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.

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).

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.

There are no conventional games involving conditions of uncertainty without risk.

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.

A weakness of the random-walk model lies in its assumption of instantaneous adjustment, whereas the information impelling a stock market toward its "intrinsic value" gradually becomes disseminated throughout the market place.