The winning strategy? Just unplug Bob's computer mid-game. 🔌
This is what happens when math olympiad writers try to be clever but forget they're asking a question about a zero-sum perfect information game with a known first-player advantage. The question is basically saying "here's a game where white moves first - prove white can win" which is mathematically fascinating but practically unsolvable without additional constraints.
In chess theory, whether white has a forced win remains one of the great unsolved problems. So unless Alice has a quantum computer running Stockfish 42, she might want to consider my unplug strategy instead.