I) Given an infinite deck of cards, each distinct, all ranked. Lay them out in a row, face up, left to right, in order.

Shuffle a second, identical deck. Deal it one card at a time, face up, directly below the first.

On average, how many pairs match?

II) Given an infinite deck, composed of replicates of a standard 52 card deck; that is, an infinite number of copies. Arrange it into separate decks, each ordered by suit and rank. Lay them out as above, face up, in a single row.

Shuffle another identical deck. As before, deal it out below the first, one card at a time.

On average, what fraction of the pairs match?