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.

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

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 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.

From a rational standpoint, it might be expected that man should be far more willing to express financial confidence in his skills rather than risking his earnings on the mindless meanderings of chance. Experience, however, has strongly indicated the reverse proposition to hold true.