Lesson
The Mathematics of Gambling
Learn how gambling is mathematically designed to ensure the house always wins.
The Mathematics of Gambling
Here’s a fact: You are mathematically guaranteed to lose money in the long run if you continue to gamble.
Why? Because the house always has the edge.
In this lesson we’ll explore how the math of gambling works against us, and how that should inform how we engage in gambling.
The House Edge
The house edge is the statistical advantage that the casino holds over players in every casino game. It ensures that, over time, the casino will make a profit from the bets placed by players.
The two fundamental mathematical principles that create the edge for the casino are the Law of Probability and Expected Value, and the Law of Large Numbers. Let’s take a deeper look at both of them to understand how they operate:
Probability and Expected Value
Casino games are designed with specific probabilities and payouts that favor the casino. These probabilities determine the likelihood of different outcomes and their associated payouts.
The expected value (EV) of a bet calculates the average amount a player can expect to win or lose on a bet based on these probabilities and payouts. ALL casino games have a Negative EV for the player.
Ever wonder why slot machines are everywhere in casinos? It’s because they are the most efficient money-making tools for the casino operators. In slot machines, the house edge is represented as the Return to Player percentage, or RTP. The RTP represents how much an individual machine has paid out over its lifespan. That is, the difference between how much money has been put in v. how much money has been paid out.
Most slot machines have an RTP of between 90-97%. Put another way, for every dollar you insert into a slot machine, the casino is taking between $0.03 - $0.10.
So yes, you may see someone hit a big jackpot on the casino floor, but if you do the math, and realize that Americans spent over $34 billion on slots in 2022 alone…you’ll see that even just 3% of that is an astronomical number.
However, it’s not just slot machines. The casino has the edge in every game they offer:
Sports Betting
Typically lower than most casino games, but it varies depending on the specific sportsbook's margins.
Slot Machines
Can vary widely, often ranging from 2% to 15% or more, depending on the specific machine and casino.
Poker
In poker games, players compete against each other, and the casino's revenue comes from rake (a small percentage of each pot) or tournament fees.
Video Poker
Varies depending on the specific variant and player strategy.
Blackjack
Typically around 0.5% to 2%, depending on the specific rules and player strategy.
NOTE, even if you have a “system” you’re still on the losing side of the house edge.
Craps
Pass Line Bet: About 1.41%
Don't Pass Line Bet: About 1.36%
Other bets in craps have varying house edges.
Roulette
American Roulette (with 0 and 00): Approximately 5.26%
European Roulette (with single 0): Approximately 2.70%
Baccarat
Banker Bet: Approximately 1.06%
Player Bet: Approximately 1.24%
Tie Bet: Approximately 14.36%
Bingo
Varies depending on the specific bingo game and location but can range from 2% to 8% or more.
Keno
Typically ranges from 25% to 30% or higher, making it one of the highest house edge games.
Lotteries
Generally very high, often exceeding 50%.
The Law of Large Numbers
The law of large numbers is a mathematical principle that states that as the number of trials (bets) increases, the actual results will get closer to the expected results.
Which means, even those “BIG” wins don’t move the needle very much toward the casino losing money. The casino is more than happy to payout a few big wins to rake in all the profit on the HUGE NUMBER of small losses.
This is why casinos do everything they can to keep you gambling. “Free” bets. “Free” drinks. Comped rooms. Entertainment. As long as you and many other gamblers keep playing, they know they’ll win in the long run.
Cost per Play
One very helpful tool to help you understand how much money you can expect to lose while playing casino games is a cost per play calculator.
To use it, simply plug in your numbers based on your favorite games and see how much you’ll pay the casino over an hour, month and year.
Let's Reflect
How has learning about the mathematics behind gambling influenced your perception of risk and probability?
How do you feel about the idea of "the house always wins" in light of understanding the mathematical principles behind casino games?
Closing Thought
Understanding the mathematics of gambling can help us make more informed decisions when wagering. By grasping concepts like probability and expected value, we can approach gambling with a clearer understanding of the risks involved.
Remember, while gambling can be entertaining, it's essential to stay mindful of the mathematical realities to gamble responsibly and enjoy the experience safely.
Keep learning and stay informed to make the most of your gambling experiences.