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?😉