Dubious Logic

Unlocking the combinations

This deal came up at a recent club pairs evening. The auction was brief, the play perhaps even briefer but the discussion afterwards filled the gap left by the earlier brevity.

At his second turn, South had something of a problem with his good looking hand. Two diamonds was an intelligent shot and, rather than confuse with some spade bid, so was his pass of three no-trump at matchpoint. With no great lead, I started the diamond ten and partner won the queen and switched to a low club. North won in hand, played the heart queen then low to the ten. There was now no way not to take the rest of the tricks and North-South had a fine score. What then provoked the discussion?

It was North's play in the heart suit. Should he play as he did, taking a finesse rather than play from the top? Well clearly so - if he knew where the cards were – but what is the best play with that holding? And, sat at the table as you are, how would you work it out?

The short-cut is to know these things as facts but perhaps you might reasonably think your memory better served elsewhere. In fact I'd say bridge players are required to remember very little - but you may not be spared a little counting. The way to think about through these choices is to count where each is successful, ignoring where both succeed or fail.

So here, taking the finesse gains over playing from the top when East holds Jxxx and West xx. Let's count all those cases. If you imagine West's two small cards listed highest first, the eight spot can have four cards with it, then the second highest three, down to the single case of the two lowest – four, three, two and one sums to ten. The finesse loses when West hold Jx – there are five of those, the knave accompanied by each small card. So we still have five arrangements (ten minus five) in the plus column. But we will also lose to West's Jxx – embarrassingly when the suit is 3-3. There are ten of those too, the same as low doubletons but alongside the knave.

So the finesse is a net loser against playing out the top cards, maybe you 'knew' that because it felt right, but there are several things worth considering. The difference though marked (it's about 10%) is still worth backing against if you have an inference from a defender – an odd lead perhaps. There might have been a case for that here, perhaps East had short clubs and so long hearts. Also, you need to keep the technique ready for every now and then non-intuitive holdings will arise; how, for example would you play this combination: ♥109 opposite ♥AKQ32?

Published Saturday 4.Feb.2006