regards to which club, i think a low club is better. If declarer has Axx, it doesn't matter. If he has AJx, it doesn't matter. The key case seems to be when declarer has AJ9 of clubs and guesses wrong.

[semeai]

Beware, this post is a bit ridiculous and not particularly salient. I wrote it at whatever AM because I like to watch numbers spin.

 

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If partner has ♦9, we want to play a diamond. If ♦QT9, we want to play a club. If ♦KT9 it likely doesn't matter which.

 

♠AJxxx ♦ K6 is enough to overcall, so based on vacant spaces and assuming spades 5-1 (this should be close enough):

♦9 : ♦QT9 is 3:11

 

If partner has ♦9, it definitely matters that we play a diamond now. If ♦QT9, it only matters to play a club now if declarer has ♣A plus ♥Q without ♣J.

 

This tips the scale back to ♦9, as ♦QT9 : (♦QT9 - ♣A - ♥Q) is 15*14:6*5, i.e. 7:1. This makes ♦9 a favorite by roughly 2:1 over ♦QT9 - ♣A - ♥Q.

 

So, assuming I haven't said something silly, and it's late, so the odds here can't be good for me, a diamond looks best.

 

Adding more: Of course, e.g. 1-5-1-6 is not so likely for partner, who would negative double with most hands this shape. I think I discounted this because I'd sleepily decided we'd overcalled (yes, I then overlooked the contradiction when checking ♠AJxxx ♦K6 was enough for declarer's bidding) and that partner wouldn't act red with this hand after our overcall. Without ♣A, it's possible partner passes, but that already puts us back at equity (i.e. loses the 2:1 factor). This makes a club seem right. A low club would then be best since we get a heart trick if declarer wins ♣J, and maybe declarer won't stick in ♣J.

 

Rather: ♦9:♦9 - ♣A is 15:4, so this puts ♦9-♣A : ♦QT9 - ♣A - ♥Q at roughly 1:2.

[shyams]

If I were to infer, I'd say partner does not have 4 card ♥. So declarer must be 5-4-2-2. I play a top ♣

[gnasher]

As Semai says, a club return is playing for partner to have ♦Q109, ♣J, and not ♥Q. - if he doesn't have ♣J, we get only one round-suit trick regardless of what we do (even if declarer is 5=4=2=2, because there's an elimination).

 

Opposite me, you could confidently return a diamond, because with x xxxx Q109 Jxxxx I would have raised to 2♦.

 

Opposite a less enthusiastic raiser, you would have no such inference, and the question would be which is more likely of:

(1) 1516-5233 or 1417-5332

(2) 1534-5224 or 1435-5323 or 1336-5422, with two honours in specific places

 

(2) appears more likely - I expect that the higher frequency of those distributions would easily make up for the restrictions on the honour location.

 

Hence I play a club. A low one isn't completely safe - declarer might have AJxxx Qx Kx AJ10x, for example. However, it seems worth it to give him a guess.

[shyams]

I have a related question. What's the weakest hand partner can hold for a negative dbl? Would x Qxxx QT9 xxxxx qualify?

 

I ask because one of (not very regular) partner and I tend to use neg x with 4+ card major and even 4-5 HCP. And that's why I wrote that declarer probably is 5422

[whereagles]

As mohitz/gnasher. Low club.