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

Alexis Coyette, Charles Modera, Candy Sonveaux, Judicaël Mohet, Francçois-Grégoire Bierwart, Sylverio Pool Marquez, Jarod Ketcha Kouakep, Cédric Simal, Komlan Fiagbe, Violaine Piengeon, Martin Moriamé, Justine Bodart, Marie Dorchain, Maxime Lucas, Rommel Tchinda Djeudjo, Gianluca Peri, Eve Tilman

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.

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

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.

Paper Structure

This paper contains 22 sections, 22 equations, 1 figure, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Methods
  3. The Bradley-Terry model
  4. The BT model on directed hypergraphs
  5. Comparison with other works
  6. Generalized Bradley-Terry Model
  7. Plackett-Luce Model
  8. Experiments
  9. Synthetic Data
  10. Games of Whist
  11. Conclusion
  12. Full derivations and pseudocode
  13. Classical Bradley-Terry model
  14. Hypergraph Bradley-Terry model
  15. Updated equation for the Generalized Bradley-Terry model
  16. ...and 7 more sections

Figures (1)

  • Figure 1: Performance of our method on synthetic data. Left: Pearson Correlation between fitted strengths $\hat{s}_i$ and true strengths $s_i$. We plot the median over $100$ replications of the correlation for multiple numbers $n$ of players and $m$ of hyper-edges. The colored bands around the points indicate the upper and lower quartiles. Right: Median execution time of the algorithm for multiple values of $n$ and $m$. Medians are computed over $100$ replications.