Note on a Coin Tossing Problem Posed by Daniel Litt

TL;DR

This paper analyzes a coin-tossing problem, deriving recursive formulas and algorithms to compute the difference in wins between players as the number of tosses increases, contributing to understanding probabilistic outcomes.

Contribution

It introduces recursive identities and algorithms for calculating score differences in a coin-tossing game, offering new analytical tools for such problems.

Findings

Derived recursive formulas for score differences.

Provided algorithms to compute sequence counts with specific score differences.

Simplified the calculation of excess wins in coin-tossing scenarios.

Abstract

We present an analysis of a coin-tossing problem posed by Daniel Litt which has generated some popular interest. We demonstrate a recursive identity which leads to relatively simple formulas for the excess number of wins for one player over the other together with its increments as the number of coin tosses increases. Formulas and recursive algorithms are provided to calculate the number of sequences with any given point-score difference.