The odds change with the bidding

In Thinking About Quality,

Clare Crawford and Lloyd Dobyns wrote, “Nothing in life is static; it either gets better, or it gets worse.” At the bridge table, a priori odds are static, but the actual odds change — get more or less likely — based on both the bidding and the cards that have been played. Take today’s NorthSouth diamond suit. Needing to avoid a loser in it, is it better to cash the ace and king or to finesse through, say, West on the second round? Does the better play change when the auction tells declarer that East started with six hearts and West with three? North had a nasty decision after East opened with a weak two-bid, and West gave a pre-emptive raise. To double with only two spades was unappealing, and bidding three no-trump with a doubleton heart was dangerous. North’s jump to four no-trump showed a minor two-suiter. (Yes, he ought to have been at least 5-5, but he decided this was the worst of the evils. Note that three notrump cannot make.) When needing these numbers, I go to Richard Pavlicek’s excellent website, rpbridge.net. Assuming I did it correctly, if you know nothing about the deal, playing out the king and ace is better than finessing on round two by just 1.69 per cent. However, given the stated heart break, the finessing odds are 6.62 per cent higher than cashing the ace and king. When you know one defender has far fewer cards in one suit, play him for a key card in another suit — unless the bidding tells you that he cannot have it!