Here is a technical problem from the County Pairs final, involving the kind of guess we all seem to get wrong more often than not.
You overbid to 4 after no opposition bidding. North leads a trump to South's ace. A club is returned, and you guess to play the king, but this loses to the ace. North gives you a reprieve by returning a trump and South shows out. After drawing the third trump, you now play the A and the K. Both follow, RHO playing the 9, then the J. How do you continue?
The fact that, writing this article three weeks later, I can insert every pip in the above problem rather than just "x"s is testament to the excellent service provided by Chris Larlham, who prepared computer dealt hands with hand records. He also directed the event this year, and kindly put up with my multiple-arrowswitched movement which ensures the most even comparisons possible across the field over the whole event.
The final was closely fought this year, and the competitors were closely bunched at the top. A good second session saw Catherine Jagger and myself (Cambridge) home, closely followed by Derek Oxbrow and Kath Haddock (Cottenham) and Harold Bergson and Paul Huggins (University). As the latter cannot make the Corwen in June, their place will be taken by Philip and Sally Wraight (Cambridge) who finished fourth.
Returning to the play problem. Should we play South for a holding of J9 or J109? Given we know North had three spades and South one, the original odds of these holdings in isolation are 1.24% to 1.77% respectively. However, there are two orders in which you could play your cards with the former and six ways you could play your cards with the latter. Assuming South plays his cards randomly from either holding, he would play the 9 then the J 1/2 the time from J9 and 1/6 of the time from J109. Therefore you should finesse because 1.24/2 is greater than 1.77/6. In practice, I suspect few players will play the J first from J9, so this tips the odds even further. If you do finesse, it works and you can't go wrong in hearts (South has AQ) so you will make your contract. I played for the drop and went off.
[I'm always a bit suspicious of secondary inferences in these `restricted choice' positions. If playing the 9 then the J is more likely to indicate a doubleton than playing the J then the 9, it's right for a J109 holder to play this way, and not at random. I don't think you can beat the a priori odds, but South's two discards and silence in the auction might lead one to do the wrong thing. (JM)]