On the Probability of Magnus Carlsen reaching 2900

TL;DR

This paper uses probabilistic models, including Brownian motion, to estimate the likelihood of Magnus Carlsen reaching a 2900 Elo rating and discusses implications for the K-factor in chess rating systems.

Contribution

It applies probabilistic methods and Brownian motion modeling to estimate Magnus Carlsen's chances of reaching 2900 Elo and explores policy implications for the K-factor in chess ratings.

Findings

Provides probabilistic estimates of Carlsen reaching 2900 Elo

Analyzes the impact of K-factor choices on rating dynamics

Offers insights into rating system policy considerations

Abstract

How likely is it that Magnus Carlsen will achieve an Elo rating of $2900$? This has been a goal of Magnus and is of great current interest to the chess community. Our paper uses probabilistic methods to address this question. The probabilistic properties of Elo's rating system have long been studied, and we provide an application of such methods. By applying a Brownian motion model of Stern as a simple tool we provide answers. Our research also has fundamental bearing on the choice of the $K$-factor used in Elo's system for GrandMaster (GM) chess play. Finally, we conclude with a discussion of policy issues involved with the choice of $K$-factor.