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1.Rg8 seems good to me.
1..Kg8: 2.Qf8 mate or 1..Qg8: 2.Qf6+ Kh6 3.Qe5: and black is busted
That looks good, but what about after 1. Rg8 Kh6
1.Rg8 Kh6
2.Qe3+ Kh5
3.R1f5+
Trefor5D
trefor5d
3.Rf5+ would be a blunder because of Qxf5!
but 3.Rf3 wins easily.
Indeed, 1. Rg8 seems to be the best move for White at this point, yet it doesn’t seem to give White that big an advantage, or am I missing something?
On a side note, this “Rook – Queen – Rook” position is in general the best permutation of these three pieces.