Is player 1 at a serious disadvantage here, or am I just bad at this puzzle? Took me way too long to figure out a winning play, and I'm still not sure if it was just by luck. Still, surprising amount of fun for 500 chars. I assume there's some parity-based solution somewhere, but I haven't figured it out yet.
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Hey, thanks for playing the game! I chose the initial position of the game so that the first player was guaranteed to have a winning strategy, but also the computer player does have perfect play if the player hands it a winning position. The colors of the squares are significant to the winning strategy: for example, you might try convincing yourself that any position where all knights are on blue squares is a position that loses for the player to move.
(In slightly more mathematical terms, if you think of the moves that push a knight off-board as not actually being available, then this is a normal-play impartial game, so it's Nim in disguise.)