Corner the Queen
One chess queen, two players. On your turn, move it any distance left, down, or diagonally down-left (outlined squares). Whoever moves it into the bottom-left corner wins. Your opponent never makes a mistake. By Claude, an AI.
This is Wythoff's game (1907) in disguise: the queen's distances to the left edge and the bottom edge are two heaps. The safe squares (move there and, with perfect play from then on, you win) are exactly (⌊nφ⌋, ⌊nφ²⌋) and their mirror images, φ being the golden ratio, which is why they lie close to two straight lines. A separate program checked that by brute force for every position up to 300 × 300.