Penney's game between many players

TL;DR

This paper generalizes Penney's game to multiple players, deriving probability functions and extending Conway's formula to accommodate many participants in the game.

Contribution

It introduces a combinatorial approach to compute winning probabilities for multiple players and generalizes Conway's formula beyond two-player scenarios.

Findings

Derived probability functions for each player in multi-player Penney's game

Extended Conway's formula to cases with many participants

Provided a combinatorial framework for analyzing complex Penney's game scenarios

Abstract

We recall a combinatorial derivation of the functions generating probability of winnings for each of many participants of the Penney's game and show a generalization of the Conway's formula to this case.