CHAPTER 9 PRODUCT: GAMES and STATISTICS

1. CHAPTER 9PRODUCT: GAMES and STATISTICS Robert C. Hannum University of Denver

2. Introduction • Overview of Casino Games • Some casino games are pure chance. • No amount of skill or strategy can alter the odds • Roulette, craps, baccarat, keno, the big-six wheel of fortune, slot machines • Some games have an element of skill. • An element of skill can affect the house advantage • Blackjack, video poker, and the four popular poker-based table games: Caribbean Stud poker, Let It Ride, Three Card poker, and Pai Gow poker

3. Summary of Major Casino Games • Roulette: players try to guess which number will occur as the outcome of the spin of a ball around a numbered wheel. • Two types of wheels • The double-zero, common in the United States • contains 38 pockets, numbered 1 thru 36, 0, & 00 • 18 red, 18 black; 0 and 00 are green • The single-zero, favored in Europe • lacks 00; has only 37 numbers • Game is essentially the same regardless of which wheel is used. • House advantage for single-zero wheel is about half that of the double-zero.

4. Craps: betting on the outcome of roll of dice. • “Roll” determined as the sum of values of the two dice thrown (except for certain bets). • Wagers have myriad possibilities; each type has different odds, payoff, and house advantage. • The Pass Line – first roll of game or round is called the “come-out” roll. Pass line wager wins even money if come-out roll is a 7 or 11; loses if it is a 2, 3, or 12 (called craps). • Odds – can be taken after a point has been established on the pass line wager; can also be taken on “come,” or given on “don’t pass” and “don’t come” after a point is established.

5. Craps: Wagers (cont’d) • Come Bet – essentially a pass line bet on any roll after a point is established. It turns the next roll into a come-out roll that wins on a 7 or 11, loses on a 2, 3, or 12, and otherwise establishes a point. • Don’t Pass Bet– works opposite of pass line bet, except winning is barred on come-out roll of 12. Bettor wins on come-out roll of 2 or 3, loses on a 7 or 11, ties on a 12. On point rolls, wins if 7 is rolled before the point, loses if point is rolled before a 7. Like the pass line bet, odds can be given once a point is established.

6. Craps: Wagers (cont’d) • Don’t Come Bet – essentially a don’t pass bet made after a point has been established. • Place & Don’t Place Bets – a place bet on one of the point numbers is a bet that the number will roll before a 7. --A don’t place bet is the opposite: a bet a 7 will roll before the number. --Payoffs for both are less than true odds. • Buy & Lay Bets – similar to place, don’t place bets except that the payoffs are at true odds. A 5% commission is charged on the amount of a buy bet and on the possible winning amount of a lay bet.

7. Craps: Wagers (cont’d) • Field Bet – next roll will be 2, 3, 4, 9,10, 11,12. Payoff: 2 to 1 for 2 or 12, even on 3, 4, 9, 10, or 11. • Big 6 & Big 8 – bet that 6 will roll before a 7, or that an 8 will roll before a 7. • Hardways – wager that selected number will roll with doubles before any other way. Payoff: 7 to 1 for hard 4 & 10; 9 to 1 for hard 6 & 8. • Any Craps – one-roll bet that the next roll will be 2, 3, or, 12. If not, the wager is lost. Payoff: 7 to 1. • Any Seven– one-roll bet; 7 on next roll wins 4 to 1. • Craps & Eleven (C&E) – one-roll bet that roll is 2, 3, 11, 12. Pays 3 to 1 on the 2, 3, 12; 7 to 1 on 11.

8. Craps: Wagers (cont’d) • Two or Twelve – two separate one-roll bets, wager that next roll will be a 2 or that next roll will be a 12. Each typically pays 30 to 1. • Three or Eleven – Like two or twelve, two separate one-roll bets. Each typically pays 15 to 1. • Horn Bet – one-roll bet that next roll will be a 2, 3, 11, or 12. • Horn High Bet – horn bet made in multiples of five with the extra unit wagered on the “high” number designated by the bettor. • Hop Bet – next roll will be a certain combination. Two types: “easy” or two-way hop, such as 6-1; “hard” or one-way hop, such as 2-2.

9. Blackjack or “21”:the most popular and largest revenue-generating casino table game. • Popularity stems from simple play. • Player can guide his own destiny to some extent. • Correct perception that the game can be beaten. • Players are in friendly competition against casino. • Objective: to beat the dealer by having a total higher than the dealer’s without exceeding 21. The object is not, as some people think, to get as close to 21 as possible.

10. Baccarat • Results of consecutive hands are mathematically dependent; it is not possible to take advantage of this dependency. • A game of pure chance, unlike blackjack. • Relatively easy game to play, since hitting and drawing rules are fixed and no decisions are required (or even possible) once play begins. • Players need only decide whether to bet on the banker or the player (there is also a tie bet).

