In 2-move chess, in which each player can make 2 moves, can Black win, assuming optimal play?

Yes
Unknown
No

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Assume, for the sake of contradiction, that Black can win no matter what White does on his first turn. Then, if White moves his knight out and back, the resulting position is a winning position. However, this position is the same as the original position, so White's original position was a winning position. This is a contradiction, so Black cannot win.