Win Probabilities After Game 9

A very quick draw in Game 9 brings us one step closer to the end. We are looking at 11 games at the least, and Magnus Carlsen’s chances of winning stay roughly the same the closer we get to the end. He now has an 89.2% chance of winning using the ratings only model and 84.6% using the adjusted model, so it is hard for him to improve the chances without actually clinching the match. The likely outcomes are as follows:

Expected match win following game 9 using the ratings only model.

Expected match win following game 9 using the ratings only model.

Expected match win following game 9 using the adjusted model.

Expected match win following game 9 using the adjusted model.

What we see is that Carlsen’s chances of winning outright have remained mostly constant since his win in Game 6, and that Anand’s chances are decreasing with each draw and his chances now are very much to try to force a tie-break. Game 10 is tomorrow.

Rating model Adjusted model
Carlsen win 82.3% 74.7%
Anand win 4.0% 5.5%
Tie-break 13.7% 19.8%

Norsk forklaring av utregningene.

PS:

Someone on Reddit asked what the probability of of Anand winning at least one game in the match was (before the start). If we know the match is going to 12 games, that can be calculated pretty easily to show that there’s a roughly 88% chance of him winning at least one game (using the probabilities in the adjusted model). However, there was less than 50% chance that the match would go to 12 games, so it’s not that easy to come up with the answer.

For fun I ran the model with the initial assumptions to try to answer that question, and what the model showed was that Anand had an initial probability of winning at least one game of 81.6%. So a pretty high chance indeed.

(Please let me know if you want me to write a longer post on how that probability was obtained).

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