Hex is a simple two-player game invented independently by Piet Hein and John Nash (of “A Beautiful Mind” fame). A nice argument shows that the game cannot end in a draw, so one of the players must have a winning strategy. Moreover, we know which one. Using a strategy-stealing argument, we will prove that if the first player plays flawlessly, then he will always win. Can such a game be any fun? Yes, because there's a catch. The proof that the first player can always win gives absolutely no hint as to how the first player should play. It is what we call a non-constructive proof. So, the first player knows that he can win, but he doesn't know how to win. Instead of being provably pointless, Hex is perfectly playable. There is even a book written about Hex strategy.

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