Guthi opened 2NT, and I straight away wondered whether we belonged in 6NT or 7NT. To bide my time I bid Gerber, intending to check the number of kings as I definitely couldn't bid 7NT with a missing king.
Alas, Guthi pulled out 5S instead of 4S, and although I suspected what had happened, I couldn't ethically use 5NT or 6C to ask for kings (plus there was a risk of misunderstanding) so I had to pick without that information. I chose the conservative 6NT with five points outstanding.
Guthi cashed his major suit winners, pitching three diamonds and a club from dummy. He then cashed the top two clubs, and no queen appeared. He then played DK and a low D to the Ace, and it turned out that his last diamond was good. East, holding the queen of clubs as well as the third diamond, had been squeezed on the run of the majors! 6NT made 7. At the other table, Aniket and Anurag were in 6D, an inferior contract that will only make 6.
Who knows what would have happened if Guthi had responded 4S and I asked for kings? Would I have bid 7? If I did, would Guthi have played for the squeeze or the finesse? The squeeze I think is a slightly superior percentage; it works whenever the person with the CQ holds more than two diamonds, and also when the person with two or less diamonds holds CQ doubleton. I think this adds up to slightly more than 50%, which is the probability for the finesse. Ashok says it will be slightly less than 50%. Can someone do the math?
Cheers
Prashanth.
(Edit: Switched to the image given by Ashok. Extraneous comment in it was also provided by Ashok :) )
4 comments:
You can get the conditional probabilitiese.g. from http://www.himbuv.com/cpe.htm and combine them appropriately. Consider only 3-2 diamonds for simplicity (to get exact numbers you'd need to do the weighted sum of this with 4-1 and 5-0). Given by hypothesis D 3-2, the CQ will be with the 3 cards 47.6% of the time (you can also get this more directly as 10/21 using the "free spots" approach, which is in fact usable at the table for mental arithmetic!). Alternatively, the 7 missing clubs will be 1/6 (singleton w/the 2 diamonds) 2% of the time, of which 1/7th of the time the Q will be the singleton; and 2/5 the same way 11.9% of the time, of which 2/7th of the time the Q is doubleton. That's in all about 26/7 = 3.7%; we can sum since we used mutually exclusive conditions and get a total of 51.3% conditioned on D being 3-2. For D 4-1, similarly we have 42.9% of the CQ being with the long D, 0.9% for 6-1 (single with the D single), 7.2% for 5-2 (double with the D double), total 2.2%; grand total 45.1%. So for the weighted sum, since 3-2 a priori is 67.8%, 4-1 is 28.2, ignoring 5-0 we get 49.5%. So, the squeeze is better if D are 3-2, but very marginally worse than the finesse overall.
However considering "IMP odds" you should also realize that the other table might well have been in 6D, as it did happen to be; then if D are 4-1 they're down anyway and there is less at stake in your making 7NT or going down -- 17 IMPs if you make, all square if you don't. If D are 3-2, 6D makes, so you win 12 IMP if 7N makes, but lose 14 IMPs if you go down, for a total swing of 26 IMPs. There is more at stake with D 3-2! So if you do the computation for expected IMP win/loss you'll find the squeeze is right (wins more IMPs in the long run) even though overall it succeeds a minute bit less than the finesse -- it wins more IMPs when it does win than it loses when it loses!
In practice, at the table, you should normally go for the squeeze when the % difference is too close for mental computation, IMHO, in part because also of considerations such as the latter on IMP swings.
I've prepared another, more complete, diagram of the same deal. Actually, there are several points of interest in this deal. The lead was H4, by the way.
1. The chances with the squeeze are a little over 50 %. I was first considering the squeeze using clubs for communication. If you use diamonds, you can play off the two top clubs. At any rate, it pays to perform a discovery play.
2. I pointed out earlier that notrump ranges were not rigid. I think a case can be made to upgrade this hand to the 22-23 range. The fifth heart gives you one extra point, bringing the total to 21, and you have 8 AK controls, which is slightly more than the average for 21-point hands. However, the poor clubs could give you pause. I think I would treat it as a 22-point balanced hand.
3. The play in 6NT at IMPs is interesting. Work it out before reading on. It's very probable that either hearts or diamonds will come good. But you need to plan for the case where you have bad breaks in both suits.
If the same opponent should hold length in both (5 hearts and 4 diamonds — a bit unlikely), you will clearly have an easy automatic squeeze for the twelfth trick. What if different opponents control the two suits?
You duck a diamond on the second trick and then cash the DA. You will know who has the long diamonds. On the second heart, you will discover / have discovered that his partner had five hearts. If West has the long diamond and East the long heart, you have an easy double squeeze when you play the ace of spades: (hand) SA H8 CT opposite (dummy) D8 CKJ.
Now for the last case: West holds the hearts and East the diamonds. You have a simple squeeze against the opponent holding the club queen, but you don't know whom to play for it. Since you can always drop the doubleton queen with the opponent you're not playing for it, you either do discovery (meaning estimate the spade distribution) or simply take a guess. You will likely not know the spade distribution, but assuming West has five hearts and East only four diamonds, it's better to play West for the possible doubleton club queen, i.e. plan a simple squeeze against East in diamonds and clubs. You will cash CAK early on. (If you want to do it the other way round, you will plan a show-up squeeze against West.)
I have not spotted a 100 % line given the lead. Is there one? And if so, what is it?
Given that East followed to only two rounds of hearts, he/she is more likely to hold the club Q, in which case the squeeze play rates better. If west shows out of hearts, I think I would finesse for the queen after drawing one round of clubs.
I just made an exact calculation (though I don't guarantee its correctness!) which shows that, assuming the remaining cards are completely randomly divided between East and West, the probability that the long-diamond hand will hold CQ or five or more clubs without the queen (meaning singleton or doubleton queen with partner) is 0.490 591 888 929 485. With the finesse, it's 0.504 844 720 496 894 41. When I wrote my earlier comment, I assumed that the doubleton-club possibility would take the percentage above 50 %. It appears I was wrong.
This, however does not take into account the discovery that you can perform. Let's just take the effect of knowing the heart distribution and knowing that each opponent holds at least three spades. The probability of success of the finesse is 0.428 904 428 904 429. The probability of the squeeze working is not reduced by much: 0.485 198 778 355 621.
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