In the recent Bermuda Bowl competition, the Men's World Championship of Bridge, with only two boards to go in the final match between Switzerland and the Netherlands, both teams bid to six hearts and the declarers were faced with deciding how to make their contracts.

The auctions were different in the two rooms but both started in the same way, with East overcalling the Stayman two clubs with two diamonds. With only nine points outstanding, this was indicative of a distributional hand and as we will see, this no doubt influenced the subsequent declarer play.

Drijver received the gift of an aggressive small diamond lead from the king and jack and took the first trick with the queen of diamonds. He then had 5 club tricks, two diamond tricks, four heart tricks, allowing for the likely play rather than the 5 he can make double dummy and one spade trick making 12 tricks in all. He actually took the spade finesse, however, and went one down when he also lost a trump trick. Declarer in the other room also took the spade finesse and went down though this time after a club lead which didn't gift the queen of diamonds.

Without the diamond overcall Drijver's line of play would be surprising since a naive analysis suggests that the probability of the club suit running is greater than 50%. The suit runs if the jack drops in 3 rounds. On average, we get a 3-3 split 36% of the time so that is a good start. A 4-2 split occurs 48% of the time so we will get jack doubleton a third of these times for another 16% bringing us up to 52%. A 5-1 split occurs 15% of the time and one sixth of these will be jack singleton 2.5% of the time bringing us up to 54.5% ( (A more accurate calculation yields 54.1%) which is better than a 50% finesse. Playing on clubs will succeed even agains a 4-1 trump split if all trumps are drawn before playing clubs and may also allow a late spade finesse if clubs fail.

With the diamond overcall, however, a more complicated analysis is required. First of all, there are only nine points outstanding. For the spade finesse to succeed, East would have to have overcalled on a poor six points (king and 3 jacks) or fewer. If we believe that this is probable, then we can estimate the possibility of the finesse succeeding from the number of vacant places in East's and West's hands. (See my previous blog on this) The more difficult question is how does the knowledge that East has a long diamond suit change the probability of the club suit running? This can be answered by direct calculation (See Wikipedia - Contract bridge probabilities) but probably not at the table unless you are a maths genius! The actual probabilities that the jack of clubs drops or the finess works for different diamond suit lengths with East are as follows:

We see that East has to have 7 or more diamonds for the probability of the Jack dropping to be less than 50% (and, surprisingly, that with 5 or 4 diamonds the probability of the clubs running is actually higher than calculated above for the average over all possible hands). The vacant places arguement wins rapidly, however, with increasing diamond length and for 6 or more diamonds with East, as seems likely from the bidding, the finesse is the better option. Note, however, that this is assuming that a world class player would regularly overcall at the two level with nothing more than KJxxxx in diamonds and possibly an outside J or two.

Two world class players seem to believe that this is a good assumption. Probably not at my club, however. I would have played for the Jack to drop.

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