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Do computers play in ordinary human grandmaster chess tournaments with time limits at 40 moves in two hours etc? If so how do they fare?

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    No. This idea was popular like 10 years ago, but it's pointless now because computers can beat any grandmaster easily. It's like Usalt Bolt against a full-speed racing car.
    – SmallChess
    Commented Aug 6, 2015 at 10:46

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No, they don't, because it wouldn't be fair. According to Wikipedia:

A recent top chess engine, Rybka, has an estimated Elo rating of about 3200 (when running on an up-to-date PC, as computed by SSDF).

This is about 500-600 points higher than an average grandmaster (rating 2600-2700). This would be the same rating difference as between a grandmaster and a top club player (2000-2200) - it is a totally different playing category.

According to how the ELO rating is set up, the expected score of a 2600 grandmaster vs. a 3200 computer is 3% - i.e. when they play 100 games, the grandmaster is expected to draw only 6 games. This is way too low to be interesting.

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This used to be the case from the sixties, when the first chess computers entered the scene, with the playing strength of a beginner, until the nineties, when computers became too strong for the normal grandmasters.

Then followed a phase of man-machine matches until maybe 10 years ago when results like Hydra-Adams, 5.5-0.5, made it abundantly clear that even the strongest human chess players cannot compete with chess computers.

Nowadays even engines on unspecialised and relatively modest hardware (like a smartphone) are playing beyond human capabilities.

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Nowadays, human vs. computer matches or tournaments where a computer participates among human players don't exist because the difference in strength became too big.

In the past, the situation was different and a couple of matches were organized. The match Kasparov - Deep Blue in 1997 is of course the most famous one. On this wikipedia page you can find a nice overview of the human vs. computer matches.

"Mixed tournaments" (humans and computers) were a lot rarer. The only one I can remember is the Dutch championship in 2000, where Fritz participated. It shared the 3rd place with 7/11 and a performance around 2600.

However, it should be added that GM Van der Sterren and IM Bosboom resigned after move 1 and 4 respectively, as a sign of protest against the participation of the machine. So, discarding these games, Fritz scored 5/9, with a performance of 2500+ (my estimation, I didn't check it).

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