Variance decompositions for extensive-form games

TL;DR

This paper introduces a method to quantify how much a player's actions influence game outcomes by decomposing variance, with applications demonstrated in poker to distinguish randomness from player skill.

Contribution

It provides a novel closed-form expression and estimator for variance attributable to individual players in extensive-form games, enhancing game analysis and design.

Findings

Variance in poker outcomes is minimally affected by randomness in dealt cards.

Variance decomposition can measure other properties of games.

Method applicable to various extensive-form games.

Abstract

Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the outcome attributable to a player of the game. We analyze poker hands to show that randomness in the cards dealt has little influence on the outcomes of each hand. A simple example is given to demonstrate how variance decompositions can be used to measure other interesting properties of games.