Critical Repetition Frequency

The Critical Repetition Frequency (CRF) is a term used in gambling research to distinguish games of skill from games of chance. It is defined as the threshold of repetitions at which a mixed game becomes predominantly influenced by skill rather than by chance.

Calculation and interpretation of the CRF

The CRF is based on the idea that skill adds up while the chance elements cancel out in the long run.

The CRF is the quantitative threshold at which the skill to chance ratio of the outcome of a game is exactly 50%. If a game is repeated more often than the CRFi, it is a game of skill, and, if it is repeated less often, it is a game of chance (for the individual player i).

If the statistical spread and the expected value of the player are known, it is possible to calculate the CRF by the following formula:

$CRF_{i}={(\lambda\sigma_{1i})^2 \over {{E_{1i}^A}}[x]^2}.$

The expression in the numerator describes the chance by using the variance of the scoring per game repetition for player i, λ being the confidence coefficient. The expression in the denominator is the expected value of a game x played by individual i, adjusted for any fees and represents the relative skill of this player against his opponents.

Implementation

The CRF is of particular interest to mixed games, e.g. poker, because the regulations of games depend on the predominance of skill or chance. For the legislator’s decision, whether a game is to be classified as a game of skill or a game of chance, the CRF acts as an objective indicator which can also be converted into the playing time a player needs to reach the threshold of a skill game by multiplying the repetitions with its length.

References

• Ingo Fiedler, Jan-Philipp Rock, 2009, Quantifying Skill in Games – Theory and Empirical Evidence for Poker, Gaming Law Review and Economics, February 2009 (13), p. 50-57.

• Jan-Philipp Rock, Ingo Fiedler, 2008, Die Empirie des Online-Pokers – Bestimmung des Geschicklichkeitsanteils anhand der kritischen Wiederholungshäufigkeit, Zeitschrift für Wett- und Glücksspielrecht, p. 412-422.

External links

• Institute of Commercial Law, University of Hamburg