Key idea. Leave a multiple of 3 after each of your turns.

1. The first player takes 2 stones, leaving 12.

2. After that, respond to an opponent taking 1 by taking 2; respond to an opponent taking 2 by taking 1. The two moves always remove 3 stones in total.

3. After each reply, the pile size is 9, then 6, then 3, then 0. These are all multiples of 3.

4. The reply is always legal. When a positive multiple of 3 is on the table, the opponent can take only 1 or 2, leaving enough for the matching reply.

5. In particular, from a pile of 3 the opponent leaves 1 or 2, which the first player takes. The first player gets the last stone.

Remember. A strategy explains how to answer every legal move, not just one possible game.