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Topic: Rating of a perfect chess player (Read 6519 times) |
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #45 on: Aug 7th, 2008, 10:21am » |
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on Aug 7th, 2008, 9:52am, omar wrote:| a 200 point differece between a 2600 vs 2800 is actually much higher than 75% winning chance for the higher rated player. Very interesting. |
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That's right. A expected score of 0.75 when there are 40% draws would mean that the stronger player wins 55% of the time and the weaker player wins 5% of the time. If we discard the draws the win ratio is actually 11 to 1 instead of 3:1, which would be a gap of 416 points instead of 191 points.
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omar
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Re: Rating of a perfect chess player
« Reply #46 on: Aug 7th, 2008, 10:23am » |
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on Aug 5th, 2008, 11:05pm, lightvector wrote:If we measure ranks purely by win percentage, then I tend to agree with Fritzlein that a larger board almost certainly means more ranks. Consider if you will, the game of N-iterated Go - play N regular games of 19x19 Go, and the winner is the player who wins more in total. Purely by virtue of involving a greater total number decisions, this will magnify any win percentage differences between players potentially many times if N is large. Essentially, we are doing a statistical sampling. A larger board size should do the same thing. More space, a longer game, more local fights, will give more room for the slightly stronger player to overcome variation and chance.
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Humm. Will the N-iterated Go actually have a larger range of ratings or are the ratings just more accurate? I would tend to think the ratings are just more accurate and the rating range is still the same regardless of how large N is.
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Fritzlein
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Re: Rating of a perfect chess player
« Reply #47 on: Aug 7th, 2008, 10:33am » |
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on Aug 7th, 2008, 10:23am, omar wrote:
Humm. Will the N-iterated Go actually have a larger range of ratings or are the ratings just more accurate? I would tend to think the ratings are just more accurate and the rating range is still the same regardless of how large N is. |
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No, the range of ratings will be larger. By definition a rank is being able to win 3 of 4 games, or 75%.
Now if I can beat you 64% of the time at Go, I am by definition less than one rank better than you. (In fact, I am about 0.52 ranks better than you.)
But now let's change the game to best-of-five-Go. I will beat you 75% of the time at best-of-five-Go. Hey, presto, at this new game I am suddenly a full rank better than you, by definition.
If Go has about 40 ranks, then best-of-five-Go will have about 80 ranks.
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| « Last Edit: Aug 7th, 2008, 10:33am by Fritzlein » |
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omar
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Re: Rating of a perfect chess player
« Reply #48 on: Aug 7th, 2008, 12:29pm » |
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You are right, N-iterations of a game would expand the rating range of the original game. So I am inclined to agree that games which last longer and have more choices at each turn will have a larger rating range. Perhaps the ultimate rating range of a game is proportional to the game-tree complexity of the game.
But maybe one could argue that the N-iteration model does apply to actual longer games because each iteration is independent of the other.
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