Hand of the Week

11/19/14

This hand would have been a good candidate for the "Misplay These hands With Me" column or for one of Jay Stiefel's articles.

Board #8
West dealer
Neither side vulnerable

	North ♠ K x x x ♥ J x x ♦ A x x ♣ x x
West ♠ A Q x ♥ 9 x x x ♦ J x x ♣ Q 10 x		East ♠ x x ♥ A Q 10 X ♦ Q x x ♣ A K 8 x
	South ♠ J x x ♥ K x ♦ K x x x ♣ 9 x x x


South	West	North	East
	P	P	1N
P	2♣	P	2♥
P	2N	P	P

I was sitting East. My partner made the imminently reasonable decision to avoid Stayman because of his 4-3-3-3 distribution and his unexciting heart holding. Actually, he had to use Stayman because he had no other way to invite to game; we play four-way transfers after a 1NT opener.

The opponents took two diamond tricks and then led a third diamond. I had discarded the queen under the king, so the board took the third trick. I then ran the ♥9, which lost to the king. South played the last diamond. All three of us discarded spades. North's was the four. North-South played standard discards.

South led a spade. I called for the queen, but North played the king to hold me to eight tricks. I don't know if she false-carded on purpose, but it cost me a very valuable overtrick because two of the other four pairs made three hearts. Their 140 beat our 120, but the overtrick would have given us 150.

I examined the hands afterwards and learned that I could have taken four club tricks, which would have obviated the need for a spade finesse. At first I thought that the spade finesse, which ceteris paribus would be 50%, might not be the right percentage play in comparison with trying to drop the jack. In fact, the calculation for the drop is a little complicated. Playing for the drop would produce four tricks in all 3-3 splits (35.53%), in all 4-2 splits in which the jack was a doubleton (16.15%), and in all 5-1 splits in which the jack was a singleton (2.4%). The drop (54.08%) is indeed a better play, but only slightly. Moreover, those calculations are based on the data available at trick 1. At the time that I made the decision to play the ♠Q, I had already seen exactly half of my opponents' cards, and none of them were clubs. This changes the calculation.

Here is what I came up with. Please check my math:
a) 3-3: 40.79%
b) 4-2 with doubleton on the right: 18.36%
c) 4-2 with doubleton on the left: 30.59%
d) 5-1 with singleton on the right: 2.45%
e) 5-1 with singeton on the left: 7.34%
f) 6-0: 0.47%
The drop works in a + (b + c)/3 + (d + e)/6 = 58.74%! This figure is approximate because one of the thirteen cards – North's discard of a spade – was neither random nor forced.

Since I had additional information about the opponents' discards, playing for the finesse in spades was, at that point, suspect but not unreasonable. Maybe I should have considered the possibility of a false card more seriously. A bigger mistake, however, occurred when I led the heart at trick four. There was no hurry; I had entries in spades and clubs. I should have tested clubs by leading a low one to my ace and then, when the jack did not fall, continued with another low one to the board's queen. If the jack did not fall at that point, I could start working on hearts with a clear conscience. As the cards lay, the ♣J would have tumbled, and I would not have needed the finesse.

This exercise was instructive. When deciding between taking a finesse and playing for a drop, the two probabilities are so close that the unlikely events (jack in the singleton or doubleton, for example) can tilt the scale. Furthermore, the longer that you can postpone a finesse, the more likely it is that the drop is better. In this case waiting increased the chance of the drop working by over 8%.