Contract Bridge

Let’s say you have a 50 percent chance of making a contract if you adopt a certain line of play. This is surely not the worst of odds, but, if you are a perfectionist, you should not settle for a mere 50-50 chance of success. Instead, you should look for some other approach that might raise your chances to 75 percent, or even 100 percent, if possible.

The opportunity to apply this principle occurs time and time again. The general idea is that if declarer cannot attain the 100 percent chance he’d like to have, he should look for the next best thing to it.

For example, if you’re declarer at five clubs in this hand, you see you must lose a diamond, almost surely a spade and possibly a heart. What you would like to do is to minimize the chance of losing a trick in hearts, where an ordinary finesse offers only a 50 percent chance of succeeding.

By far your best hope for achieving this goal is to try to set up an endplay. So after ruffing a diamond continuation at trick two, you cross to dummy with a trump and ruff dummy’s last diamond. You then draw a second round of trumps and play the A-K and another spade.

You don’t know which opponent will win the third spade, but you hope it is West. If so, you are sure of making the contract whether he returns a heart or gives you a ruff-and-discard.

In the actual hand, East wins the third spade, which is not ideal but much better than relying on a straight finesse. When he returns a low heart, you play low, which traps West’s queen and puts you on easy street.

Note that even after East wins the third spade, you go down only when West started with both the queen and ten of hearts -- just a 1-in-4 possibility. This is certainly better than taking the straightforward heart finesse by leading to the jack, which has about an even-money chance of losing, and would cost you the contract in the actual deal.