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1. 05 Aug '10 11:05 / 1 edit
I noted Michael Adams beating Stuart Conquest in the British Open. Apparently this is the 12th win in a row by Adams against Conquest. Whilst this may be a statistical oddity it got me thinking as to how many levels of chess there are.

For this purpose, please assume that x is a level better than y if he would get 8 points out of 10. (I have avoided 4 out of 5 so each player at least gets the same number of Whites)

In the British grading system I had understood that a 40 point grade difference means you would indeed get 8/10 against the lower rated opponent suggesting that there are about 6 levels within the grading system.

I guess that there are 6 "levels" before you get to a grade? I would also guess that there are a further 3 levels or so above the normal british grading system rules to get to the Super GM?

I would then guess that there are a further six levels to get to chess perfection.

This makes approx 21 chess levels.

I appreciate that nothing is so cut and dried given different playing styles etc but any guesses whether i am overestimating or underestimating the number of levels.
2. 05 Aug '10 11:36 / 1 edit
I'm not sure where you're going with this thought. The "levels" are dependent upon your definition of 8/10. Change the definition, and the number of levels change. (In the elo system, a winning expectancy of 0.8 correlates to about 240 rating points.)

More importantly, I don't understand how this information would be useful to anyone. (I guess what I mean by this - Is there any significance to the 8/10 number, or is it just plucked of of thin air? )
3. 05 Aug '10 11:55 / 1 edit
The answer is of little use to anyone. I agree that the number of levels would change with the definitions. I am most interested in the number of "levels" above the general rating systems.

On my scale Magnus would score about 2 draws every 15625 games against a perfect player (by presumably playing the perfect game on those occasions). Have i pitched perfection too highly or too lowly?

The 8/10 is plucked from the british grading system as being a 40 point gap. Curiously if the gap is indeed bigger, the grading system still assumes a 40 point gap, i.e. a 160 gets the same credit for beating a 200 as he does against a 240. I agree the figure might as well have been plucked from thin air but I have to start somewhere.
4.  nimzo5
Ronin
05 Aug '10 12:58 / 1 edit
An 80% win expectancy is something like 240 rating points. So there are currently about 12 "levels" between someone who doesnt know how to move the pieces and Magnus.

What chess perfection is beyond that is complete speculation.
5. 05 Aug '10 13:03 / 1 edit
Originally posted by Habeascorp
The answer is of little use to anyone. I agree that the number of levels would change with the definitions. I am most interested in the number of "levels" above the general rating systems.

On my scale Magnus would score about 2 draws every 15625 games against a perfect player (by presumably playing the perfect game on those occasions). Have i pitche ...[text shortened]... agree the figure might as well have been plucked from thin air but I have to start somewhere.
I'm not very familiar with the ECF grading system, although I did read the related Wikipedia information. How does the ECF define perfection? Under the elo system, there's no such thing as perfection, since a winning expectancy of 1.0 makes the elo rating calculation blow up. (You end up trying to take a logarithm of zero, which is undefined.)

BTW, the USCF's answer is 13 levels (rating classifications) ranging from Senior Master at the top to Class J at the bottom. This also appears to be an arbitrary definition, with 200 rating points between classes.
6. 05 Aug '10 16:17
A 40 point difference in the ECF system would be a 90% expectation for the better players, not 80%. An 80% expectation would be 30 points. Assuming top ECF rated Mickey Adams would score ~35-40% against the best in the world, the worlds top ECF rating at about 285, meaning there are about 9 1/2 levels. Ropey logic based on an idiosyncratic system with a relatively small player pool and very few top players ðŸ˜‰
7. 05 Aug '10 16:26
Originally posted by Habeascorp
[b]In the British grading system I had understood that a 40 point grade difference means you would indeed get 8/10 against the lower rated opponent
With a 40 point difference in British grading you would be expected to score 9/10 against the lower player. Over 10 games you would expect; 9 wins = 9x50 = +450, I loss = -50, opponents grade = 10x-40 = -400, giving no change in grades.
In a similar way a 30 point difference the expected score would be 8/10.
8. 05 Aug '10 16:29
Thanks for putting me right on the ECF grading.

Anyone care to speculate on how many further leaps (at 4/5 or 4.5/5) there are until chess is played perfectly?
9. 05 Aug '10 17:17
As of today, there is one level in chess. In the future there will be 5. Have you never seen the original Star Trek series?
10. 05 Aug '10 18:12
Originally posted by Habeascorp
Thanks for putting me right on the ECF grading.

Anyone care to speculate on how many further leaps (at 4/5 or 4.5/5) there are until chess is played perfectly?
An infinite number? This reply depends on how ratings are calculated and some implications of how a rating difference translates to percentage of wins between two players. Let's use 4/5 to define a level difference of one, and say two players differ by that. Assume one of them, A, is "perfect" and the other is one level below. In this case, A will be predicted to score 4/5 points over the long run. B will be 80% of perfect.

But can that be? If A is perfect, shouldn't A's win rate against ANY player B with a lower rating, that is, any non-perfect player, no matter how high B's rating is, be 5/5? Is that not the logical implication its being a "perfect player?" (Actually for this to hold, we have to define "perfect player" in such a way that "A always defeats any imperfect player" is an implication, not "A always defeats or draws against any imperfect player."

Once a perfect player is developed, its rating will never find a resting point. Its rating will keep increasing indefinitely, as it piles up more wins. But there will be an upper limit.

If the rating system provides diminishing returns in terms of a rating increase when a high rated player defeats a low rated one, the upper limit of the rating of the perfect player will be determined by the ratings of its opponents. If its opponents improve, its rating will approach a new plateau as it keeps winning.

Here's a related question: Take the highest ranking of any actual player today and calculate the ranking of a player A who always beats that actual player, as a function of the number of games played. That difference, if it has an asymptotic limit, is the ranking of a "practically" perfect player, if not a "theoretically" perfect player. Now increase the opponent's rating and have them play more and keep calculating as A continues to win. Does a new rating for A emerge? Does this elevation of the limit repeat if you increase the opponent's rating again? ? If so, then the theoretic upper limit of a chess rating is dependent on the ratings of the opposition and there is no theoretical upper limit on the rating of a perfect player.

But what happens if it plays itself?ðŸ˜‰
11.  AThousandYoung
Just another day
05 Aug '10 18:31
As of today, there is one level in chess. In the future there will be 5. Have you never seen the original Star Trek series?
Nice ðŸ˜‰
12. 05 Aug '10 19:49
As of today, there is one level in chess. In the future there will be 5. Have you never seen the original Star Trek series?
Too true, and I seem to remember that normal chess had been solved too.
13. 05 Aug '10 19:54
Originally posted by Habeascorp
Too true, and I seem to remember that normal chess had been solved too.
And Fischerandom didn't catch on? It's truly a cruel future. ðŸ˜ž
14.  JonathanB of London
05 Aug '10 20:26
As of today, there is one level in chess. In the future there will be 5. Have you never seen the original Star Trek series?
For those that haven't ...

http://streathambrixtonchess.blogspot.com/2010/06/definitely-got-something-to-do-with.html

Forgive the shameless self promotion but this is probably the blog posts that I'm most proud of ... it got mentioned on a star trek fan site :-)
15. 05 Aug '10 21:36
Originally posted by JonathanB of London
For those that haven't ...

http://streathambrixtonchess.blogspot.com/2010/06/definitely-got-something-to-do-with.html

Forgive the shameless self promotion but this is probably the blog posts that I'm most proud of ... it got mentioned on a star trek fan site :-)
And rightly so!