Consider a form of solitaire, 'sometimes called “frustration solitaire.” In this particular game, a deck of cards is shuffled, and then dealt out, one card at a time. As the cards are being dealt, the player counts from 1 to 13, and then starts again at 1. (Thus, each number is counted four times.) If a number that is being counted coincides with the rank of the card that is being turned up, then the player loses the game.' (from Combinatorics, Dartmouth]

Why is figuring out the odds of losing this game not as straightforward as it might at first appear?