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I often come across chess commentary mentioning phrases like "this is just a weak browser engine, let's see what the proper engine says." As far as I understand, Lichess's browser engine is essentially the same as Stockfish, albeit potentially slightly slower due to browser architecture.

Can someone confirm if my understanding is accurate? I'd like to know if Lichess's in-browser Stockfish is indeed similar to the standalone version (given versions are the same), or if there are notable differences that might justify these comments in chess commentary.

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Your understanding is accurate, but generally, the online engines limit the "depth" that the engine can go. The "depth" used to refer to ply, but with NNUE engines, it does not really map to that anymore. When I really want to see what's going on, I will bring the position down to my local instance of SF16, put 32 cores against it and let it run for a long time. It can generally reach "depth" of 45-50 in many positions. That's a much "better" evaluation than the limit of "depth" 20 that most online engines will go. However, you can easily use a tool like Chessify to reach very high "depths" and then it's really equivalent.

More in-depth (hehe) discussion of depth.

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