Discrete bidding games

TL;DR

This paper explores discrete bidding variations of combinatorial games, analyzing their properties, differences from real-valued bidding, and suitability for recreational play, with specific focus on games like Tic-Tac-Toe.

Contribution

It introduces and analyzes discrete bidding game variants for well-known games, highlighting differences from Richman games and demonstrating their recreational potential.

Findings

Discrete bidding games differ significantly from Richman games.

Discrete bidding versions of classic games are suitable for recreational play.

Analysis of Tic-Tac-Toe illustrates key differences between discrete and real-valued bidding.

Abstract

We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences between discrete bidding games and Richman games, which allow real-valued bidding. Unlike Richman games, discrete bidding game variations of many familiar games, such as chess, Connect Four, and even Tic-Tac-Toe, are suitable for recreational play. We also present an analysis of Tic-Tac-Toe for both discrete and real-valued bidding.