ELO System for Skat and Other Games of Chance

TL;DR

This paper introduces a new ELO ranking system tailored for Skat and similar games, addressing challenges like incomplete information, chance, and existing scoring systems to improve player skill assessment.

Contribution

A novel ELO system designed specifically for trick-taking card games that accounts for game-specific factors and aligns with established scoring methods.

Findings

Effective in ranking players in Skat tournaments

Addresses issues of incomplete information and chance

Aligns with existing scoring systems

Abstract

Assessing the skill level of players to predict the outcome and to rank the players in a longer series of games is of critical importance for tournament play. Besides weaknesses, like an observed continuous inflation, through a steadily increasing playing body, the ELO ranking system, named after its creator Arpad Elo, has proven to be a reliable method for calculating the relative skill levels of players in zero-sum games. The evaluation of player strength in trick-taking card games like Skat or Bridge, however, is not obvious. Firstly, these are incomplete information partially observable games with more than one player, where opponent strength should influence the scoring as it does in existing ELO systems. Secondly, they are game of both skill and chance, so that besides the playing strength the outcome of a game also depends on the deal. Last but not least, there are internationally established scoring systems, in which the players are used to be evaluated, and to which ELO should align. Based on a tournament scoring system, we propose a new ELO system for Skat to overcome these weaknesses.