You say “bad split”, I say “endplay”

[iamadeus]

We came across a very interesting hand at Brian & Oliver’s practice session today.

As North I had QJ7, 72, A, AJ86543. East opens the bidding and it goes

East South West North
(P)    1     (X)   1N*  [transfer to clubs]
(P)    2     (X)    XX   [we think 2 is making]
(P)      P    (2 )  2N* [Relay to 3 ]
(P)    3     (P)    3N* [to play with stopper in ]

I thought 3N was a reasonable place to play. Even if partner has a minimum like xxx, AQxxx, QJx, Qx, we can handle most 4-1 club splits and take 1 spade, 1 heart, 1 diamond and 6 clubs for 9 tricks. I got the expected 3 lead but got a rude shock as dummy hit with.

Dummy:
642
AKJ94
KQ852
-

Me:
QJ7
72
A
AJ86543

Defense played 3 rounds of spades all following, RHO showing up with AK as expected. So spades split 4-3. Since we had 25 HCP it became clear that the second double of 2 was for penalty, and the subsequent 2 did not show a monster hand with spades. We have 7 top tricks: 1 spade, 2 hearts, 3 diamonds and a club. If diamonds split 4-3 (likely since RHO doubled and didn’t bid 2 ), we can get one more. The 9th trick has to come from a heart finesse.

1. There’s a problem because we have to unblock A to set up the suit. We then can’t cash A immediately because defense would then take KQ of clubs when they get in with a diamond - that’s down 1 already (at least 2 spades, KQ clubs and a diamond). So we need 9 tricks without cashing A .

2. The other problem is that we cannot afford to lose a finesse in hearts since the defense can put us back in dummy with a diamond and wait for 3 spades, a heart and a diamond for down one. So we have to assume that both Q and 10 of hearts are onside, since we know that hearts are splitting 4-2 or worse, given the auction. We lead a heart to dummy’s 9.

3. In order to score 4 hearts we need 2 entries to finesse twice. However, there’s no entry back to hand since we have already unblocked A . Our only hope is to endplay one of the opponents by putting them in with the 4th diamond.

4. When the defense gets in with a diamond, they can take the 4th spade but then they have to either lead back a heart and allow us to finesse the J, OR they lead a club to our Ace, which magically gives us an entry back to hand to finesse again in hearts.

5. This line allows us to make the contract even if hearts split 5-1 or 6-0, since we only need 1 spade, 4 hearts, 4 diamonds OR 1 spade, 4 hearts, 3 diamonds and a club (assuming they return a club).

6. An alternate line is to play for 5 heart tricks, by assuming that the suit splits 4-2 with Q & 10 onside. In this case, we don’t need to set up diamonds so we would keep A !d and use it as the second entry to finesse hearts. The original line that involves an endplay is superior because it can handle 5-1 heart splits as well as 4-2. Hence the title of this post! 

See the full deal here: https://tinyurl.com/y9vbpz8w

In retrospect, defense should have let us play 2 redoubled, which is very difficult to make after defense plays three rounds of spades.

[brian_m]

I understand your logic, Aravind, but I'm still not 100% convinced. The problem I have is that the deep finesse risks losing to a singleton 10 or Queen in West's hand. Let's try something a little different.

We know West has the 13th  from the 2 bid. I think it's also highly unlikely, unless West has taken leave of his senses, for him to have less than five  , possibly even six, to make what we know (following your logic) is a penalty double sitting underneath your suit. So, we've placed at least nine cards in the West hand, leaving only four red cards. Since West doubled the opening 1 , rather than overcall, I think it's fair to place him with 4-1-3-5 or maybe even 4-0-4-5, although the fact that he ran to 2 rather than 2 after your redouble is at least circumstantial evidence for for 4=1=3=5, or possibly 4=0=3=6. We have to assume that the  are 4-3, I think, if West has made an off-shape takeout double with only two  , and East is 3=5=5=0, I don't think you can make that contract without risking everything on the read and cashing the  A before you end up in dummy.

I think it all depends on your reading of the opponents' hands. The line of play I come up with is :-

We take, by force, the 3rd round of  , thinking ourselves lucky that West didn't duck the first round of  - I think that kills the contract.

Play a  , putting up the A or K from dummy. This protects against West's singleton  being the 10 or Queen.

Come back to the Ace of  , and now you can cash the Ace of  , removing East's (presumed) only remaining black card. Now it's time for your deep  finesse, then set up your fifth  in dummy, and East has to give you another  finesse.

It's quite honestly giving me headaches trying to work out which of these lines is superior. The one thing of which I'm certain is that your line is off if West's stiff  is the Q or 10 - you're going to lose 3 , 1 and 1 . My line is still alive, because I crash that high  . It all depends on how you read the E-W hands, I guess. 

[iamadeus]

I agree with everything you said but there is a problem in the argument.

Essentially you are setting up diamonds AFTER playing Ace of clubs. You assumed that diamonds were 4-3 (which is likely) but you have to hope that East has the 4th diamond. Instead, if West has 4=1=4=4 or 4=0=4=5 shape then they can take KQ of clubs when they get in with the diamond. Another problem is that if West has 4=2=3=4 shape, then it means East has 2 clubs so they can play clubs from their side when they get in with a diamond. Granted that West may not double 2 with this shape but it is possible, nevertheless.

I think that the likelihood of these shapes is more than the chance of catering to a singleton Q or 10 of hearts in the West hand. I didn’t have time to do the math at the table so I took a chance on the line that only assumes Q & 10 of hearts in the East hand.

[brian_m]

Yes, I agree that I'm making those assumptions, for the reasons I gave in my earlier post. I just don't buy the idea of West penalty doubling under your club bid with less than 5 clubs, even if he has all the missing strength except for  !HQ. I agree my logic for playing for 4=1=3=5 rather than 4=0=4=5 might be a little less certain.

Anyway, I certainly wouldn't be capable of working out the probabilities at the table. It gives me headaches just trying to think through them now!  One thing is certain, though, and that's if the hearts are split 5-1, the chances of a stiff  Q or  10 in the West hand are not negligible.