Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory

Abstract

In this work, we focus on using reinforcement learning and game theory to solve for the optimal strategies for the dice game Pig, in a novel simultaneous playing setting. First, we derived analytically the optimal strategy for the 2-player simultaneous game using dynamic programming, mixed-strategy Nash equilibrium. At the same time, we proposed a new Stackelberg value iteration framework to approximate the near-optimal pure strategy. Next, we developed the corresponding optimal strategy for the multiplayer independent strategy game numerically. Finally, we presented the Nash equilibrium for simultaneous Pig game with infinite number of players. To help promote the learning of and interest in reinforcement learning, game theory and statistics, we have further implemented a website where users can play both the sequential and simultaneous Pig game against the optimal strategies derived in this work.