An Experimental Mathematics Perspective on the Old, and still Open, Question of When To Stop?

TL;DR

This paper investigates the decision-making problem in a coin-tossing game, exploring when to stop to maximize expected payoff, using experimental mathematics methods to analyze various strategies for an open problem.

Contribution

It applies experimental mathematics to analyze stopping strategies in a coin-tossing game, providing new insights into an open problem in optimal stopping theory.

Findings

Different strategies have varying success rates.

Experimental analysis offers new perspectives on the open problem.

Insights into optimal stopping points in coin-tossing games.

Abstract

In a recent article in American Scientist, Theodore Hill described a coin-tossing game whose pay-off is the number of heads over the total number of throws. Suppose that at a given point during the game you have 5 heads and 3 tails, should you stop and get 5/8, or should you keep playing, hoping to get a better score? This is still an open problem. In the present article, we explore different strategies to this game from the Experimental Mathematics perspective.