1. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. CHAPTER 9 PRODUCT: GAMES and STATISTICS Robert C. Hannum University of Denver

2. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Gaming Devices House advantage for slots: theoretical win % or theoretical hold % Flip side is proportion of wagered money returned to player: payback, or return percentage. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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. Hashimoto: Casino Management: A Strategic Approach © 2008 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. 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.