Why Does a Casino Make a Profit if the Games Are Random?

I have a friend I’m really fond of who believes in all kinds of conspiracy theories. He’s a nice guy, but he thinks the earth is flat.

He’s also convinced that the casino makes all its money from cheating. In fact, he told me once that the only fair game in the casino is craps, because you can’t fake the roll of the dice.

I’m not sure why he thinks dice are immune to being “fixed” while roulette wheels and playing cards aren’t. I understand how any of those devices could be fixed.

But casinos don’t need to fix any of these devices to make a profit.

They have a really simple means of making a profit and keeping their games completely random.

They examine the odds of winning for a game, then when they set their payout odds, they set them lower than the odds of winning.

What Are Odds and How Do They Work?

One of the ways of looking at the probability of something happening is by looking at the odds that it will or won’t happen.

Probability is just a ratio that compares the number of ways a specific event can happen with the number of ways it can’t happen.

That’s the probability expressed as a fraction, as a percentage, and as odds.

1 to 1 means there’s one way to lose and one way to win.

When you roll a 6-sided die, what’s the probability of rolling a 6?

There’s one way to roll a 6, and there are 5 ways to roll something that’s not a 6.

So the odds are 5 to 1.

But there’s more to odds than that.

Odds also is a way of describing how much your bet pays off.

If you received 1 to 1 odds on guessing a coin toss, that would be called even money. You could bet $100, and if you won, you’d win $100. If you lose, you’d lose $100.

If you received 5 to 1 odds on guessing the outcome of a die roll, you’d break even over the long run. You’d win $500 every time you won, but you’d lose $100 on the 5 out of 6 times that you lost.

The way the casino makes its profit is by paying you winnings that are lower than the odds that would make a game break-even.

For example, if the casino made you risk $110 to win $100 on a coin toss, in the long run, the casino would make a profit.

50% of the time, they’d lose $100. The other 50% of the time, they’d win $110. It’s easy to see how they could make a profit doing that, right?

Or, if the casino paid off at 4 to 1 on guessing the correct outcome on a roll of a single die, they’d be making a clear profit, too, right?

5 out of 6 times, you’d lose $100. Only once out of 6 times would you win $400, which means the casino would come out ahead in the long run.

The Effect of Short Term Variance

If this is how the bets are set up, and if most people know it, why do people still gamble on casino games?

There are 2 reasons:

The first is that people are woefully uneducated about basic math in this country. Fewer casino customers than you think understand how the math behind these games works.

The second is that when you’re dealing with random events, in the short run, anything can happen, no matter how unlikely.

If you guess that a 6 will come up on the next roll of a 6-sided die, you’re PROBABLY going to lose.

But sometimes you’ll win.

In math, there’s something called the Law of Large Numbers.

This is the premise that if you repeat something random often enough, eventually, your actual results will resemble the statistically predicted results.

If you roll a 6-sided die 6 times, you might get the same number 3 or 4 times.

But if you roll a 6-sided die 6000 times, you’ll usually see a pretty even distribution for which number comes up.

This short term variation is what gamblers call luck.

That’s how some gamblers walk away from the casino winners even though the odds are against them.

How the Casino Makes Its Profit from Blackjack

Blackjack seems like a game where the casino couldn’t have an edge. In fact, it seems like a game where a smart player might get an edge over the house just by knowing how to play his cards.

After all, the odds of getting various cards are the same for both the player and the dealer.

AND the player gets a 3 to 2 payout anytime he gets a 2-card total of 21.

It’s simpler than you think, actually. The house edge in blackjack comes from the fact that the player has to play his hand before the dealer plays hers.

If your hand busts, you lose your chips immediately, before the dealer plays her hand. Even if the dealer busts, too, you’ve lost your money.

That, by itself, is enough of an advantage for the casino to make a profit.

Even if you play with perfect basic strategy, you’ll probably bust your hand around 30% of the time.

Even if the casino busts, too, you’ve already lost your bet.

The other advantage the casino has is if the dealer gets a natural, you don’t even get to play your hand. Your only hope is if you also have a natural, which is treated as a push. You don’t win any money, nor do you lose any money in that situation.

How the Casino Makes Its Profit from Craps

Craps is known for being exciting and for having a wide variety of bets you can make.

But every bet at the craps table (save one) pays off at less than the odds of winning. The only bet where that isn’t true is called (appropriately enough) the odds bet, and it pays off at true odds.

But to place that bet, you must have first placed a bet on the pass line or the don’t pass line. (Or the come or don’t come.)

Those are the best bets at the craps table, by the way, but they still give the house an edge of 1.41% or 1.36%. The other bets at the craps table are all far worse, and they all result in a profit for the casino because they don’t pay off at the same odds they have of winning.

