If you’re a casino novice, you probably have no idea how the casino can give away all this money and stay in business. Maybe you have buddies who claim to win on the slot machines in Oklahoma more often than not. Or maybe you have a friend who loves to play blackjack and claims to be a winner.

Your friends’ claims might or might not be true, but understanding the house edge is the critical thinking skill needed to understand how the casinos stay in business.

I’m a firm believer that a well-educated gambler can make better decisions, so I’ve decided to explain the house edge and how it works in detail in this post.

It’s impossible to discuss the house edge without talking about some math, first. And the branch of math we’re interested in for these purposes is called “probability”.

Most people understand what probability means in a general sense.

But it’s important that we look at it in a much more specific sense.

Probability is a mathematical way of looking at how likely it is that something will or won’t happen.

And anything that can happen can be given a number representing its probability. This number is always a number between 0 and 1.

An event with a probability of 0 can never happen, and an event with a probability of 1 must always happen.

Then there’s everything that lies in between.

Numbers between 0 and 1 can be expressed in 3 common ways:

- As fractions
- As decimals
- As percentages

A less common way of looking at a probability is in odds format.

Let’s start with a common probability—the probability of flipping a coin and having it land on heads.

To determine that probability, you divide the number of events that you’re solving for by the total number of possible events. In this case, you’re solving for heads, which is one of 2 total possible events.

Represented as a fraction, the probability of getting heads is 1/2.

You can convert that into a decimal easily enough—just divide. You get 0.5.

You can also convert that into a percentage. Just multiply the decimal by 100 and add the % symbol. You get 50%.

Most people know that when something happens 50% of the time, that means half the time.

A useful way of expressing this number for gamblers is to express it as odds. You compare the number of ways something can’t happen with the number of ways that it can happen. In this case, we’re looking at 1:1 odds, also called even odds.

You can also look at probabilities of multiple events. You might want to know what the probability of getting heads twice in a row, for example. Or you might want to know the probability of getting heads at least once if you flip a coin twice in a row.

The operative word for figuring this out is the conjunction being used:

- And
- Or

If you’re calculating the probability that event A AND event B will happen, you multiply the probability for each of them.

If you’re calculating the probability that event A OR event B will happen, you add the probability for each of them.

In the coin-flipping example, the probability of getting heads on both tosses of the coin is 0.5 X 0.5, or 0.25%. That’s 25%.

This makes sense, too, because there are only 4 possible results when tossing two coins:

- Both coins land on heads
- Both coins land on tails
- Coin A lands on heads, and coin B lands tails
- Coin A land tails, and coin B lands on heads

Each of those are equally likely.

Let’s look at an example based on rolling a six-sided die for an “or” question.

Suppose you want to know the probability that you’ll get either a 2 OR a 3 when rolling a six-sided die?

Each of those outcomes has a 1/6 chance of happening.

Since it’s an “or” question, you add the probabilities together:

1/6 + 1/6 = 2/6, which is the same as 1/3.

When a casino game designer puts together a casino game, she sets up the bets so that they pay off at odds which are lower than the odds of winning.

We can create a quick casino game right now to demonstrate this.

Let’s design a gambling game where you predict the outcome of a roll of a single six-sided die. If you’re right, you get 4 to 1 on your money.

The odds of being correct are 5 to 1, but the payoff is 4 to 1. The difference is the house edge.

Why are the odds 5 to 1?

Because no matter which number you choose, there is only one way to roll it. There are 5 ways to roll something else.

Let’s now assume that you’re betting $100 per die roll on this game, and you play 6 rounds.

We’ll also assume that you see a mathematically perfect set of results. (We both know that in the short run this won’t happen, but the house edge is a mathematically predictive number.)

You’ll lose $100 on 5 of those rolls, for a total loss of $500.

You’ll win $400 on one of those rolls, for a total win of $400.

Your net result is a loss of $100.

If you average that out over all 6 bets, you lose $16.67 per bet.

Since we used $100 as our betting amount, it’s easy to turn this into a percentage.

The house edge for this game is 16.67%.

Of course, that’s an incredibly simplistic example, but it’s brilliantly illustrative, too.

Let’s now take a look at some of the things we can do with this number, this “house edge”.

