On getting unlucky

Abstract

This paper addresses the question of how unlucky a rational actor can get while attempting to solve a problem without any guarantee of success, compared to a sure-thing alternative. It presents a mathematical model to calculate the probability of an actor taking longer than a specified amount of time to solve the problem while still acting rationally. The paper considers various scenarios, including the actor’s ability to give up and switch to the sure-thing alternative at any time. It concludes that a rational actor has a probability of at most 1/exp(N-1) of taking N times longer than the sure-thing alternative. – AI-generated abstract.