How to know if the opponent is cheating or using a bot or something like that?

I am curious to know the signs of a cheating opponent. Yes, I have played with opponents who simply leaves the game, and I feel they are human players. There are those whose moves suddenly change from being simple to marvelously amazing, those moves that are too good to be true.

For me, it is when there are two competing plans every x moves, that just doesn't make sense, like sometimes they're playing in direct competition with their previous moves that raises a red flag for me.
Other than the obvious static time taken per move and they played amazingly throughout the entire game (and backed by stockfish).

If you suspect cheating, best to simply let the admins know. It is pretty complicated, let the experts figure it out and don't try to accuse folks publicly, which can be difficult if you're salty from losing and you suspect cheating is involved :)

- Same 5 - 10 seconds taken for both hard moves and obvious recaptures and easy moves.

- Obvious computer style moves (forceful centralized moves that don’t forgive any mistakes, you will immediately feel positional and tactical pressure, it’s super obvious, you will feel more and more strangled for options with each passing move)

- Lack of fear (computer doesn’t care about your mating attack if there is no mate, so a computer can often calmly continue it’s plans on the other side of the board or play in the center or even weaken it’s own king position further, humans don’t do that, humans have fear, they usually react at least in some way to your attack)
I once had this cheater leave his queen and king in the same line with my rook for 4 moves straight, no human does that, every single human would move the king and queen out of the line of fire just in case, but engine saw that I have no mate, so it calmly left it’s king and queen looking right at my rook thru maybe one or two pieces that could have easily moved out of the way at any moment.

- With decisive advantage the opponent continues to play slowly, humans don’t do that, they put you away quickly by mate or simplification into a won endgame, computer keeps slowly finding the best moves. The cheater is a weak player and thus doesn’t sense that he already has it in the bag, so he continues to rely on the engine and plays slowly, making it obvious that it’s an engine.

A sudden change from patzer to GM quality play is one of the signs as you mentioned, but there are indeed others. Here's ten out of many. Alone, they don't necessarily mean the opponent is cheating, but they can be used together to build confidence.

1. Taking approximately the same amount of time for moves regardless of complexity. IE: 5 seconds for a forced recapture and 5 seconds to find a brilliant tactic.

2. Creating needless complications in a clearly winning position. IE: Rather than win a piece, your opponent plays a curious line that ends up winning an extra pawn via a temporary exchange sacrifice.

3. Mastery of simultaneous play on both sides of the board.

4. Finding mating lines a mile out.

5. Finding tactical replies to everything rather than sticking to a cohesive development plan.

6. In known positions, moves are often favored by top engines, but rarely played by humans. IE: Black trades off their dragon early on in the Sicilian to grab a temporary pawn advantage despite it being the key positional asset.

7. Consistent mastery of theory. The opponent never seems to run out of book until you make a mistake. IE: A 1200 rated player goes deeper into theory than most top level tournament prep.

8. The opponent suddenly halts after rapid play, takes a couple minutes, and then continues at the original pace (engine crash)

9. If you are higher rated and your opponent keeps offering a draw in a superior position (they know the longer they play you the more they will look like an engine and just want the quick rating boost).

10. They have a lot of benchmark games against Stockfish in their play history with odd results (trying to tune their engine strength down and set the time control on their software correctly).

Worst case scenario, your cheater knows how to play. They will tend to manually initiate their recaptures, only play the moves that make sense to them after being shown, waste clock time to make it seem like they were thinking in a critical position, use a more subtle/positional engine than SF like a low depth Leela or Zappa, mix in their own play, complete their profile like a normal player etc... They will still be banned. It may take a couple hundred games or some time, but it will happen. All you can really do is focus on your game. You will have ways to improve regardless of who/what you are playing against, and letting yourself get discouraged or calling them out just feeds their ego and warns them to make yet another account due to the incoming ban. It won't make them feel remorse. It always feels like such a waste of time, but that game you lost becomes data to catch the next generation.

You don't worry about it. You let the administrators catch cheaters and you just play chess.

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