hex

Background Hex is a board game Hex (board game). It can be proven that the first player wins on boards with any size n×n (without swap rule) using a non-constructive proof. But the proof cannot provide specific strategies of how to win. Question Original question on MathOverflowOn an n×n board, assume the first player tries to minimize the length of the game to win, and the second player tries to maximize the length to lose. Call the optimal length F(n). (F(n) is the sum of move numbers of two player, not one player).What are the asymptotics of F(n)? Brief results…