The rating of a perfect player

This is the (closest to) correct answer I can find.

The number can be anywhere (in certain range above 3200) depends on assumptions taken. The problem is that there are so many variables to assume. But first you have to understand how the rating is calculated, and how each variable affects calculation. This is purely mathematical once you agree on the assumptions.

You can't have a rating unless You lose or draw one game.

It may be purely mathematical, but that doesn't mean realistically calculable by any means in this present time. We don't know exactly how perfect play compares to the best players of today -- e.g. would the top players be able to get draws as white sometimes, or would they indeed lose nearly every time?

In solving real world problem by means of mathematical calculation, we have to build a formula with constants and variables. The hardest part is of course to form constants by means of acceptable assumptions. But once it is agreed, formula is a formula.

A simple assumption will sound like this: "current (Jul 2011) FIDE rating formula and calculation procedure will be used, refer to FIDE Handbook chapter bla bla bla". This is simple assumption because everyone will easily be agree with the formula used.

A rather fuzzy assumption will sound like this: "the perfect player will be able to join 360 rated tournaments a year with 100 participants per tournament". Note that as uhohspaghettio implied, it needs won games (hence tournaments) for the rating to keep going up and up.

A debatable assumptions will be the capacity of the perfect player relative to the other players, even whether chess is a draw or won for White. But as I can see it, the majority of high rated players already have the same conclusions, for example: chess is a draw. The problem is, not everyone can see the relationship of these assumptions with the formula.

That is the unanswerable question that makes the original question impossible to answer. How many if any games could they draw?

I hope you realize that this is really just a question of how close GMs and computers are to perfect play, because that's what the basis for the rating will be, not stuff like the practical amount of games they can play in a year or whatever.

To see how assumptions affect calculation, ponder with the following proposed assumption:

There is only ONE perfect player (starting as 2350 rated player after beating 12 rated players with an average rating of 2200), and the opposition is as can be found in the real world today.

Note that we don't assume that everybody else are also perfect players.

Imagine that the two strongest chess engines (latest versions of Rybka and Houdini) are playing against eachother (at five to six hour long time controls), and one of them makes a significant positional error. The other will be capable of exlpointing that error and playing an easy game where it avoids errors. Can I get you to agree on this?

EDIT: Sorry about the longwindedness; Basically, would a top engine be able to make an error like that decisive? (And how often?)

Now, what is important is the relative strength of the perfect player with the average of his oppositions. Please note that in any rated tournament this perfect player will play many weaker GMs than Anand, and when Rybka is a participant, the perfect player is free to withdraw.

A perfect player is assumed to be able to see ALL possible moves, which moves lead to win and which to draw. He will never gamble, he will always choose the best move (win or draw), the most difficult position he can over to his opponent (we don't need to assume that the time control is 60/5 and the perfect player will be able to think only in one second per move!).

I don't see a problem for a perfect player to continue adding points to his rating. It is about probability. If you doubt it, just assume and tell me first what is your probability score of this perfect player against the current world champion in 20 matches. If you think it is fifty-fifty, then I will give my reasoning why I disagree. Some high rated players already stated their imo correct opinion. If necessary we can make a wheighted poll to determine this probability, where high rated players opinion will have higher value. Just do this mathematically (if it is the only fair way to build a conclusion) and you will find the answer.

Let me explain how amount of games in a year affect the result (like I said before, this problem is as simple as how you can see how each variables affect the calculation)...

To add point you need won games. The higher your rating the smaller this rating increase (as stated by uhohspaghettio it can only +0.0000001 point). You need plenty of games in a short time, to ensure that there is no change to other players' strength. Otherwise, somebody would argue that the other players will learn from the perfect player and so on

My own damn fault for trying to engage in this.

Mathematically, the perfect player needs at least 50% wins (50% draws, 0 losses) to maintain his rating when playing against these top players. His rating increase of course can be caused by playing non-top players.

How many % do you think a Rybka or Houdini will score playing in a tournament of the top 100 FIDE participants? Less than that? A perfect player will score higher than Rybka!

The problem I am seeing here is that we are looking at two situations.

One, a perfect player's rating when playing versus today's GMs.

Two, the theoretical assesment of chess.

Analysing the first situation, the perfect player's rating would be lower against today's GMs than a theoretically highest possible rating based on the pool of players.  A perfect player's rating would show a dominance, which has been shown in this thread to peak at around 800 points maximum difference, where no decernable increases would occur.  The assumption is that all the games would be won by this player.  So in effect, the highest rating a perfect player could achieve in this pool would be 3600.  Now if draws are included, then this maximum number will be lower.

Now, what if there were two great players dominating the field.  Lets say player #2 dominates the field of players and player #1 dominates player #2 and the rest of the pool.  Player #2 would approach the 3600 peak, but player #1 would eclipse 4000 showing the dominance of the pool.  I am not sure if you can postulate a perfect rating as ratings reflect the strength of a player against the pool of players.  For that to be evaluated, there will have to be perfect statistical results based on a 32 piece database, in effect, the solving of chess.  If all players play perfect based on this database, then all the ratings should centralize around one number. 

Two, with increasing rating, white tends to show an increase in the percentage of wins and draws.  So in effect, a perfect white game would not end in a loss according to the statistics.  But can the statistics show that with even further increasing rating, is there an increased tendency towards a draw or win?  At some point, one of these statistics will hit a peak and will experience an decrease while the other will show a continual increase.  This will show the theoretical result of chess.

the highest rating I have ever seen on chess.com is 3006. 

The second is 2920.

If the assumption is that the perfect player won all the games, the rating will go up infinitely. This is what rating is all about. It is a RELATIVE measure of strength with others. The perfect player's rating will never stop increasing because for every win he gets at least (after he is at least 400 points higher than his opponents) +0.8 point. Just make the number of games of 1000000 and he will get 800000 points.

The problem is to calculate the winning probability of this perfect player against the average of his oppositions. The minimum achievement can be modeled with a single tournament between the best engine (and the best computer) with a pool of top players.

How far a perfect player can play better than the current best engine can be explained  further by logic.

Imagine this player plays 1000000 rated games with you. Can you guess what will be his rating after the games?

3006