A solitaire type of card game is played as follows: The player has two shuffled decks, each with the usual 52 cards. With the decks face down the player turns up a pair of cards, one from each deck.

• If they are matching cards (for example, if both are the seven of spades) he has lost the game.

• If they are not matching cards he continues and turns up another pair of cards, one from each deck.

Again he has lost if they are a matching pair. The player wins if he can turn up all 52 pairs, none matching. What is the probability of a win?