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Can bots resign?

Both can happen, depending on the conditions agreed on before the match/tournament.
If the operators configure it, bots can resign as soon as their evaluation goes under a certain threshold (usually -9 or -10 pawns).

It is also possible to offer draws if the engine's eval is very drawish in endgame for a certain number of moves (0.1 pawns or less).

Though I think a lot of operators (including me) just don't configure this, either because it is not possible with the framework used to run the bot, or because it requires modifying a bit of code (which can be problematic if you're not a developer).

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