 
Summary: Poker, Chance and Skill
Noga Alon
1 Introduction
The question if poker is a game of skill or a game of chance received a considerable amount
of attention mainly because of its potential legal implications. See, for example, [3] and
its many references. Most of the material dealing with the subject focuses on legal issues,
and only briefly touches the question from a purely scientific point of view. In the present
article we address the question as a scientific one. To do so, we provide a detailed analysis of
several simplified models of poker, which can be viewed as toy models of Texas Hold'em, the
most popular variant of poker. The advantage of considering these simplified models is that
unlike the real game, they are simple enough to allow a precise mathematical analysis, and
yet there is every reason to believe that this analysis captures many of the main properties
of the far more complicated real game, and enables us to estimate the advantage of skilled
players over less skilled ones. The analysis suggests that skill plays an important role in
poker. As explained in the second half of the article, this fact, together with the Central
Limit Theorem, imply that skill is the major component in deciding the results of a long
sequence of hands. As the common practice is to play many hands, the conclusion is that
poker is predominantly a game of skill.
The article is organized as follows. In Section 2 we describe the rules of Texas Hold'em
which is probably the most popular poker game played in casinos and cardrooms through
