From the perspective of mathematical game theory is in memory to a zero-sum game with perfect information. With only two players so that each item has a uniquely determined value at which it is the expected value of the excess of obtained pairs of the currently withdrawing player with flawless game on both sides. In this case, the error-free game involves not only remembering previously exposed cards. Rather Memory allows a strategic influence. This refers in particular, as a second card sometimes not uncover an unknown card at random. The reason for such an approach is that in certain situations the advantage thus achieved because only a small probability of a random hit is too low compared to the risk to deliver the enemy information about the location of a complete pair.
The Memory Healer program review

A complete analysis of recursive two-person memories was the first time in 1993 by Uri Zwick and Michael Paterson published [3], where the results had been previously found in 1983 by Sabih Gerez without publication [4]. Since in some very late endgame situations on both sides destructive behavior would be optimal, in which both players only discover already known cards, the tournament rules were adjusted accordingly [5].