A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.

While no rigorous proof of an optimal strategy has been achieved, Robbins has proposed the principal of "staying on a winner" and has shown it to be uniformly better than a strategy of random selection.

Generally, a betting system for which each wager depends only on present resources and present probability of success is known as a Markov betting system.

The assumption that individuals act objectively in accordance with purely mathematical dictates to maximize their gain or utility cannot be sustained by empirical observation.

One of the oldest mythological fables tells of Mercury playing at dice with Selene and winning from her the five days of the epact (thus totaling the 365 days of the year and harmonizing the lunar and solar calendars).

The essence of the phenomenon of gambling is decision making. The act of making a decision consists of selecting one course of action, or strategy, from among the set of admissible strategies.

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.