Casino Games and Numbers (How They Work Together)

I read a post by another gambling blogger where he contends that “almost all casino games are based on numbers.”

That’s a silly statement for a couple of reasons:

  • The first is that ALL casino games are based on numbers (not “almost” all).
  • The second is that such a statement is so obvious that it doesn’t even need to be said.

When you’re betting on something, you’re putting up a certain amount of money that you risk losing. You also have the possibility of winning a certain amount of money.

In many cases, the amount you risk and the amount you stand to win are the same, but not always.

Even when the amounts are the same, though, you’re dealing with math – it might be as simple as addition and subtraction, but it’s numbers, nonetheless.

An Example of How Important Numbers and Math Are to Roulette Players

One of the phenomena I noticed early in my career as an online gambler is that casinos almost always offer both single-zero and double-zero roulette.

This implies that some players are deliberately choosing the double-zero game over the single-zero game.

But there’s not a single reason to choose the double-zero game over the single-zero game.

If you know ANYTHING about the math behind the game, you’ll understand why. It’s baffling how many gamblers don’t bother to educate themselves even on the basic probability involved in roulette.

Here’s why it’s so important:

A double-zero roulette wheel has 38 numbers on it.

This means that the odds of winning a bet on any single number are 37 to 1. (In other words, you have 37 ways to lose and only 1 way to win.) The payoff for that bet is 35 to 1.

It’s easy to see how the casino makes a profit in that situation. If they win 37 times out of 38 spins, but they only payout 35 to 1, they’re going to profit until the cows come home.

A single-zero roulette wheel, though, doesn’t have 38 numbers on it. It only has 37 numbers. One of the zeros is gone.

How does this change the odds?

Dramatically.

Instead of a 37 to 1 shot at winning 35 to 1, you now have a 36 to 1 shot at winning 35 to 1.

On average, in the long run, the player on the double-zero roulette wheel is going to lose 5.26% of every bet.

The player on the single-zero roulette wheel is going to lose only 2.70%.

Why would you spend twice as much money, in the long run, to play what is, virtually, the same game?

Craps Is Another Good Example of How the Numbers Work in a Casino Game

You have 11 possible outcomes when you roll a pair of dice:

  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 11
  • 12


But some of those totals are more likely to come up than others because there are multiple ways to roll them.

In fact, there are 36 possible outcomes when you roll a pair of dice, even though those outcomes always fall into one of those 11 totals.

For Example:

There’s only one way you can roll a total of 2 in craps.

Each of the two dice must land on a 1 for this to be possible.

But there are two ways you can roll a total of 3 in craps. You can roll a 2 on the first die and 1 on the second die, or you can roll a 1 on the first die and a 2 on the second die.

This means that a total of 3 is twice as likely to come up than a roll of 2.

You can continue that analysis through all the possible totals.

The next thing to think about in craps is the odds of winning versus the payout odds.

Let’s say you bet on snake-eyes – the possibility that the shooter is going to roll a 2 on his next throw. Let’s also assume it’s a single-roll bet.

Since there are 36 possible outcomes, and only one of them is a 2, you have a 35 to 1 probability of winning that bet.

The payout for this bet, though, is 30 to 1.

Can you see why the casino might make a considerable profit from a bet on “snake-eyes?”

Let’s assume you bet $100 on snake eyes 36 times in a row and see statistically perfect results.

In other words, you win once and lose 35 times.

  • This means you win 30 X $100, or $3000.
  • But you’ve also lost $100 X 35, or $3500.
  • Your net loss is $500, which can be averaged out over those 36 bets by just doing some division.
  • 500 divided by 36 is $13.89.

Do you really want to take a bet where your average loss is 13.89% over time?

If you think that roulette sounds more attractive compared to this bet on the craps table, you’re right.

But craps does have other bets with better odds. Stick with the pass, don’t pass, come, don’t come, and free odds bet, and you’ll be facing some of the best odds in the casino.

What Is the House Edge and What Does It Have to Do with the Payback Percentage?

When writing about or talking about casino table games, we discuss “the house edge.”

The house edge is just a statistical way of measuring the payout odds versus the odds of winning so that we know what the average amount lost per bet will be over the long run.

Payback percentage, on the other hand, is a measurement usually used to describe gambling machines like slots and video poker.

The reason that’s done differently is that the payout odds for table games are expressed as odds in “to” format, while gambling machines use odds expressed as “for” format.

In other words, in a table game, if you win even money (1 to 1), you show a profit of a single unit. You win a unit on top of your initial bet.

But on a gambling machine, an even money payout is done as 1 FOR 1, which means you’ve traded the single unit you bet for the single unit you won. In a table game, this would be called a “push.”

Table games do have a payback percentage, though, and gambling machines do have a house edge, too.

The payback percentage just measures how much of each bet you’re mathematically expected to get back over the long run on average.

If you subtract the house edge from 100%, you’ll get the payback percentage for the game.

If you subtract the payback percentage from 100%, you’ll get the house edge for the game.

The house edge and the payback percentage, when added together, always total 100%.

Conclusion

Those are just a couple of examples of how numbers work in casino games, even if the game doesn’t use numbers to determine your outcome.

Understanding these basics of probability in casino games is a critical part of being an educated gambler.

I don’t think you should eat out at a restaurant if you don’t know how many calories are in a dish.

I also don’t think you should gamble on a casino game if you don’t know what the house edge and/or payback percentages are.

If you’re perceptive, you probably realize this means I think you should avoid slot machines altogether.

What do you think?

How do the numbers affect your view of casino games?

Let me know in the comments.

Michael Stevens: Michael Stevens has been researching and writing topics involving the gambling industry for well over a decade now and is considered an expert on all things casino and sports betting. Michael has been writing for GamblingSites.org since early 2016.