How to Lose with Least Probability

TL;DR

This paper analyzes a two-player game involving biased coin tosses, quantifying the first player's advantage and identifying the coin bias that minimizes this advantage.

Contribution

It introduces a mathematical framework to compute the first player's advantage and finds the bias that minimizes this advantage in the game.

Findings

First player advantage varies with coin bias.

Bias minimizing the first player's advantage is identified.

Quantitative analysis of game fairness based on coin bias.

Abstract

Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin the player going first certainly wins. For other coin biases, the player going first has the advantage, but the advantage depends on the coin bias. We calculate the first player's advantage and the coin bias minimizing this advantage.