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.

Treatment of the apparently whimsical fluctuations of the stock quotations as truly non stationary processes requires a model of such complexity that its practical value is likely to be limited. An additional complication, not encompassed by most stock market models, arises from the manifestation of the market as a nonzero sum game.

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.

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.

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.

Coin matching and finger flashing were among the first formal games to arise in the history of gambling. The class of Morra games extends back to the pre-Christian era, although not until comparatively recent times have game-theoretic solutions been derived.