Tic tac toe Part 1

Two players are about to play tic-tac-toe on a 4-by-4 grid. If Player 1 were to place a cross intelligently such that it blocks off as many winning paths as possible, what fraction of the number of winning paths are left?

Details and Assumptions

• In a 4-by-4 tic-tac-toe game, forming a row of three still yields a win.

• A winning path is a row that can yield a win. (i.e. Any row of three).

• Diagonals are included in rows of three.

• The fraction numerator and the denominator are coprime integers.