Cloud Quantum Coin-Tossing Gambling

Abstract

Quantum computers are an alternative way to create multipartite probabilities for a game as a function of participant’s inputs. In some situations, quantum gambling could be an improvement over the predictability of certain types of random number generators. However, NISQ computers require a protocol whose expected statistical gains (losses) can be confirmed empirically given the participants’ inputs. A zero-sum coin-tossing protocol with Nash equilibrium [1] is tested with a quantum computer where hypothetical players enter parameters, in their respective qubits, and are compensated 1 or R coin(s) after each outcome. In theory, independently of R, the protocol implies that there is no gain improvement for a player when the other maintains the equilibrium parameter; gain is zero or better for the player maintaining it. However, outcomes obtained with several setting combinations imply Nash equilibrium only when R is a small fraction. For R≫1, given thousands of outcomes, there is Nash-like equilibrium such that a player may not improve gain significantly by changing the parameter if the other maintains it, that is, losses (gains) are considerably minimized with the parameter. The data suggests that gains (losses) would be expected statistical functions of the participants’ choices if two played in this manner.