If a contract depended on say, a finesse, most good players would look for plays that would give a better than 50-50 chance of succeeding. (Unless the finesse was marked by the bidding or early play.)
Most good players would make, or consider making, a safety play to guard against a 4-1 split (except maybe in matchpoints). This occurs with a greater than 28% frequency (or 14%+ if it was relevant with the singleton on one side and not the other).
But I read of a situation in a tournament where a world class declarer took an inordinately long time to study the play of a hand, to the point where his opponents called the tournament director (TD). When the TD asked the player why, the player answered that he had just worked out a way to make the hand against a distribution with only a 2% chance of occurring (a 5-0 trump distribution with the 5 "offset" a finesse).
He looked like a genius when the relevant opponent admitted to having that hand. Apparently, there was little time to play the game out, but the TD awarded the point to the player after the player described his game plan and the opponents conceded, showing down their hands. All the other declarers on that board went down.
Is that unusual? Do good players routinely study ways to guard against 2% chances over the board? Or do most players have a higher threshold, say in the 5%-10% range?