Games of chance are one-player games against nature, but ones in which the single player is not making decisions under the conditions of certainty. In other words, nature affects the outcomes resulting from the player's choices in an unpredictable way. Games of chance either involve risk, where the probability of nature's response is known; or involve uncertainty, where the probability of nature's response is not known.

Those who seek to understand games of risk fully cannot but benefit from some knowledge of the concepts which underpin probability theory. It is not strictly necessary, but it is desirable. There are many outstanding texts on probability theory for readers wishing to deepen their understanding of gaming in its more esoteric forms, but the following synopsis should be sufficient for the average non-specialist reader to understand the link between game theory and the probabilistic notions of distribution function and expected value.

The following sections describe some of the underlying concepts of probability theory – probability spaces, distribution functions, random variables and expected value – as a prelude to discussing games of chance involving risk. Subsequently, utility value and games of chance involving uncertainty are considered along with the various minimax strategies used for their solution.