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.
翻译：Magnus Carlsen的Elo评级为2900美元的可能性有多大?这是Magnus的目标,也是国际象棋界当前非常感兴趣的。我们的论文使用了概率方法来解决这个问题。我们研究了Elo评级制度的概率性能,我们提供了这种方法的应用方法。我们用Brown的Brown运动模型作为简单的工具提供了答案。我们的研究对于选择Elo系统中用于GrandMaster(GM)国际象棋游戏的K$因素也有着根本的影响。最后,我们讨论了与选择$K-master(GM)游戏有关的政策问题。
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