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After the move 4...Kh4, i think white's best move is 5. Rf4+. Black has no choice but to respond with 5...Qg4. It seems white would be up an exchange after 6. Nxg4 with the threats of mate and gxh3.
When I first saw this thread 5.Rf4+ seemed like the natural move and it is probably best and I think it is at least equal but I don't think 6.Nxg4 wins the exchange because again 6...Bg5 comes to the rescue, doesn't it?
(Also, did my funny pic of the aftermath of a party get moderated?... why? There was no nudity or drug use that I noticed, beyond some empty beer bottles and some sleeping/passed out people. Seems an odd choice to moderate.)
I had thought white would move the rook along the 4th rank to keep up both threats.
Edit: I see now that the mate threat is weakened, but it's still there. If black chooses to save the rook, white can move the knight in a discover check, and white would be in trouble of mate again because black can't defend the bishop.
@Sunshiny... by golly I think you are right.
An immoderate moderation indeed.
@Duck and cover...
Nice. That looks air-tight.
Exactly, it seems even Kg3 walks into a mate. I didn't analyze it that far.