Three way fork-Why take the rook instead of the queen? I just finished off a game and decided to do some analysis because I had a position that I was thinking about for a little bit.
I ran the game through Stockfish and the move I was thinking about was one Stockfish disagreed with.
[FEN &quot;r1b1k1r1/pppq1pB1/2nb1N1p/8/8/5N2/PPP1BPPP/R2QK2R b KQq - 2 12&quot;]

1. Nxd7+ Ke7

I played Nxd7, however, Sockfish suggested that I should play Nxg8+.
The only thing I can think of is looking at relative value.  The suggested move would result in a rook (5) and Pawn (1) for no material lost, while Nxd7 move would result in a queen (9) and pawn (1) for a knight (3).  Doing the math, the Nxd7 move still results in a better move. That or it doesn't like me opening up Black's white bishop
I let the engines play it out from this position and in both instances the Nxd7 results in a mate faster than the Nxg8+ move.
Because I can't see any reason the the Nxh8+ move is better than the Nxd7 move, is anyone able to assist or is Stockfish drunk?
Both moves lead to crushingly won positions for White, so all things considered it doesn't matter which one you choose. For me, Stockfish shows +14 for Nxg8+ and +9 for Nxd7. The difference between +9 and +14 is a lot less significant than the difference between, say, +0.5 and +2.5.
About the material calculation you gave: Nxd7 costs two minor pieces for the queen rather than just one, since if Black responds to Nxd7 with ...Rxg7 then the knight on d7 is also lost. So to the extent that this matters, on balance it probably favours Nxg8+ (which gains a whole rook).