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Interesting desperado pattern

(warning: 1 0 quality)
en.lichess.org/TMNJr6B7

In this game, still bad play up to middlegame, but I was quite happy to have constructed an unavoidable checkmate. But I did not understand why there was not checkmate sequence by computer analysis at move 33.

I envisioned 33. Rb3 34. Ke4! (scared of the rooks by taking the knight, and wanted to get out of checks) ... Re3+! 35. Rxd4 (Rxe3? Nf5! and I lose my rook! Still won endgame, but in 1 0 I can mess up the ending) and now it's won, right? 36 Rd8 loses the rook on e3... but then it is stalemate tricks with the desperado rook on! I amazed that white can actually get away with it by... interposing the knight on the 8th rank!

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