Random Perturbation in Games of Chance
Cheng–Der Fuh, Yeong‐Nan Yeh · Studies in Applied Mathematics · 2001
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.