Match Made in Heaven
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?
Give your answer to 3 decimal places.