Play Like the Pros? Solving the Game of Darts as a Dynamic Zero-Sum Game

TL;DR

This paper models the game of darts as a dynamic zero-sum game, demonstrating how strategic play influences winning probabilities, especially in professional matches, and introduces novel skill estimation methods based on match data.

Contribution

It is the first to formulate and solve darts as a dynamic zero-sum game and to estimate player skills using a new dataset of professional matches.

Findings

Playing strategically increases win probability by 0.2%-0.6% in single legs.

Strategic play can increase win chances by up to 2.3% in best-of-35 matches.

The study highlights the importance of strategy in professional darts.

Abstract

The game of darts has enjoyed great growth over the past decade with the perception of darts moving from that of a pub game to a game that is regularly scheduled on prime-time television in many countries including the U.K., Germany, the Netherlands, and Australia among others. The game of darts involves strategic interactions between two players but to date the literature has ignored these interactions. In this paper, we formulate and solve the game of darts as a dynamic zero-sum-game (ZSG), and to the best of our knowledge we are the first to do so. We also estimate individual skill models using a novel data-set based on darts matches that were played by the top 16 professional players in the world during the 2019 season. Using the fitted skill models and our ZSG problem formulation, we quantify the importance of playing strategically, i.e. taking into account the score and strategy of one's opponent, when computing an optimal strategy. For top professionals we find that playing strategically results in an increase in win-probability of just 0.2% - 0.6% over a single leg but as much as 2.3% over a best-of-35 legs match.