STRATEGIES FOR GAMBLING: THE PLAYER’S VIEW SEVENTH LECTURE September 18, 2012 William R. Eadington, Ph.D. Professor of Economics, College of Business Director, Institute for the Study of Gambling and Commercial Gaming University of Nevada, Reno www.unr.edu/gaming
PRINCIPLES OF WINNING GAMBLING STRATEGIES • “Finding the Edge” => Find out when EX >0 • Winning Strategy => Wager only when EX > 0 • Casino exploitable wagers: Sports betting, poker, video poker (under unusual circumstances), progressive Keno games (under unusual circumstances); blackjack • Most casino games: Fixed odds wagers, where EX < 0 • NYG -1.5 CAR for Thursday’s game. What is the House Advantage?
PERSPECTIVE ON HOUSE ADVANTAGE “Percentages never lie. We built all these hotels on percentages. We stay rich on the percentage. You can lose faith in everything, religion and God, women and love, good and evil, war and peace. You name it. But the percentage will always stand fast.” Mario Puzo, Fools Die (1978)
PRINCIPLES OF CASINO MARKETING “Casinos make their living encouraging people to believe in systems, in luck, cultivating the notion that some people are better gamblers than others, that there is a savvy, macho personality that can force dame fortune to obey his will.”Peter Griffin, The Theory of Blackjack
HOW DO CASINOS MAKE MONEY AT GAMES & GAMING DEVICES? Each wager is offered at a “price” and generates a “quantity” of the product sold • As with any other retailer, total revenues for the entire casino equal price times quantity over all the different gaming offerings • Price = House Advantage • Quantity = Handle • Unlike other products, there are short term fluctuations in realized price away from House Advantage, and therefore performance => “luck” • Realized Price = Actual Player losses/Actual Handle
Compare table and gaming device play on the Las Vegas Strip to casinos in Reno, Boulder Strip, Downtown Las Vegas Fundamentals of Pricing: • Monopoly or under-supply gives pricing power to the casino • What is scarce for the player: time or money? • Some players are very sensitive to “time on the machine” or “time at the table”
GENERAL OBSERVATIONS ON PRICING • Tourist areas price higher on gaming products than locals’ casinos • Economically desperate areas will price lower than successful areas • Low denomination slot machines are more expensive to players than high denomination machines • Penny slots and multi-denomination machines have been taking over the market in recent years • Some players are very sensitive to “time on the machine” or “time at the table” => Need to look at variance as well as HA as a behavioral variable • Variance (V) is defined as the average squared distance from the mean; Standard deviation is the square root of V • Lower variance makes the trend of outcomes more predictable
VIEWING CASINO GAMES AS COMMODITIES PRICE = HOUSE ADVANTAGE (HA) =“THEORETICAL WIN RATE”: Limiting value of the ratio of casino win/handle as number of plays gets very large, or HA = W*p + L*q per 1 unit wager, where p = probability of win, q = probability (lose) HA = (Wi*pi + Lj*qj) over all wagers W = amount to be won, and L = amount to be lost (i.e. $1 to “normalize”) QUANTITY = HANDLE = amount wagered CASINO EXPECTED WIN = HAi* Handlei, added up over all games VARIANCE = P(WINi)*($WINi – HA)2
A VERY SIMPLE GAMBLING GAME Flip a coin once. • Heads => You win $1.00 • Tails => You lose $1.00 • EXPECTED VALUE? • VARIANCE? • Change the game: Heads => You win $0.95 • Tails => You lose $1.00 • EXPECTED VALUE? • VARIANCE?
THE PRICE OF CASINO GAMES *STRATEGY GAMES