A 3000 could easily beat a 2000, but could a 4000 easily beat a 3000?

There should be a setting in programs to allow positions with illegal number of pieces to be set up. If I want to set up 25 knights vs 10 queens, it should let me!

Not stockfish

The question is not whether a 4000 would beat a 3000 easily, the question is whether a 4000 can exist.

There is a hypothetical perfect chess player. This player can be enhanced to pick moves that make the task of the opponent more difficult when the theoretical result is not already a win. Such a player has some rating on the Elo scale, based on its play against other players of intermediate strength.

We don't know how strong this perfect player's Elo is. We know it must be a bit stronger than the strongest chess player at present (perhaps AlphaZero) but we don't know if it is a little or a lot - only guesstimates can be made.

As I pointed, this is conditional on it being possible for any player of any type to have a rating of 4000. There is some upper limit, corresponding to perfection.

Not the point of contention. We're saying IF they existed.

This proves rating isn't linear. The higher ratings get, the more complex the games be, and regardless of the strength of players, The point is, people make these BS arguments that a 2300 vs a 2500 will be boring cause the 2500 will win easily. My argument is that the significance of the difference in rating decreases as the ratings increase. An 1600 can easily wipe out a 1000, but a 2900 could not EASILY wipe out a 2300. Even if the end results are still the same, the higher player wins 75%..etc, the games will still be useful and instructive.

by definition of what a chess rating is, a 4000 rated computer would crush a 3000 level one. (They would likely be however quite a few draws). for a its limitations, the stockfish vs alpha zero match is a good example of what such crush would look like. a bunch of draws, quite a few wins with white, and few black losses.

the deeper question is, is a 4000 chess rating by anything even possible?chess seems to be a draw with best play, and most decent openings should be a draw with best play, not just the most played ones. so  probably after a certain level of strength, even if one engine plays better than another, the result will still be a draw, so there is a theoretical highest rating area.

Then what is this BS that they say a 100 point difference results in a 75% more chance of winning. I've beaten players all the time that were 300+ points higher than me. By definition, rating is an approximation, you can't quantify how good someone tactics are by a 4 digit number.

I mean in standard chess.

ratings are an AVERAGE, they do not determine individual matchups  or individual games. beating someone 300 points higher than you is hardly a rarity.

and after a certain threshold of rating, YES they do determine tactical ability, chesss strength begins as put anything on the blank slate and you will get better all the way until the 2000's by then, it becomes  morea matter of perfecting the weaknesses you have as the amount of room for improvement becomes smaller and smaller. 

Well, unfortunately, a ton of people on this site have a dellusion that they refuse to play anyone 50 points lower than them cause it will be TOO EASY LMAO. Those stupid rating filters.

If you look at 3400 vs 3000 rated chess engines, the 3400 wins the vast majority of games.

I would guess that 3000 would have no chance against a 4000 engine and 3000 would require a blunder by a 4000 human to win.

If they never lost to anyone 50 points lower, their rating would be rising steadily.  Sometimes in tournaments, I get an opponent a few hundred points lower than me and I have to work very hard to win.  Usually they will make a move resulting in a weakness I know how to exploit at some point in the game, but not always!

But I always assume they will make the best move and would be foolish to do otherwise.

That doesn't mean the game won't be interesting!

I'm talking about the ridiculous people on this site who set their rating filters to -10 cause they want someone EXACTLY the same level of them and by doing so, waste a ton of time for people trying to find matches.

The definition of a k point Elo difference is that the stronger player scores (1 - 10^(k/400) )/ (1 + 10^(k/100). (This is a logistic function, or sigmoid, for those familiar with such things).

For k= 400, this is 91% and for k=1000 it is 99.7%, regardless of how strong the players are.

For stronger players, the only difference is that there are more draws. This is why when two strong players with a 400 point difference meet, there are almost 80% wins for the stronger and almost 20% draws, the weaker playing winning once in a blue moon. When two weaker players with such a difference meet, the stronger wins more often than for the two stronger players, but the weaker wins more often to a similar extent, displacing some of the draws.

How do they derive the algorithm though?

you are right according to this chart they have only 57% chance of winning

Interesting, but that last row is wrong. It's NEVER 100%