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the likes of stockfish and komodo are much stronger than humans. The 3300 plus ratings of these engines suggests that even the top humans would find it impossible to draw even 1 game, but is this really true? Also, are these high ratings meaningful?

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Today's engines running on suitably powerful computers will most likely beat any top grandmaster.

Ratings are essentially numbers assigned to players such that a player is expected to beat some other player (a draw being counted as a half-win) some fraction of the time, based on their difference in rating. An important point is that the absolute ratings are irrelevant: if every player in the world got a 1000-point boost to their rating, nothing fundamental would change.

The mathematical details imply that according to the rating model, no matter how big the difference in rating, the weaker player will still win some fraction of the time. In the case of Elo, we assume that even the lowest-rated player in the world has a 9% chance of beating Magnus Carlsen. This is clearly a flawed assumption, but it's the kind that almost every rating system makes; and it's not too bad anyway, it works well for the most part (i.e. when rating differences aren't too big), and even at the extreme ends, the best human players can still blunder.

However, today's engines beat humans 100% of the time in a fair game (I wouldn't say there's explicit proof, but the fact that they don't even bother to hold such matches anymore says a lot, so let's just say this is true); thus it's completely meaningless to assign a FIDE rating to these silicon monsters: there is absolutely no difference whether a 2800 player meets a 3300-rated engine or a 4300-rated engine, as far as the Elo rating system is concerned. Even for an engine running on a desktop, if we assume that a top grandmaster could score some 5%, we'd still be looking at what statisticians call a tail event; rating systems (and statistics in general) are really bad at these.

So top computer engines have their own rating lists, no humans involved. But they still run on the Elo system, albeit apparently with a different 'base'. You can meaningfully compare engines here; a 100-point rating difference will probably correspond to a sensible winning percentage.

On the other hand, the difference between the FIDE rating list and computer chess rating lists (CCRLs) are completely meaningless. While CCRL base ratings were probably chosen to be higher because most computers are simply better than the best humans, this base rating is just arbitrary (at least as far as I know); we could subtract 2000 points from every rating in the CCRL and add 2000 to every rating in FIDE, and both lists will continue to function the way they have.

It seems that the modern way to compare humans to computers today is to look at scores from matches where players are given a handicap. If I recall correctly, this is reminiscent of the pre-Elo days, when players' strengths were gauged by how they fared against the best players under a handicap!

Long story short: the high ratings are meaningful when compared with other engines in the same list. On the other hand, they are absolutely worthless for comparison against humans.

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For the first part, see my answer to a related question. Humans have no chance - they'd be lucky to even draw a game.

About the second part, engine elo isn't directly translatable to human elo. The way elo works, it depends on the anchor. The bottom of the elo ladder is 0 elo. What does 0 elo mean to you? If you rate a complete human novice as 0 elo, there're still players who can be worse than you (e.g. an engine that selects moves at random). So no, you cannot say that an engine that is 2800-rated on engine elo lists would be expected to draw a match with 2800-rated Carlsen.

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Statistics state that for a 400 point rating difference, the higher rated player should win 99.9% of the time. The slight chance for the lower rated player is due to the player's increased knowledge and human error. Since at the grandmaster level, there is no huge increase of knowledge, and the computer will never tire, the human has, if effect, zero chance of even getting a draw.

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    What statistics specifically? Anyway, the Elo rating system is calibrated to about 90% of the score for a rating difference of 400, which could be two draws is ten games. – quid May 27 '17 at 11:09
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    Really? I see a 1500 player beating the 1900 many times – SmallChess May 27 '17 at 12:47
  • @11684 An IM with 2100 Elo?? For that to happen, the IM needs to have stagnated A LOT from the time where they got the title. Also, starting out with 1500 Elo I'm not sure where you get that from. AFAIK, most players begin with a rating of ~1000-1200 Elo, since that is roughly corresponding to advanced beginner strength. – Scounged May 27 '17 at 13:30
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    Thus for a rating difference of 560 there is a chances of 120% of winning the game? Clearly that makes no sense. You must not exptrapolate this linearly this is just not how the system is set up. You might want to look up how the Elo rating works. – quid May 28 '17 at 16:07
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    fide.com/fide/handbook.html?id=172&view=article gives a probability of a player of 400 more rating points as 0.92. – Fred Knight May 29 '17 at 2:35

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