I think you're just straight up winning after that misguided sacrifice.
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I played 2 1|0 games against this guy and he did the same thing. He made a sacrifice you would never make in a slower game to try to upset the balance. Fortunately it didn't work on me in either game.
After each attempt, what I did was just maneuvered in to an artificial castle while he continued to try to attack. From the second game, 4...f2 is just dumb. But it prevents castling and the only possible purpose for this is to make your opponent waste time thinking about how to get out of it. Incidentally, I had 23 seconds left on the clock when he ran out of time.
I am not a bullet chess expert. I've played 373 games played and a 771 rating. I guess that's part of the point. I'm not particularly good at bullet chess and these opening strategies are so obvious as to be useless. Do they actually work on other people?
How do you respond to unusual openings in bullet?