The French philosopher Pierre-Hyacinthe Azaïs (1766-1845) formalized the statement that good and evil fortune are exactly balanced in that they produce for each person an equivalent result.

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.

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

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.

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.

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.

In our most Puritan of society, gambling-like other pleasures-is either taxed, restricted to certain hours, or forbidden altogether. Yet the impulse to gamble remains an eternal aspect of the irrationality of man. It finds outlets in business, war, politics, in the formal overtures of the gambling casinos, and in the less ceremonious exchanges among individuals of differing opinions.