Mathematics – Optimization and Control
Scientific paper
2000-07-21
Mathematics
Optimization and Control
35 page LaTeX article, with figures. See also http://pierre.albarede.free.fr/
Scientific paper
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.
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