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.

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.

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.

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

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.

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.

Reflecting an amalgam of economics, monetary, and psychological factors, the stock market represents possibly the most subtly intricate game invented by man.