A Markovian approach to darts

The aim of this paper is to study and simulate a classical Darts-501 match using Markov chains to describe score evolution. The Markovian approach, indeed, fits the problem since the probability of obtaining a certain score at each step depends only on the result of the last throw and on the score at the previous step. We first study the single dart throw, in order to determine the probability distribution on the dartboard and calculate the probability of hitting each score region, fixed an aiming point; these preliminary results have already been studied in other works. Then, we determine the best strategy the player would choose at each step and we construct the transition matrix of the Markovian process describing the score. We simulate the whole match obtaining results about the average number of steps needed to win it and about the chosen strategies at each step, that both depend on player skill. It is interesting to observe the influence the variance on the player throws has on these data.