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.

One of the oldest mythological fables tells of Mercury playing at dice with Selene and winning from her the five days of the epact (thus totaling the 365 days of the year and harmonizing the lunar and solar calendars).

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.

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.

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