[zenbiddist]

7NT by South, ♦ lead (no EW bidding)

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I played this contract the other day, and tried to figure which was better: ♠ finesse, or, squeeze player with 4+ ♥ & either queen?

Is this how you figure it out?

Finesse: 50%

Squeeze: a defender has one of two queens (75%), but the player with four or more hearts has at most nine vacant spaces (multiply by 9/10).
3/4 X 9/10
Squeeze: 67.5%

Using that logic, the squeeze is more probable until hearts split 6-1 or 7-0. At the table I got as far as thinking that hearts were probably 3-4 or 5-2 due to balanced hands, and that the squeeze is probably better than 50%. I'm curious now if my maths is right (probably not ). Also - if any of the mathematically inclined could be give me shortcuts for doing this kind of thinking at the table quickly, I'm sure my opponents would appreciate it

[Fluffy]

If LHO has 3 diamonds to the queen and ♠Q you cannot squeeze him since he pithes behind you.

However the location of ♦Q is not 50-50, it is overwemly more likely to be on your right, if that's the case, the spade finese never wins over cashing ♦AK, 5 clubs and 3 hearts, since RHO will have to surrender before you play a spade.

[CSGibson]

Fluffy, on 2014-January-09, 18:05, said:

If LHO has 3 diamonds to the queen and ♠Q you cannot squeeze him since he pithes behind you.

However the location of ♦Q is not 50-50, it is overwemly more likely to be on your right, if that's the case, the spade finese never wins over cashing ♦AK, 5 clubs and 3 hearts, since RHO will have to surrender before you play a spade.

I think he was thinking of the 4 card ending with dummy having 4 hearts, declarer 2 hearts and both pointed jacks, an auto squeeze, not a positional one.

Squeeze is the far better chance, also add in the Q doubleton possibilities and the JT doubleton/third in hearts falling. I also don't think the finesse is 50%; there is a restricted choice position on the opening lead if you assume that they would never lead from a Q in NT.

[inquiry]

First for your calculations, as noted above you missed the chances of a doubleton ♦Q or ♥JT or ♥JTx as well, I guess spade queen doubleton. Also you are assuming clubs are worth 5 tricks, which they might not happen. But let's assume that clubs do in fact run (thus no worse than 4-2).

How would you play the hand if the @SJ was replaced by the lowest outstanding spade? Would you be surprised that the hand would be makeable somewhere above 90% even in that case (assuming you can read the position correctly)? The only failing cases are when EAST holds four hearts and West the @DQxx or better and spades are divided 3=4 or 4=3. If spades are 5=2 or 2=5 you would have a simple squeeze. If the red suits were reversed you would have a double squeeze. If the red suits were in the same hand you would have a simple squeeze.

Now you have the ♠J on this hand. This raises the bar. The failing hand (West with ♦Qxx(x) and east with four + hearts no longer works. Who has the ♠Q? If East, you are back on a squeeze (Well a show-up squeeze), but if West it, you will still be defeated. This cuts the failing case in half from the hypothetical hand where you lacked the ♠J.

Now the fact that some squeeze will work (heart-diamond on West, heart-diamond on East, double squeezes either hearts on west-diamonds one East spades both and some squeezes where the small diamond in dummy is a threat card not the ♦Jack in hand) does not mean you will manage to cash your winners in the correct order for the squeeze that works at the table.

So let's take a look at how you might play the hand. First, you make if diamond queen is singleton or doubleton, that happens about 18.5% of the time. IF that fails, you can try for JT or JTx of hearts, that happens about 10.3% of the time (but, this doesn't help you if the ♦Q has fallen, so you have to take the 10% of the 81.5% of the time the diamond queen didn't fall, or about 8.2% of the time. So after no luck dropping the red suit honors, 26.7% of the spade finesse will work about 50% of the remain (100-26.7) or 1/2 of the 73.3% or roughly 36.6%. Adding this up, 36.6 + 8.2 + 18.5 = 63.3%.