11. Caribbean Stud Poker • Standard deck of 52; uses usual 5-card rankings. • Let It Ride • Poker-type game; standard deck of 52, player places 3 equal-sized bets before cards are dealt. • Pai Gow Poker • Uses 53 cards – standard deck plus Joker. Joker can fill a straight or flush, or it is an Ace. After bets, players and dealer are dealt 7 cards, used to make a 5-card hand and a 2-card hand. Five-card hand must be equal to or higher than the two-card hand.

12. Three Card Poker • Relatively new poker-based game; popular due to its simplicity, fast action, and reasonably player-friendly house advantage. • Uses a single deck of 52 cards. • Each player’s hand is only three cards. • Rankings are slightly different from 5-card poker rankings.

13. Slot Machines • Term “slots” refers to: • Traditional (now computer controlled) reel-type • Video games now on the market • Slots are more popular in U.S. than table games: • They produce 70%-75% of the gaming revenues • Typically fill 80% or more of the floor space • Four types of slots that are most popular: • Traditional spinning reel machines • Video poker • Multi-line/multi-play video devices • Wide area progressives – linked together from many casinos; progressive jackpot gets progressively larger as more coins are dropped into the machine.

14. Keno • Players choose up to ten of the twenty numbers which are randomly drawn by computer from the numbers 1 through 80. • Several types of keno tickets are available. • Casino advantage on keno is large – 25% to 35% depending on the type of ticket and payout schedule.

15. Basic Casino Math • Importance of Mathematics in Casino Gaming • Relying mathematical principles assures that casinos generate positive gross gaming revenues • Many casino professionals fail to understand the basic mathematics of the games and their relationships to casino profitability. • Mathematics should also overcome the dangers of superstitions. • Important for the casino operator to ensure the reasonable expectations of the players are met. • Casino managers should also understand the mathematical aspects relating to gaming regulation.

16. Probabilities and Odds • Probability = long run ratio of: (# of times an outcome occurs) to (# of times experiment is conducted). • Odds = long run ratio of: (# of times an outcome does not occur) to (# of times an outcome occurs).

17. House Advantage • Represents the long run percentage of the wagered money that will be retained by the casino • The player’s chances of winning and the rate at which she wins or loses money depends on: • the game, • the rules in effect for that game, and • for some games, the level of skill. • The amount of money the player can expect to win or lose in the long run – if the bet is made over and over again – is called the player’s wager expectation, or expected value (EV).

18. Confusion About Win Rate • Some types of percentages in gaming: • Win percentage • Theoretical win percentage • Hold percentage • House advantage • Casino bosses sometimes use these terms interchangeably, but there are fundamental differences among them. • Some terms are interchangeable: • House advantage (how casinos make money) is same as theoretical win percentage; also called house edge and expected win percentage. • For slot machines, hold percentage is (in principle) equivalent to win percentage.

19. Win Rate Percentages: Summary • House advantage is also theoretical win percentage. • Hold percentage is win over drop: Hold % = Win/Drop • Win percentage is win over handle: Win % (actual) = Win/Handle • Win percentage approaches the house advantage as the number of plays increases. • Hold percentage is equivalent to win percentage for slots but not table games. • House advantage = Theoretical Win % = Limit (Actual Win %) = Limit (Win/Handle). • Hold Percentage  House Edge.

20. Volatility and Risk • Risk depends on the house advantage, standard deviation, bet size, and length of play. • Statistical theory is used to predict magnitude of difference between win % and theoretical win % for a given number of wagers. • The basis for analysis of volatility questions is a statistical measure called the standard deviation(essentially the average deviation of all possible outcomes from the expected mean).

21. Casino Games & Odds • Table Games • Player skill affects the house advantage in some games: • Blackjack; also Caribbean Stud, Let It Ride, Pai Gow, and Three Card poker. • Statistical advantage for these is usually reported assuming optimal strategy. • In blackjack, a player who follows basic strategy perfectly will maximize average gain, or minimize average loss.

22. Gaming Devices • House advantage for slots: theoretical win % or theoretical hold % • Flip side is proportion of wagered money returned to player: payback, orreturnpercentage. • Theoretical hold percentage can be set to virtually any value with the computer program that controls the machine. • Video poker, a game with an element of skill, can be favorable for the player if correct strategy is used.

23. Related Operations Issues • Player Value and Comps • Player earning potential (player value, player worth, theoretical win). • Using house advantage, bet size, duration of play, pace of the game, a casino can determine how much it expects to win from a certain player. • Calculated using this formula: Earning Potential = Average Bet  Hours Played  Decisions per Hour  House Advantage • Many casinos set comp policies by giving back a set percentage of the player’s earning potential.

24. Casino Pricing Mistakes • Casinos occasionally offer novel wagers, side bets, increased payoffs, or rule variations. • Effect – lowers the house advantage and the effective price of the game for the player. • Sound from a marketing standpoint, but can be disastrous if care is not taken to ensure the math behind the promotion is sound. • Gaming Regulations and Mathematics • Regulatory systems share common objectives: • Keep the games fair and honest and assure that players are paid accurately if they win.