Games of skill are one-player games. Since they do not involve any other player, and when they involve nature it is under the condition of certainty, they are not really regarded as genuine games. Nature does not constitute a genuine second player, as in the case of games of chance, because nothing nature does affects the outcomes of the player's choices. The solitary player in games of skill knows for certain what the outcome of any choice will be. The player completely controls the outcomes. Solving a crossword puzzle is a game of skill, but playing golf is not, since the choices that the player makes do not lead to outcomes that are perfectly predictable. Golf is a game of chance involving uncertainty, although some would call it a form of moral effort! Nature influences the outcomes to an extent which depends on the player's skill, but the probability of which is not known.

The operation of single-player decision making is discussed in the following sections. The problem of linear programming and optimisation, where a player wishes to optimise some utility function within a set of constraints, is considered with the help of some realistic examples. The application of some basic concepts from calculus, including the Lagrange method of partial derivatives, is also discussed.

Linear programming, optimisation and basic calculus

The branch of mathematics known as linear programming or optimisation is devoted to games of skill.