I was teaching myself how to play a hex board game by reading some books. I learned how to do $2$ x $2$ and $3$ x $3$ hex games by starting at the principal diagonal. I wanted to know what the winning strategy would be for player one (white) in a $4$ x $4$ Hex game starting from the principal diagonal.
Consider a $4$ x $4$ Hex.
Show that White has a winning strategy, starting anywhere on the principal diagonal that is in any of the hexagons $1,6, 11,$ or $16$.
Here is what the setup would be:
Let the Hexagons be represented by numbers such as:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Let White have the first move. Let black have the second move.
White opens up at 6 (principal diagonal).