von Neumann and Newman Pokers with Finite Decks

TL;DR

This paper explores finite and infinite versions of simplified poker games, using computational methods to analyze strategies and outcomes, and provides Maple implementations for these analyses.

Contribution

It introduces finite analogs of von Neumann and Newman poker games and develops computational tools for their analysis.

Findings

Analysis of finite and infinite poker variants

Development of Maple packages for game computation

Insights into strategic differences between finite and infinite decks

Abstract

John von Neumann studied a simplified version of poker where the "deck" consists of infinitely many cards, in fact, all real numbers between $0$ and $1$. We harness the power of computation, both numeric and symbolic, to investigate analogs with finitely many cards. We also study finite analogs of a simplified poker introduced by D.J. Newman, and conclude with a thorough investigation, fully implemented in Maple, of the three-player game, doing both the finite and the infinite versions. This paper is accompanied by two Maple packages and numerous output files.