Simulating a die roll by flipping two coins

TL;DR

This paper presents a method to simulate an n-sided die roll using one biased coin flip and a logarithmic number of fair coin flips, optimizing the process of generating uniform random outcomes.

Contribution

It introduces a novel algorithm that efficiently simulates an n-sided die with minimal coin flips, combining biased and fair coin flips in a new way.

Findings

Efficient simulation of n-sided die with fewer coin flips.

Uses one biased coin flip and logarithmic fair coin flips.

Provides a practical method for fair random number generation.

Abstract

We show how to simulate a roll of a fair $n$-sided die by one flip of a biased coin with probability $1/n$ of coming up heads, followed by $3\lfloor\log_2 n \rfloor+1$ flips of a fair coin.