# House Edge

It’s impossible to understand how a casino makes its money without understanding the house edge. That one number is the key to a casino’s profits. It’s also a way of comparing casino games to decide which games are better than the others. And once you understand what the house edge is and how it works, you’ll also understand other important numbers in the casino, including:

• Average hourly loss
• Payback percentage

## What Is the House Edge and How Does It Work?

One of the most commonly asked questions regarding gambling is whether or not casino games are rigged. The truth is, they ARE rigged, but probably not in the way you think. Casinos can’t decide which pocket a ball on a roulette wheel lands in order to force you to lose, for example. Their dice aren’t loaded, and their cards aren’t marked. Blackjack dealers aren’t forcing you to get certain cards at certain times.

Casino games are rigged because all their bets pay off at odds that are lower than your odds of winning.

## An Example of How Casino Games Are “Rigged”

Here’s an easy example to understand:

Suppose you’re playing a simple casino game involving a coin toss. You guess whether the toss of the coin is going to be heads to tails. You have to bet a dollar to play. If you guess right, you win 95 cents. If you guess wrong, you lose your dollar. Since the odds of winning and losing are the same, and since you win less money than you would lose, the casino will win over time. You might get lucky and guess right a few times in a row, but if you play long enough, the casino will inevitably profit.

The difference between the odds of winning and the odds that the bet pays off at is the house edge. It’s expressed as a percentage, and it’s the amount of money the casino expects you to lose per bet over the long run.

## The House Edge in Roulette – Another Example of Odds in Action

My favorite example is roulette, because it’s so easy to understand. Let’s assume you’re betting \$100 on every spin of the roulette wheel. A roulette wheel has 38 possible outcomes, numbered 0, 00, and 1-36. When you bet on a single number and win, you get paid off at 35 to 1. But the actual odds of winning are 37 to 1.

Let’s stop for a second and talk about odds. The word “odds” is just a way of expressing a probability or a payoff. If you’re using odds to describe a probability, then you’re looking at the number of ways something can’t happen versus the number of ways it can happen. In that example, there are 37 ways to lose and only 1 way to win. If you’re using odds to describe a payoff, then you’re looking at how much you’re getting paid if you win compared to how much you’re risking. In this example, you win \$35 for every \$1 you bet.

## The Long Run versus the Short Term

The house edge assumes that in the long run the actual results are going to mirror the results you’d predict using probability. If you play long enough, your ratio of losses to wins on single number bets will start to get close to 37 losses for every win. What does that do to the amount of money you’ve won or lost?

Since we’re assuming a \$100 bet every time, we can look at a mathematically perfect sampling and calculate the house edge easily. You make 38 roulette spins, losing 37 of them and winning one of them. You lose \$3700 on the losing spins, and you win \$3500 on the winning spin. Your net loss is \$200. Since you’re wanting to know the average of what you’ve lost on every spin, you divide that \$200 by the total number of spins (38). \$200/38 = \$5.26. So you’re losing an average of \$5.26 every time you bet \$100. That’s a house edge of 5.26%.

Casinos use this number to predict how much money they’ll make on any given casino game over a long period of time. Since they’re running multiple games over multiple hours with multiple players, they’re going to see results that resemble their long term expectation a lot sooner than any individual gambler would. Let’s say an average casino has 4 roulette tables with an average of 4 players running 24 hours a day. And let’s say the average player is betting \$100 and making 55 bets per hour. This means the casino is seeing 4 X 4 X 24 X \$100 X 55 = \$2,112,000 in action per day. They expect to win 5.26% of that, or \$111,091.20.

An individual player is more likely to spend 4 hours at a single table making 55 bets at \$100, but since in the short run anything can happen, that player might walk away a winner. He might even walk away a winner in multiple sessions. But the odds are against it. And if he plays long enough, the math will inevitably catch up with him, and he’ll see a net loss similar to the expected loss.

## Average Hourly Loss Rates

The casino isn’t going to worry about that, though, because they know that the average hourly loss is going to make up for it. The average hourly loss for a player at a casino game is simply the average amount bet multiplied by the house edge by the number of bets per hour. In this example, the casino expects the individual player to average out to an average hourly loss of \$289.30. But some hours the player might be up \$300 and other hours he might be down \$600.