Playing Several Patterns Against One Another

TL;DR

This paper analyzes a multi-player pattern matching game, providing methods to compute winning probabilities and game duration distributions, extending previous work with simplified approaches.

Contribution

It introduces a novel approach to calculating winning probabilities and durations in multi-player pattern matching games, building on and simplifying prior results.

Findings

Computed exact winning probabilities for each player.

Derived the distribution of game durations.

Extended previous models with simplified methods.

Abstract

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning this game, and find the distribution of the game's duration. Our presentation is an extension (and perhaps a simplification) of the results of Blom and Thornburn.