A non-iterative algorithm for generalized Pig games

TL;DR

This paper introduces a polynomial, non-iterative algorithm for solving generalized Pig games by decoupling Bellman equations, enabling efficient computation of game values and strategies.

Contribution

The paper presents a novel polynomial-time algorithm that avoids iterative methods for solving generalized Pig games modeled as Markov decision processes.

Findings

Algorithm requires O(s log(s)) steps, where s is the number of states.

Successfully applied to classical Pig and Piglet variants.

Provides explicit solutions for game values and optimal strategies.

Abstract

We provide a polynomial algorithm to find the value and an optimal strategy for a generalization of the Pig game. Modeled as a competitive Markov decision process, the corresponding Bellman equations can be decoupled leading to systems of two non-linear equations with two unknowns. In this way we avoid the classical iterative approaches. A simple complexity analysis reveals that the algorithm requires O(s log(s)) steps, where s is the number of states of the game. The classical Pig and the Piglet (a simple variant of the Pig played with a coin) are examined in detail.