(Suggested by Sam Kaufmann, Indiana University MBA, who has run Harrah's Lake Tahoe Casino)
A high roller comes to the casino intending to play 500 hands of blackjack for $1 a hand. On each hand, the high roller will win $1 with probability 0.48 and lose $1 with probability 0.52.
After the 500 hands, what is the probability that the casino has lost more than $40?