(Not) Throwing the Game - An Application of Markov Decision Processes and Reinforcement Learning to Optimising Darts Strategy

Abstract

This article determines an aimpoint selection strategy for players in order to improve their chances of winning at the classic darts game of 501. Although many studies have considered the problem of aimpoint selection in order to maximise the expected score a player can achieve, few have considered the more general strategical question of minimising the expected number of turns required for a player to finish. By casting the problem as a Markov decision process and utilising the reinforcement learning method of value iteration, a framework is derived for the identification of the optimal aimpoint for a player in an arbitrary game scenario. This study represents the first analytical investigation of the full game under the normal game rules, and is, to our knowledge, the first application of reinforcement learning methods to the optimisation of darts strategy. The article concludes with an empirical study investigating the optimal aimpoints for a number of player skill levels under a range of game scenarios.