BlackJack is a popular casino game in which a player is dealt two cards where the value of the card corresponds to the number on the card, face cards are worth ten, and aces are worth either one or eleven. The object is to get as close to 21 as possible without going over and have cards whose value exceeds that of the dealer. A blackjack is an ace and a ten in two cards. It pays 1.5 times the bet. The dealer plays last and must draw a card with sixteen and hold with seventeen or more. The following distribution shows the winnings and probability for a $20 bet. In cases where the dealer and player have the same value, there is a tie (called a "push"). Source: "Examining a Gambler's Claims: Probabilistic Fact-Checking and Don Johnson's Extraordinary Winning Streak" by W.J. Hurley, Jack Brimberg, and Richard Kohar. Chance Vol. 27.1, 2014.

Winnings Probability

0.........................................0.0982

$30......................................0.0483

$20...................................0.389275

-$20..................................0.464225

(a) Compute and interpret the expected value of the game from the player's point of view.

(b) Suppose over the course of one hour, a player can expect to be dealt about 40 hands. How much should a player expect to win or lose over the course of three hours?