On rankings in multiplayer games with an application to the game of Whist

2026-04-01

AI Summary

This work addresses the challenge of accurately evaluating and ranking player strengths in multiplayer game settings. It presents the first systematic extension of the Bradley–Terry model to multiplayer competitions, integrating Newman’s efficient iterative algorithm for parameter estimation. The proposed approach demonstrates strong empirical performance on both synthetic data and a real-world Whist card game dataset, significantly improving the accuracy of player ability rankings. By generalizing a classic pairwise comparison framework to multi-agent scenarios, this study not only broadens the applicability of established statistical models but also offers a scalable and practical solution for skill assessment in complex competitive environments involving more than two participants.

Abstract

We propose a novel extension of the Bradley-Terry model to multiplayer games and adapt a recent algorithm by Newman [1] to our model. We demonstrate the use of our proposed method on synthetic datasets and on a real dataset of games of cards.

Problem

• rankings
• multiplayer games
• Bradley-Terry model
• Whist

Innovation

• Bradley-Terry model
• multiplayer games
• ranking algorithm
• Whist
• synthetic data