How many coin tosses would you need until you get $n$ Heads or $m$ Tails?

TL;DR

This paper investigates the expected number of coin tosses needed to reach specified counts of Heads or Tails, using symbolic computation and providing a Maple package for efficient calculations.

Contribution

It introduces a computational approach and a Maple package for analyzing the stopping times in coin toss sequences with specified head/tail counts.

Findings

Provides formulas for expected number of tosses to reach n Heads or m Tails

Includes a Maple package for fast symbolic computation of moments

Analyzes related problems of reaching n Heads and m Tails

Abstract

We harness both human ingenuity and the power of symbolic computation to study the number of coin tosses until reaching $n$ Heads or $m$ Tails. We also talk about the closely related problem of reaching $n$ Heads and $m$ Tails. This paper is accompanied by a Maple package that enables fast computation of expectations, variances, and higher moments of these quantities.