In the proof they prove that player 2 cannot have a winning strategy, but why does this imply that player 1 can win? Does player 1 have a winning strategy? My book has a similar proof to the one on Wikipedia and says that there is a winning strategy for player 1. Even though player 2 does not have a winning strategy, does it mean that player 1 has one? If yes, Why? Why is it enough to prove that player 2 does not have a winning strategy?