Winning strategy

In Hex, there exists a winning strategy. When you play without the swap rule, the first player can always win. When you play with the swap rule, the second player can always win.

The reason for the second player's sure win strategy is simple: After the first player's move, there are two possibilities:
 * 1) The move was so good that no matter what the second player does, the first will win. In this case, the second player should swap colors.
 * 2) The move was bad, so that the first player cannot win. Because the game cannot end in a draw, this means that the second player can win. In this case, don't swap colors.

The only remaining problem is to decide whether the situation after the first move can be won by the first player or not.