  The game of memory is played with a deck of n pairs of cards. The cards in
each pair are identical. The deck is shuffled and the cards laid face down. A
move consists of flipping over first one card then another. The cards are
removed from play if they match. Otherwise, they are flipped back over and the
next move commences. A game ends when all pairs have been matched. We determine
that, when the game is played optimally, as n tends to infinity: 1) The
expected number of moves is (3 - 2 ln 2)n + 7/8 - 2 ln 2 (approximately 1.61
n), 2) The expected number of times two matching cards are unwittingly flipped
over is ln 2, and 3) The expected number of flips until two matching cards have
been seen is asymptotically sqrt{pi n}.
