This is reminiscent of a car-talk puzzler of some time ago:
Two decks of cards, each of 52 cards, are mixed into one 104 card pile,
and then split into two 52 card piles - A and B. What are the chances
that the number of red cards in pile A equals the number of black cards in
pile B?
Bonus Question:
How many cards do you have to look at to be sure of your answer?