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I remember GM Daniel Naroditsky commented that you can tell that you're playing a computer if you do calculations and none of your plans work because specific moves that were done 3-4 moves ago start mattering a lot (can't find the reference).

Does this statement apply to all modern top engines?

Are there other ways one can distinguish between different engines and humans (multi-way comparison)?

I'm only interested in differences that can be detected by a (possibly superGM) human, especially during a game.

I am particularly interested in differences between different engines. This includes (but is not limited to) differences that don't distinguish them from human players.

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First of all, the phrasing "you can tell" is far too assertive, because it is very hard to convict somebody based on his play in a single game. Think of the recent cheating accusations of Magnus Carlsen against Hans Niemann. There was extensive analysis and thousands of people investigated this single game by multiple means - and while there are some clues (e.g. (un-)likelihood, suspicious interviews, ...) there is no proof that Hans Niemann really cheated instead of having superb opening preparation and a really great day, playing at his best.

Magnus Carlsen had exactly the same feeling that GM Naroditsky described: Getting outplayed. You would have the same feeling when playing against GMs (without them cheating, of course). They understand the position better and look deeper into the variations and therefore appreciate nuances in the position (moving to square x instead of square y, because in some obscure variation, it might take away some of your options or give them more). The important part is, that the playing strength differential must be very large in order for it to happen that a player gets the feeling that he doesn't get any play at all. As GM Naroditsky is a very strong player who wouldn't easily allow others to take all his options from him, he would always have some ideas against other human players (who, playing not perfectly, would leave him at least some of them in the majority of the games).

Of course, every engine that clearly is above human level (3300+) is capable of outplaying even the strongest GMs; it is not a question of 'style'. And if that happens, they become suspicious (even though it happens occasionally in clean tournament games too, of course).

Other indications that humans can use to substantiate suspicion are

  • people taking the same amount of time for every move (most likely 'beginner cheaters' / kids entering the moves into a program).
  • frequently playing top (~3) engine moves (even non-obvious or "non-human" ones, as judged by the strong player), but occasionally playing serious inaccuracies not matching the previous quality of play (that even much weaker players would likely not make) or not matching the plan (most likely 'post-beginner' cheaters who try to conceal themselves by playing on their own for a few moves or deliberately making mistakes in order to impede detection).
  • thinking on very obvious moves (e.g. recaptures, only moves, follow-up-moves)
  • people playing pretty meekly suddenly recovering from a completely lost position by generating enormous piece activity and counterplay
  • people first outplaying their opponents and obtaining a winning position, but struggling to convert even trivially won games (e.g. massive material advantage without technical difficulties) in time trouble.

All that being said, human observations are almost never enough to justify a cheating accusation. Big platforms like chess.com or lichess use sophisticated machine learning algorithms to discover cheating, that capture much more complex features and patterns than those that can be judged by humans without assistance. Such features include technical parameters (e.g. mouse movement, active browser windows, ...). And even then, usually, multiple cheating games are needed to turn suspicion into "certainty".

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