English

A non-iterative algorithm for generalized Pig games

Probability 2018-08-22 v1

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.

Keywords

Cite

@article{arxiv.1808.06707,
  title  = {A non-iterative algorithm for generalized Pig games},
  author = {Fabián Crocce and Ernesto Mordecki},
  journal= {arXiv preprint arXiv:1808.06707},
  year   = {2018}
}