There are multiple ways in which a website like [chess.com](https://chess.com) or [lichess.org](https://lichess.org) would check for cheating. It might involve checking what kind of moves you are making and how long it takes you to find them. Finding the best move isn’t suspicious. Finding it over and over again in 5 seconds when you’re a 500 rated player is. Also, some moves just aren’t natural for a human player to find, not even for the best of the best without thorough analysis. Finally, they might also check if you keep switching between browser tabs, or how your cursor moves while playing.
That said: this mostly involves non-professional players. For professional players playing in an online tournament, other techniques are used. This mostly involves the use of one or (usually) more cameras to check what the player is doing during the game. When a player keeps looking in a certain direction inbetween moves, that might indicate the use of a second screen where a chess engine is running. This famously happened earlier this year in a match between GM Wesley So and GM Tigran L. Petrosian. The latter was disqualified for violations of fair play regulation. Needless to say, for a high level chess player, such a controversy is not good for your reputation and can get you banned from professional play for life.
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