Average Controllability Measures for Solitaire Games

We discuss several ways to measure the extent to which a player can exert control over a one-player game, relating them to the existing literature on the "skill vs chance" dichotomy. We focus on measures that depend only on the rules of the games, and not on how people actually play them. After presenting a set of desirable properties, we show that two statistical measures of effect size satisfy them and we estimate the value of such measures on several wellknown games.