Random Perturbation in Games of Chance

In this article, we consider a problem in games of chance. Our result shows that two losing games ( A and B , in the sense of a negative expectation) can become a winning game (in the sense of a positive expectation), when the two are played in a suitable alternating order; for example, ABBABB ....... By using a regrouping technique in Automata and the concept of Markov chain embedding, we give proof of this gambling result. A signal-to-noise ratio is also presented to explain this counterintuitive phenomenon.