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 earliest full-length account of a chariot race appears in Book xxiii of the Iliad.

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.

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.

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.

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

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

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.