Why does it take stockfish depth 35 to find mate in 7? - Chess Stack Exchange

My underlying question here is: What is depth? I know depth is supposedly the number of half-moves or plies from the starting position that it has calculated, in at least one line. But I feel this

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strategy - Why doesn't Lichess' Stockfish suggest this bishop sacrifice? - Chess Stack Exchange

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Stockfish will analyze a chess position through to (for example) depth 45 and announce a mate in 10. When it reaches depth 56 it finds an improvement, to mate in 9. Why

I though this move was genius, stockfish not impressed : r/chessbeginners

Chess stockfish gives this position 67+ advantage for white - please explain why. Bit new to chess so apologies if obvious. : r/chess

Stockfish will analyze a chess position through to (for example) depth 45 and announce a mate in 10. When it reaches depth 56 it finds an improvement, to mate in 9. Why

Stockfish Depth 22 couldn't find mate in 2 : r/chess

I composed a puzzle stockfish can't solve. (Black to play, mate in 11) : r/ chess