Here’s an example of a craps bet, its odds of winning, and the payout odds for that bet:

The “any 7” bet is a single-roll bet that the results of the next roll of the dice will total 7.

The odds of winning that bet are 5 to 1.

The payout is 4 to 1.

I used the same example in the introduction when I talked about the probability of rolling a single die.

How the Casino Makes Its Profits from Roulette

Roulette is my favorite example of how probability works, especially as it relates to casino games and the house edge. It’s a simple game, too.

You have a spinning wheel with 38 possible outcomes. The pockets in this wheel are numbered 0, 00, and 1-36. The 0 and the 00 are both green. Half the numbers 1 through 36 are black, and the other half are red.

You have a variety of roulette bets available to you, but all of them share the same house edge. (Well, except for one bet, which I’ll explain here, too.)

The easiest bets, and the ones which win the most often, are the even money bets. These are the bets where if you bet $100 on them, you win $100.

An example of an even-money bet is a bet on red. Since almost half the numbers are red, you have an almost 50% chance of winning this bet.

But the 0 and the 00 make it so that the bet doesn’t pay off at the same odds as the odds of winning.

You have 38 possible results, and 18 of them are red. That’s 18/38, or 47.37%.

If you had a statistically perfect set of 38 spins, you’d win that bet 18 times, but you’d lose 20 times. You’d win $1800 on your winning spins, but you’d lose $2000 on your losing spins. Your net loss would be $200.

If you averaged that by the number of spins you made, you’d have an average loss per spin of $5.26.

All the bets on an American roulette wheel pay off at odds that would be a break-even proposition IF the 0 and the 00 weren’t on the wheel.

The bet that wins the least often in a roulette game is a single-number bet. This is a bet on a specific number, like 18, for example.

You have a 37 to 1 shot of winning this one, but when you do win it, you only get paid off at 35 to 1. The same averages apply—this bet also has a 5.26% edge.

One bet at an American roulette table has a higher house edge than that, though. It’s the 5-number bet, which is a bet that the ball will land on 0, 00, 1, 2, or 3.

That bet has an even higher house edge—7.89%.

The only correct strategy in an American roulette game is to place any bet you want as long as it’s not the 5-number bet. No strategy can overcome the inherent mathematical edge built into the game.of people come up with roulette systems based on changing the size of your bet based on what happened on previous spins of the roulette wheel. None of those systems improve your probability of winning in the long run.

The best explanation I ever read of how the various roulette betting systems work is that it’s like trying to add up negative numbers to get a positive result. No matter how you size those negative numbers, they’re still negative, and you’ll still wind up with a long-term loss.

How the Casino Makes Its Profit from Slot Machines and Video Poker

Slot machines and video poker do the same thing. They just have more possible prize amounts on their pay tables.

But each of those potential payouts has a probability.

The payout for that possibility is always lower than the probability that you’ll hit it.

What’s the probability of having that outcome?

It’s 1/10 X 1/10 X 1/10, or 1/1000.

If you make 1000 statistically perfect spins, you’ll lose $1000 (betting a dollar per spin). You’ll win $900. That’s a net loss of $100 over 1000 spins, which means that this slot machine has a 90% payback percentage and a 10% house edge.

Video poker games work the same way, although the probabilities are driven by the probabilities inherent in poker hands and decks of cards. The probability of getting a flush playing Jacks or Better video poker is the same as it would be if you were dealing out of a deck of 52 cards.

I should point out one big difference between gambling machines (like slots and video poker) and table games.

The payouts for table games are made on an X to Y basis. For example, a payout on a single-number roulette bet is 35 to 1.

This means that if you lose, you lose $1.

If you win, you keep your bet, and you win $35 on top of it.

But with a gambling machine, the payouts are made on an X for Y basis.

This means that if you lose, you lose the amount you bet.

But if you win, you get the winnings, but you don’t get your original bet back on top of it. You traded your wager FOR the winnings.

This implication is important, because you’ll find many games that offer an even-money payout on a specific hand or combination of reel symbols.

On a gambling machine, this is just a push. You haven’t really won anything. You just got the size of your bet back. If you were playing blackjack, this would be considered a push.

Conclusion

Why do casinos profit from random casino games?

It’s simple.

They offer payout odds that are lower than the odds of winning.

In the short run, you can still win in a situation like that, but in the long run, the casino will always win. You can think of this disparity between the payout odds and the odds of winning as the house edge.

And you can think of the house edge as being like a tax on each bet you place. Another way to think of it is as a negative interest rate on an investment.

Playing casino games can be fun, but in the long run, playing casino games is a costly endeavor for a casino gambler.

It’s also a profitable endeavor for the casino.