Question

On January 20,2000 , the International Gaming Technology company issued a press release: (LAS VEGAS, Nev.) - Cynthia Jay was smiling ear to ear as she walked into the news conference at The Desert Inn Resort in Las Vegas today, and well she should. Last night, the 37 -year-old cocktail waitress won the world's largest slot jackpot - \(\$ 34,959,458\) - on a Megabucks machine. She said she had played \(\$ 27\) in the machine when the jackpot hit. Nevada Megabucks has produced 49 major winners in its 14-year history. The top jackpot builds from a base amount of \(\$ 7\) million and can be won with a \(3-\operatorname{coin}(\$ 3)\) bet. a) How can the Desert Inn afford to give away millions of dollars on a \(\$ 3\) bet? b) Why did the company issue a press release? Wouldn't most businesses want to keep such a huge loss quiet?

Short answer

Casinos win overall due to payout percentages and jackpots are advertising. The press release attracts more players and builds trust.

Step-by-step solution

Understanding the Casino Business Model

Casinos make money by providing games where the odds are in their favor. The slot machines are programmed to return a certain percentage of all money wagered over time, known as payout percentage. While a large jackpot may seem like a loss, it is a part of this programmed payout.

Jackpot Building Mechanism

The Megabucks jackpot is progressive, meaning it builds up over time from all the bets made in the network of linked machines. The base jackpot is set at $7 million, but with every bet, a portion contributes to increasing the jackpot.

Probability of Hitting the Jackpot

The probability of hitting such a high jackpot is extremely low, which means most players do not win it, and the casino collects more than it pays out in the long run.

Press Release as Marketing Strategy

Issuing a press release about a huge jackpot winner serves as advertising for the casino. It attracts more visitors and players eager to try their luck, thereby increasing business despite the apparent "loss."

Publicity and Trust

Such public acknowledgments also build trust in the fairness of the casino games, as they demonstrate that real people win and the process is transparent.

Key concepts

Casino Business Model

Casinos operate on a business model designed to generate profit through games that offer a statistical advantage, known as the "house edge." This edge ensures that, over time, the casino will make more money than it pays out. Here's how it works:

• **House Edge:** Every game is structured in a way where the odds are slightly in favor of the casino. For instance, in roulette, betting on a single number has a probability of 1 in 38, giving the casino a slight advantage.
  
• **Payout Percentage:** Each game, particularly slot machines, is programmed to return a certain percentage of all the money wagered. Although occasionally a player wins big, like with Megabucks, the average payout percentage ensures that the casino profits over time.
  
• **Volume of Play:** Casinos also rely on the high volume of plays, meaning thousands of small losses from players accumulate into significant revenue, which can cover large payouts.
  

By efficiently leveraging these aspects, casinos can offer huge jackpots while ensuring long-term profitability.

Probability Theory

Probability theory is fundamental to understanding how gambling works. It explains why casinos can afford to offer massive jackpots without financial ruin.

• **Odds:** The odds of hitting a Megabucks jackpot are extremely low — often one in millions. This means that while the occasional player wins big, the vast majority of players contribute to building up the jackpot without winning themselves.
  
• **Expected Value:** This is the calculated average outcome of an event that considers all possible outcomes. In gambling, while a single game might result in a win for a player, the expected value is usually negative for the player, meaning they will lose money over time.
  
• **Randomness:** Slot machines are driven by random number generators (RNGs), ensuring each spin's outcome is independent and unpredictable, maintaining fairness and ensuring the rarity of hitting the jackpot.
  

Understanding these principles helps explain why casinos can manage massive payouts without financial instability.

Progressive Jackpots

Progressive jackpots are a fascinating aspect of gambling, adding excitement and potentially life-changing wins. Here's how they work:

• **Jackpot Accumulation:** In a progressive jackpot system, a small portion of every bet made in a network of linked machines contributes to the jackpot, causing it to grow incrementally over time.
  
• **Base Amount:** For games like Megabucks, the jackpot starts at a base amount (e.g., $7 million). This ensures that even early on, the potential winnings are substantial.
  
• **Drawing Players:** The allure of a rapidly increasing jackpot entices more players to participate, fueling the jackpot's growth. This also increases overall play volume, benefiting the casino's profits.
  
• **Community Aspect:** Many progressive jackpots require a network of machines, creating a sense of community as players across various locations contribute to building the jackpot.
  

By understanding the mechanics of progressive jackpots, players can appreciate both the rare chance of winning and the excitement they bring to the gambling experience.