I was reminded of the first line of the lyrics of a song by the up and coming Durham group The Thieves by a hand last night:
Vacant thoughts flow through my mind
Empty words are all I can find
No doubt the reader is thinking of the present writer from the second line above, but it is the first line that I want to focus on. In bridge there is a theory that the chance of a player having a particular card is proportional to the number of vacant spaces he has in his hand. "Que?" I hear you say, Manuel-style. Well let us look at the following hand.
We had a less ambitious auction than Paul Saunders and Keith Bush, who were the fine winners of the overall competition this week. The club managed the difficult technical task of merging the online and live boards, roughly equivalent it would seem to the recent separation of two Siamese twins who shared a brain.
Paul Saunders is a bit of a gambler and South's injudicious double told him how to play the spades and 12 tricks were the result for a top.
At our table, we bid 1S-(3D)-Double-(Pass)-4C-(Pass)-4S-All Pass and I was in the top spot as West. North led the three of diamonds and I knew that the diamonds had to be 8-3, as South would have raised with four-card support. I won the diamond with the ace, and started to work out the odds before playing trumps. The chance of South having the king of spades is 10/15, as South has ten non-diamonds to North's five. Similarly for South having the jack of spades. The chance of South having both the king and jack of spades is not quite that squared, but is 10/15*9/14. Or 43%. Against the odds, but it is still right to take a "deep finesse" on the first round, as I did, as the only other line for 12 tricks, playing for singleton king or jack with North is quite a bit worse. You have to pick one of them to play for as well, and that comes out at only 7%. Of course, taking two finesses may lose to KJ doubleton with North, but that would be unlucky. The fine software program, Suit Play, confirms that the best play in the suit at matchpoints is running the ten, which generates 3.98 tricks against silent opponents.
Interestingly, with no opposition bidding, one should play the same line, but it is worth mentioning that with nine spades, the percentage line is to finesse the queen on the first round. So I guess that my mind was full of vacant thoughts and all I could find was some empty words to explain what I was thinking!