The first thing to understand is that all these probability figures are estimates that are expected to hold true under a large number of repetitions. In the short run, anything can (and often will) happen.

It’s unlikely that you’d win 6 bets in a row in our example casino game from earlier, but it’s far from impossible. Someone who doesn’t understand math might get lucky and have no idea that the casino is going to come out way ahead in the long run.

This difference between short run results and long run results is where the casino makes its money.

In the short run, a certain percentage of gamblers go home winners. These are the people we were talking about in the introductory paragraph of this post. They’re at a complete loss to explain the math behind it, they just know they’re going home winners as often as not.

But in reality, they’re probably not going home as winners as often as they think they are or say they are. The human mind is a funny thing. It’s common for people to have confirmation bias and selective memory.

In other words, it’s human nature to remember the winning sessions (the exceptions) and forget the losing sessions.

How do we even define the long run, for that matter?

The long run is the point at which the mathematically predicted results are almost certain to mirror the actual results.

Over 6 or even 12 die rolls, we’re liable to see dramatic differences between the expected results and the actual results.

But over the course of 6000, 60,000, or even 600,000 repetitions, we grow increasingly likely to see actual results which resemble the mathematically predicted results.

This is exactly what the casino is counting on. They know some of the players are going to go home winners in the short run. In fact, they’re counting on it.

If no one ever went home a winner, no one would ever play a casino game to begin with.

But for every gambler who has an exceptional winning session, another gambler is almost certain to have an exceptional losing session—especially when you start dealing with thousands of players over the course of a year.

And since casinos have a relatively unlimited bankroll compared to most gamblers, they can afford to wait for the edge to kick in.

Casinos use the house edge in conjunction with a couple of other factors to forecast how much money they expect to win at a particular game. They even compare this number with how many square feet the game takes up in the casino. This is a standard revenue management tactic.

The factors they take into account for these forecasts include:

- The house edge
- The average number of bets per hour at the game
- The average amount wagered per bet at the game

Let’s suppose that your local casino has a roulette table. The house edge for that game is 5.26%. The local casino operates from the assumption that the table will average 4 players over the course of the year, and that the average player will place 50 bets per hour. This is a low rent casino, so they assume the average bet size is $10.

4 players betting $10 each 50 times per hour and losing 5.26% of that amounts to an average win for the casino of $105.20 per hour.

That doesn’t sound like much, but the casino is forecasting that for an entire year’s worth of action. 24 hours a day, 365 days a year.

They’re expecting to win $921,552 per year on that roulette table.

But the manager then thinks he can fit two slot machines into the same space. He doesn’t know if it makes sense to do that or not, so he looks at the numbers.

The average slots player makes 600 bets per hour, but only one person can play at a time. Still, with two machines in that space, we’re looking at 1200 bets per hour.

Let’s assume, too, that these are low stakes slot machines, and the average player is only betting 50 cents per spin. That means they’re putting $600 per hour into action.

Finally, we’ll assume that the house edge on these slot machines is 8%. (Not an unusual amount.)

The casino is expecting to win $48 per hour from those machines. Over the course of a year, that’s only $41,472.

The casino manager can compare those two numbers easily and see that the roulette table is a better deal.

In fact, it makes a lot of sense to the casino manager to have higher minimum bets on their slots games and a higher house edge, too.

You’re probably thinking, well, great—but what does that have to do with me managing my money and budgeting for my next casino trip?

The answer to that is simple, too.

You can estimate how much you’re expecting to lose at any casino game, too.

You can then budget how much money you’re going to bring accordingly.

AND best of all, you can use this information to decide which games you want to play.

I’m fond of pointing out that the house edge is only one factor to consider when deciding which casino games you want to play. Personal preference is important, too. How fast the game operates is also important.

Here’s an example:

Roulette has a house edge of 5.26%.

Blackjack has a house edge of 1%, if you play well.

But you hate making strategic decisions. Roulette is better for you simply because you’re too stressed out to think about the correct play in every situation.

On the other hand, I don’t mind thinking strategically, but I’m also open to games of pure chance.

But I am frugal, and I want to get the most entertainment for my money.

I know that I’ll probably see 50 spins per hour at the roulette table, and that I’ll probably be betting $10 per spin. That’s $500 in action per hour.

