As far as I know, nowadays the chess engines can judge that a move is the best or that it is brilliant (usually denoted by ! or !!). I was wondering what is the precise criterion for this classification.
I was reading some forums and stepped on this discussion. There, some people claim that a brilliant move is one that the engine does not find and, a posteriori, finds it to be brilliant. Some other people claim that a move is marked as brilliant only if the player continues the game responding with the absolute best moves, for some number of moves ahead. Finally, there is also the opinion that a brilliant move simply cannot be reached by the engine up to a certain depth, which is what I would instinctively think too. Thus, this would imply that if the engine performed a sufficiently large-depth analysis then there would not any be brilliant move markers. Is this correct?
Finally, my question: What is (if it even exists) the specific criterion, based on which a chess engine marks ones move as brilliant, rather than simply the best.