Best play in a hand – III

This is one of a series of analyses of the play of the hand that I did in rec.games.bridge newsgroup during the late 80’s (that would be the 1980’s, not the 1880’s.)

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Micah Fogel presented the following hand:

AK984  QJ76 | 1S P 2N P
KJ     AT97 | 3S P 4N P
Q8     A96  | 5H P 5N P
KJ72   A8   | 6S P 7S all pass

and asked:

The question is what is the best play to make? I figured the only way was to find the queen of hearts for a diamond pitch from hand, and proceeded to pull trump (they are 2-2), and play KH, AH, heart ruff trying to drop the lady. This works whenever either opponent holds Q, Qx, Qxx, plus RHO holding Qxxxxx. On reflection, I believe this is worse than the 50% for guessing the finesse. Is there a line better than 50%?

Analysis

A – Vienna coup: Ruff out the clubs, play off the DA and go for the squeeze on HQ and DK in the same hand.

B – Drop, squeeze, or dummy reversal squeeze: Play three rounds of hearts. If the queen doesn’t drop and if North has Qxxxx(x) in hearts play for a dummy reversal CQ-DK squeeze on South; otherwise play for the HQ-DK squeeze on North.

C – Drop or squeeze: Same as number two, missing the dummy reversal squeeze.

D – Finesse: Take the H finesse.

Which of these lines is best? What is the chance of making 7S?

The calculation of the odds for each of these lines is tedious because there are many minor contigencies that affect the odds. For example, the Vienna coup fails if clubs split 6-1 and the club QC is not singleton and the person with one C holds more than one trump. You also have to take into account the chance that S has the singleton HQ in the coup line and in the finesse line. In addition you have to take into account the two honors are more likely in to be different hands than in the same hand. It’s all very messy and all very tedious. I won’t waste bandwidth on the calculations, but the numbers I came up (rounded to nearest percent) are:

A - Vienna Coup:                              50%
B - Drop, squeeze, or dummy reversal squeeze: 57%
C - Drop or squeeze:                          55%
D - Finesse:                                  50%