Theory of Optimal Gammas

Abstract

Ross¹ asks for a definition of the goodness of a game. A reasonable answer, though presumably incomplete, is that a game is good in so far as it involves skill. A measure, γ, for the degree to which a game is one of skill may also be of legalistic interest in those countries where gambling is somewhat against the law. Several years ago I suggested a definition for γ, and it may now be appropriate to publish it. The definition is relative to a population of learners and trainers and to the number of learners, and is relative to the training time and to the duration of play. If we assume all these parameters to be fixed we should find that the players would fall into γ grades, C ₁, C ₂, C ₃, …, C _γ such that, on average, a player in grade C _g would have a probability of say 2/3 of beating a player in grade C _g+1 (g = 1, 2, …, γ − 1). The number, γ, of grades, is then the suggested measure of the degree to which the game is one of skill. It is not a good measure of difficulty, since some games, such as the child's game of ‘boxes’, are so difficult for human beings that training and ability do not count for much.