In many hands, declarer is faced with a choice of several possible lines of play. In such cases, he should select the approach that offers the greatest chance of success, even if that chance is not a very good one.
Take this case where West found the most effective lead against six hearts, a trump. Without this lead, South could have gotten home safely by cashing the ace of diamonds and leading the queen through West.
However, the opening trump lead completely altered the situation. Now the ruffing finesse in diamonds would do declarer no good: After West covered the queen with the king and dummy ruffed with its last trump, South would still be left with a diamond loser as well as a spade loser.
Declarer therefore considered his remaining options. One possibility was to win the opening trick in dummy and lead a diamond to the queen. If the finesse succeeded, he could next cash the ace of diamonds and ruff a diamond in dummy, hoping that the king would fall on either the second or third round.
The only viable alternative to this was to try to establish dummy's clubs by cashing the A-K, playing the ace of diamonds, ruffing a diamond and ruffing a club. If the opposing clubs broke 3-3, South would later discard a spade and a diamond on dummy's good clubs to make the slam, losing only a diamond to the king.
Confronted with these two options, declarer had to rely on percentages. He knew that a 3-3 club division would occur only 36 times in 100 — certainly not the best of odds. But he also knew that his chance of winning a diamond finesse and then dropping the king doubleton or tripleton with eight diamonds missing was even worse — roughly, a bit more than 10%.