Casino House Edge

Understanding how casino gambling works starts with an examination of probability, especially as it relates to the concept of the house edge. Related concepts include odds and probability, expectation, and payback percentages. Without understanding these concepts, it’s impossible to discern between a good bet, an average bet, and a bad bet.

Some people hate math. Those people probably shouldn’t gamble at all, but I promise to keep this guide to the house edge as mathematically simple as possible. Most of the calculations involve nothing more than a little bit of subtraction, addition, division, and multiplication, all of which you should have learned before going to high school.

Odds and Probability

Probability is the branch of mathematics that covers the likelihood of whether or not something will happen. It’s a type of math that’s used in almost all endeavors, but nowhere is it more important than in the business of casino gambling. The entire reason for the casino gambling is based on probability and odds.

To calculate the probability of something happening, you have to know what all the possible outcomes are. For example, if you’re flipping a coin, you know that there are only two possible outcomes—heads or tails. You’re also reasonably confident that you have just as much of a chance of getting on outcome as the other. You probably even know, instinctively, that the probability of getting heads is 50%, and the probability of getting tails is also 50%. But how do we arrive at that number?

The answer is a mathematical formula that determines the probability of a specific result. In math terms, the probability of something happening is expressed as P(X). That looks scary to math-phobes, but it’s just a symbol. Don’t freak out.

P(X) = number of potential ways to get result A/number of all possible outcomes.

The slash means “divided by”.

With out current example, that means that the probability of getting a result of heads when flipping a coin is ½, or 0.5, or 50%. There’s only one way to get heads, and there are two total ways of that coin landing.

You can apply this formula to other common gambling activities, too, like rolling a six-sided die, or drawing a card from a 52 card deck.

The probability of rolling a “1” on a six sided die is 1/6. There’s only one way to roll a 1, but there are 6 total possible outcomes.

The probability of drawing the ace of spades from a deck of 52 cards is 1/52. There’s only a single ace of spades in the deck, but there are 52 cards total in the deck.

Expressing Probability

You’ve probably already noticed that probability is expressed as a fraction, and if you remember anything from your math classes, it should be this—a fraction can be expressed in multiple ways. You can express a fraction as a decimal or as a percentage. When discussing probability, percentages are a common way of expressing probabilities.

In our three examples so far, we have a percentage probability of 50% for getting heads on a coin flip. We have a probability of 16.67% of rolling a 1 on a single six-sided die. And we have a probability of 1.92% of drawing the ace of spades out of a deck of 52 cards.

You can also express a probability in terms of “odds”. When you do that, you’ll use the word “to” in between the number of ways to achieve the outcome versus the number of ways NOT to achieve the outcome.

So in our existing examples, we’re looking at odds of 1 to 1 for getting heads on a coin flip, 5 to 1 for getting a “1” on a single roll of a die, and 51 to 1 for getting the ace of spades when drawing a card from a deck of 52 cards.

Understanding the difference between the actual odds of something happening and the odds that a bet pays off at is the beginning of gambling probability wisdom. For example, if you’re betting on a single number on a roulette wheel, there are 37 numbers that are losers and 1 number that’s a winner. The odds, therefore, are 37 to 1.

But that bet pays off at 35 to 1. The difference between a 35 to 1 payoff on a bet that you’ll win once out of every 38 bets is the house edge. Once you understand that, you’ll realize what a great business the casino biz is.

Probability is always a number between 0 and 1. When you’re discussing a probability, you’re discussing the likelihood of a given result. If something will never happen, then its probability is 0. (For example, you’ll never roll a “7” on a six side-die.) If something will always happen, then its probability is 1 (although it’s usually expressed as 100%). An example of something with a 100% probability is rolling a six sided die and getting a result of between 1 and 6.