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A friend of mine, who is an International Master at chess, told me that humans were superior to machines provided you didn't impose the time constraints that exist in competitive chess (40 moves in 2 hours) since very often games were lost, to another human or a machine, when a bad move is made under time pressure.

So, with no time constraints and access to a library of games, the human mind remains superior to the machine is my friend's contention. I'm an indifferent chess player and don't really know what to make of this. I was wondering if any research had been made that could back up that claim or rebut it.

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    $\begingroup$ The performance of a computer chess program is measured with the Bratko-Kopec experiment. It implements example chess problems which have to be solved by the chess engine. The outcome of the test is converted into an ELO score which allows to compare humans with computers. According to the latest information, the ELO score of computer programs is higher than from the best human grandmaster. $\endgroup$ – Manuel Rodriguez Nov 10 at 10:27
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    $\begingroup$ He's assuming the computer isn't under time pressure. It is. Removing time limits is not giving an advantage to the human player, it's giving even more advantage to the computer. Of course, unless the game simply goes on forever :) $\endgroup$ – Luaan Nov 11 at 8:53
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    $\begingroup$ The problem seems under-specified to me, because if you stipulate "no time constraints," then surely a computer could in principle search the entire game tree of chess and only play optimal moves (even though you wouldn't even be 1% done by the heat death of the universe). You have to have some time constraints to make the question meaningful. $\endgroup$ – David Zhang Nov 11 at 19:41
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    $\begingroup$ @DavidZhang I guess what I have in mind is time constraints that are so lax that Zeitnot is not an issue at all, like, for example, 40 moves in 40 weeks or 40 months. Enough time at any rate to make it possible for the human mind and its creativity to seriously challenge the computing capacity of the machine and maybe defeat it. $\endgroup$ – petitrien Nov 11 at 20:09
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Losing games to computers because of mistakes made under time pressure was probably a thing about 20 years ago, when Kasparov lost to DeepBlue after such a mistake(correction: it was Kramnik with the blunder, not Kasparov (see edit 2)). But after Kramnik's loss in early 2000s, no world champion ever tried to play against a computer (to my knowledge). Nowadays, there are computer only tournaments among programs with ratings well above 3300 (for comparison, Carlsen's peak rating was around 2880), and it is not uncommon for computers to make moves with no apparent meaning to humans.

No time limit for humans also mean no time limit for computers so I doubt any human can win a single game against a computer. Older models like Stockfish 8 depend on their computational power as it can look at several millions of position per second, Google AlphaZero managed to beat Stockfish with 80000 positions per second: they don't seem to depend on brute force calculations any more. Keep in mind that this is without any prior knowledge of openings etc, they are trained using reinforcement learning, starting from the rules of the game only. From there, they can develop their own strategies and implement them without making any mistakes. They create their own openings from scratch, so existing libraries is not going to be very useful.

I am not aware of any research on this but lack of a challenge from humans is probably enough evidence. Also, Grand Masters regularly use chess engines in their training routine to analyze positions, so there is that.

A few years ago there was a game between Stockfish against GM Nakamura + Rybka, which Stockfish won. It is possible that human GM + Stockfish might have better chances against AlphaZero in correspondence without any time limits, but we probably will never know.

Edit: Here is an interview with Carlsen after a game, very interesting to show what he thinks about AlphaZero.

Edit 2: As reminded by @Akavall, both Kramnik and Kasparov made serious mistakes in their matches against computers. Kasparov resigned in a drawn position and missed a knight sacrifice; and Kramnik missed mate in 1.

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    $\begingroup$ Nice answer @serali. I think it could be even better if you add some links to support the events you mention though! $\endgroup$ – John Doucette Nov 10 at 14:10
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    $\begingroup$ Which events? Kasparov and Kramnik? $\endgroup$ – serali Nov 10 at 14:11
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    $\begingroup$ With regard to (the many myths surrounding) AlphaZero vs. Stockfish, I'd like to point out this commentary: stats.stackexchange.com/a/308784 $\endgroup$ – Jim Nov 10 at 22:28
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    $\begingroup$ I anticipate that this is the pattern for all human-AI competition: humans are way better; the competition falls briefly within the range of human expertise; then computers are better so we can only pit them against each other as our understanding of the rationale for the moves made shrinks smaller and smaller. As it was with chess, so it'll be with driving and linguistic problems and image recognition. At the moment AI's at the low end of human ability in all these, but it's rising faster than we are. $\endgroup$ – Dewi Morgan Nov 11 at 19:49
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    $\begingroup$ Kramnik and Kasparov both blundered against super computers. Kramnik missed mate in 1, and Kasparov resigned in drawn position, and he allowed Nxe6 in Game 6 against Deep Blue. $\endgroup$ – Akavall Nov 11 at 22:07

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