Stronger opposition may make it easier to win

Suppose that in a three-player tournament the strongest player, A(1), meets the winner of the match between A(2) and the weakest player, A(3) It is shown that, for A(1) and A(2) of fixed strength, A(1)'s chances of winning may be increased if A(3) is replaced by a stronger player. The paradox is studied with special emphasis on probability models important in the method of paired comparisons.