So the question is which squeeze line offers the best chance (one that is better than 63.3%). The good news the ♦Q is greatly likely to be to your right. So at the very least you have a show-up squeeze on East in case west has doubleton ♠Q. This line gives you the same 63.3% chance plus the chance to drop the ♠Q off side doubleton. So you know it has to be better than the simple spade hook after cashing winners. However, it also has a huge additional bonus chance. If West happens to have four (or more) hearts and the spade queen then this line is also a legit squeeze on him (it would even work if you didn't have the spade jack but a low spade, btw) when you were hoping to show-up squeeze East. So this has to be much better than the 63.3 line where you cash all side suit winners before trying the spade finesse. If this fails, it means East had four hearts and the diamond queen where a different squeeze would have worked, but you can't try them all. For that squeeze to work, you had to cash spades early.

Anyway, I am not great at math, but this might help you compare lines, even if the above rambling is wrong, figuring out where I went off the rails will be useful.

[uday]

I like the simple logic of the OP, tho I wouldn't bother w/the vacant spaces part. Someone has the long hearts. That someone will be squeezed if he hold either the SQ or the DQ ( and that's if they don't come down after the AK ). That's much better than 50% .


However, i'm also with Fluffy. OP doesn't present an auction but I can't imagine that a human is leading away from the DQ. If you're willing to make that assumption and are confident in your card reading/counting, the hand is more fun to play as a compound squeeze, and is then makable regardless of how the cards lie.

Cash the D tops, and run all but one club. Everyone is down to 7 cards

RHO will have to hold the DQ, and thus can't guard both spades and hearts ( that would need 8 cards ). Depending on what he gives up, and assuming you can guess from that who has the H/S stopper, you can always squeeze RHO in H+D (cash the blacks) or LHO+RHO (cash the spades then the last club)

[zenbiddist]

CSGibson, on 2014-January-09, 18:21, said:

I think he was thinking of the 4 card ending with dummy having 4 hearts, declarer 2 hearts and both pointed jacks, an auto squeeze, not a positional one.

Squeeze is the far better chance, also add in the Q doubleton possibilities and the JT doubleton/third in hearts falling. I also don't think the finesse is 50%; there is a restricted choice position on the opening lead if you assume that they would never lead from a Q in NT.

Yes - I won the lead, cashed the other top diamond, cashed the ♠K, and ran the clubs, ending with:
♠-
♥AQ96
♦-
♣-

♠J
♥K3
♦-
♣J

[zenbiddist]

Thanks for the in-depth analysis everyone! I'll read over it thoroughly when I'm properly awake

[kenberg]

I begin by assuming no one leads an unsupported Q against a grand. If he has done so I congratulate him on his brilliance and hope to play against him often. So I play on the assumption that the ♦Q is on my right. A cash the ♦AK and then all of my clubs, throwing two diamonds and a spade form the table.

Everyone is down to six cards, E with the ♦Q.


If W started with 4+ hearts the ♦-♠ squeeze against E is set since W has already abandoned spades. If E started with 34+ hearts, I have a heart diamond squeeze against him. Can I tell which? In the first case I must run my hearts, in the second case I must run my spades.


So the "answer" is that a squeeze always works if the cards are played face up (assuming only that the ♦ Q is with E) but there is a choice of squeezes and I will need to decide which one. My default plan would be to cash hearts at tricks 5,6,7 throwing a diamond on the third heart and then the ♠K and small to the Ace. This works whenever E started with the spades Q and it works whenever W started with four or more hearts. And perhaps W was dealt a doubleton ♠Q. If I can read the hesitatins as the hand progresses, I might change my mind, but this is my default plan.

[Lovera]

E' preferibile la compressione all ' impasse per questione di maggior probabilità' di riuscita. In questo caso si tratta di una compressione alternativa ( simple as double ): verrà' compresso chi possiede una Donna insieme alle Cuori.


edit: uday via google translate

And 'better compression at' impasse issue of greater probability 'of success. In this case it is an alternative compression (simple as double): will be 'squeezed out who owns a woman along with Hearts.