The benefits of capacity seeing yourself through the eyes of others

Three hats are offered to two players – one white and two red.
They close their eyes and are told that each of them will receive either a white hat or a red hat.
They should raise their hand if they guess the colour of their hat. The first to guess the colour of his or her hat correctly wins.

After the players have seen each other for a few minutes without guessing, one player announces “Red”, and wins.

How did the winner do it?