ABSTRACT
In all games the outcome is determined by a mixture of chance and skill. The world chess champion could in a single game lose to a lesser player, just because he is tired, has a headache, or is distracted by a lady in a red blouse. It is possible to define skill in such a way that resistance against fatigue, illness and distraction are included. In that case, skill would be a continually fluctuating property. But usually the concept of skill refers to an underlying, more or less stable property that emerges when short-term variations are levelled off. When two top chess players like Karpov and Kasparov play 24 games, one player just does not win nor the other lose all the time. A world chess championship consists of 24 games, just to exclude the fluctuating elements, and to let the underlying small but structural difference of skill emerge. The same is true for bridge, soccer, tennis, and many other spons and games of skill. In the following we will assume that skill is a latent trait, and that playing the game provides a test of this skill, obscured by measurement error. We will call the component of error: chance. No game can ever be an error-free measurement of skill, hence every game involves a
mixture of chance and skill. In this chapter I will discuss whether the two components can be usefully distinguished, and how this should be done.
