Generally, a betting system for which each wager depends only on present resources and present probability of success is known as a Markov betting sy… - Richard Arnold Epstein

Because the fluctuations in the composition of the deck as it is dependent over successive (and dependent) trials, it is intuitively apparent that altering decisions or the magnitude of the wager or both in accordance with the fluctuations should prove advantageous to the player.

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 hope of a positive expected gain lies in detecting a wheel with sufficient bias.