Fate stochastic management and policy benchmark in 421, a popular game

Abstract

Using game and probability theories, I study the French popular game 421, a perfect information stochastic stage game. The problem is to find strategies maximizing the probability of some expected utility. I only solve a player's round against providence, a problem of fate stochastic management: beyond the backward induction solution, bounded complexity motivates heuristic policies. For a unique goal utility, a simple optimal policy, ratchet, is obtained. Its result probabilities are compiled and used, for arbitrary utilities, as the logic of goal identification policies. Various policies appear, close to human behavior, and are exactly evaluated by solving the Kolmogorov equation.