With a 5.26% edge, that game is expected to cost me $26.30 per hour in the long run. I don’t mind losing that much money for an hour of entertainment, but I also know that on any given trip and in any given hour, my results might vary dramatically from that amount.

Blackjack, on the other hand, is a faster game. I can expect to see 70 hands per hour there, for $700 per hour in action.

I’m confident that with my knowledge of basic strategy, I can keep the house edge to 1% or less.

My predicted loss per hour at blackjack is only $7.

I know which game I’m going to choose.

I also have a reasonable idea of how much money I should budget for gambling for my trip. I calculate it thus:

I start by assuming I’ll gamble 4 hours a day every day I’m in Vegas.

I’ll also assume that I’ll need significantly more than my expected loss per hour in bankroll—probably at least 10 times that much.

I’m planning a 3-day trip, so that’s 12 hours at the blackjack table. My expected loss is $84.

I’m going to take $840 with me and earmark it for playing blackjack. If I lose all that, I’ll have to find something else to do besides gamble.

I also have money for food and entertainment in a separate budget.

You can use the same approach when planning your trip. You might decide you have a higher tolerance for risk than I do. You might just multiply your expected losses by 5 when determining your bankroll size.

Here’s a list of the most common casino games and their house edge figures:

- Blackjack
0.5% to 1% if you’re using basic strategy, 4% or more if not.

- Craps
1.4% if you’re sticking with the best bets. As much as 16%+ if you’re not.

- Roulette
5.26% on a standard American game. 2.70% if you can find a European-style, single-zero wheel.

- Slot Machines
5% to 25%, depending on where you play

- Video Poker
0.5% to 8%, depending on where you play and whether you can use near-optimal strategy.

Some dedicated players can and do get an edge over the casino. It’s not easy. Most people don’t have the temperament for it, either.

Blackjack is the most common example of a game where you can get an edge over the casino. But you can’t get an edge by just making the correct play on every hand.

Most blackjack experts who get an edge over the house use card counting to get that edge. Counting cards doesn’t involve tracking which specific cards have been played. Instead, you use a system to track the approximate ratio of high cards to low cards in the deck.

A blackjack deck that has a relatively large number of aces and tens in it is more likely to produce a blackjack (a natural 21). This hand pays off at 3 to 2, so if you’re more likely to get this hand, you’ll want to bet more.

By raising the size of your bets in situations where the casino pays you more when you win, you get an edge over the casino.

But the rule of large numbers applies to you, too. Even if you have an edge of 1% over the casino, you are still likely going to have losing sessions. Some of these might last a long time, too.

Unlike the casino, you don’t have a near-limitless bankroll, either.

It’s also going to take you a lot longer to get into the large number of hands and bets required to almost guarantee that the expected results start to mirror the actual results.

The trick with card counting in blackjack, besides learning how to do it, is to keep your expectations reasonable. It’s also important to have a large bankroll, so that you can weather the almost inevitable losing streaks.

Another casino game where you can get an edge is video poker.

Getting an edge at video poker requires near perfect strategy AND the use of players’ club points. Here’s how that works:

The best video poker games have pay tables which lower the house edge to 0.5% or less.

The players’ club card entitles you to 0.2% or more in rebates.

If you can find a video poker game with a low enough house edge and combine that with a players’ club card that offers a reasonably high rebate percentage, you can get an edge over the casino.

This isn’t the easiest thing in the world to pull off.

For one thing, most video poker games have less-than-optimal pay tables and payback percentages.

For another, many gamblers don’t have the patience to develop the requisite levels of skill. You have to play with near-perfect strategy to get the house edge that low.

It also helps to find casinos which offer double and/or triple player rewards during certain hours.

Even if you get an edge at video poker, the game is played for such low stakes that you won’t earn much per hour.

And all the stuff I mentioned about having a big bankroll at the blackjack tables?

That applies to video poker, too.

Understanding the house edge is a critical part of being an educated gambler. I don’t judge people who enjoy gambling. I like to gamble, myself.

But if you’re going to gamble, you should understand what you’re doing.

A basic understanding of probability and the house edge is just the beginning, but it’s an essential beginning.

May 24, 2017 12:00 am

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