Play It Again, Sam

Abstract

There are probably few players who are able to optimize their strategies with the help of the simplex algorithm. And moreover, most games people play are much too complex for such calculations to actually be carried out. But can good strategies be found without such calculations. One must say that mixed strategies are as strange to many players as they were to mathematicians for many centuries. Strategic games such as poker, mixed strategies play a central role in usual play. Thus, the concepts of a mixed strategy can be brought into play based on empirical experience. This chapter focuses on a two-person zero-sum game presented in normal form. It sets up a series of games in which both players attempt to improve their strategies progressively. Each game is played according to the normal rules. Each player seeks a pure strategy that brings the best result against the opponent’s previous average strategy.