In order to try both you must cash the AK of hearts before cashing your diamonds. If West started with AK103 of spades, the K of clubs and three or more hearts you will go down if the Q of hearts doesn’t drop (losing three spades, a heart and a club)

Not necessarily! You’ll also make in this line if the ten of hearts drops doubleton — you’ll then knock out the HQ and refuse the club finesse, taking 1 spade, 3 hearts, 4 diamonds, and a club before the defense gets its 5 winners.

I have to admit that I didnt find the spade return: my thought was to win the opening lead and play a heart towards the J — winning if W has the HQ, or hearts are 3-3, or the T drops doubleton, and (in all cases) spades started 4-3 — or if West had 5 spades and errs by ducking the heart, what Eric Rodwell calls a “speed of lightning play”. This last is unrealistic though, since presumably West knows from the bidding that you don’t have 4 spades, so his spades are now ready to run. (One last note: if spades were 4-3, you can still make it even if East started with QT 4th, 5th, or 6th of hearts, as long as he has the CK also.)

Both these lines are IMP lines, I think, playing to increase the chance of making with less chance of an overtrick. At matchpoints it looks right just to take an immediate club finesse.

Okay, now I’ve been doing more thinking about the probabilities, and I’ve just come up with a somewhat counterintuitive result:

In the case where West started with AKT3, after you find this out and then cash the AK of hearts, the best play when no honor drops is a third heart! Consider: the low heart plays eliminate all the 6-0 and 5-1 breaks, and 60% of the 4-2; so at this point the chances are about 65% of a 3-3 split, and 35% of 4-2…and of those 4-2, about half will have West starting with QTxx. (Another way to look at it: the third heart loses only if East started with specifically QTxx, which is a lower probability that that West holds the CK.)

My low heart is definitely inferior. It loses whenever West started with 5 spades, which on the lead is about a 33% chance. Just crossing to dummy with a diamond and taking an immediate club hook is better than that: it wins when spades were 4-3 or the club finesse is right, which I make to be about 83%.

…and, now that I’ve had more time to think I realize that the above is just silly: if spades are 4-3 then you are 100% to make by playing on clubs. (This is actually noted in the article!) So the only relevant case is when spades are 5-2, and in that one you can’t afford to lose another trick, so the only extra chance is the doubleton HQ. This risks an extra undertrick if West started with the CK and at least 3 hearts, for a 12% extra chance of a make — clearly right at IMPs, harder to judge at matchpoints.

(I make cashing the HAK about a 4% extra chance of making, overall.)

Hi Dave. I am gratified that you found the hand interesting enough to give it considerable thought (as did I). You correctly note that I neglected to mention the doubleton 10 possibility (thanks), but I believe you have concluded that my recommended line is best.

Followup – Some have suggested stripping west of diamonds and throwing him in with a spade. This line has a fatal flaw: if west started with five spades then south will be squeezed by the 4th diamond and the 5th spade.

Cazare Cu Piscina

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