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## Arvind Narayanan's journal

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How to cheat at chess [Jun. 30th, 2005|11:27 pm]
Arvind Narayanan
 [ Tags | chess ]

Specifically, how to improve your online chess rating.

The skill of a chess player is measured by their Elo rating, named after a guy called Elo and uses the logistic distribution. Although statisticians tend to needlessly confound the issue in the hope of keeping lay people in the dark about the arcana of their profession, all that there is to know about the rating system can be summed up thusly: "The probability of player A beating player B is proportional to the power of their rating difference". Equivalently, if players A, B, and C are rated 2400, 2300 and 2200 respectively, then A has the same chance of beating B as B has of beating C. Childishly simple, and even obvious in retrospect.

Elo's original method using the normal distribution wasn't very accurate, and you could beat the system by always playing against higher rated players, which would give you a higher expected performance than what the system predicted. However the logistic distribution doesn't have this problem, so it isn't clear if there's a way to maintian a higher rating than you deserve.

The problem with any rating system, though, is that it assumes that a player's performances in successive games are uncorrelated. i.e, how you play each game is not in any way influenced by the previous game. This assumption is completely accurate in games of chance, which is why you can never win against a casino in the long run. But it is a very poor approximation to human behavior. Players tend to have winning or losing streaks, particularly in blitz/lightning games, based on their level of concentration. So this gives you a very simple strategy: always play someone who's on a losing streak (more concretely, always play someone who's losing significantly more games than they would be expected to based on the rating difference).

Its not always easy to do this. When I'm playing against a lower rated player, my policy is to stop if I lose a game. Against a higher rated player, I stop if I lose two games in a row. Balancing such rational considerations with the thirst for "revenge" can be challenging.

My own rating regularly fluctuates by over 200 points. Assuming everyone's rating fluctuates that widely, by following my system, it is possible to pick your opponents so that their performance is over 100 points worse than what it would be if you picked them randomly! Equivalently, you can maintain your own rating at about 100 points more than your true rating.

There are so few players on FICS with a rating over 2000 that I often don't get much choice picking opponents. Maybe I'll cough up the \$25 for an ICC membership.