How Casinos Mathematically Earn Money

Breaking the bank is the popular term used to describe how much you won in a casino. It basically means that you won so much, the casino has no more funds. While this is a dream of many, casinos are pretty much still in place. So, how do they make money, if you lose a little but stand to win a lot?

The Advantage

If you place a bet, you stand to lose some money. If you repeat the process, you stand to lose more. If you win, however, the sum of money you are taking with you is larger. Here we have something called expected value. That is the amount of money you are expected to win or lose in the long run.

This is done by calculating the result of an outcome and multiplying it with the odds of it happening, after which you add together all of the product. Figure out what the results mean.

For example, I play heads or tails. If the coin lands on heads, I win a dollar, and if it lands on tails, I lose a dollar (this is out there, but this is just to show the math in action). The probability of either one happening in 50%. So the expected value is: heads ($1 x 50%) plus tails (-$1 x50%). The total expected value is $0.5 + (-$0.5). In other words, $0, so I will neither win nor lose money for every dollar I invest.

The House Edge

Now, suppose I didn’t win a dollar. Suppose I only win 80 cents with each win, but still lose a dollar every time I hit tails. Again, casinos give you better odds at first glance, but that’s not the point here. That means that the expected value is now $0.40 -$0.50, or -$0.10. Ergo, the house has an advantage over me that equals 10% of my bet.

The casino in this example wins a dollar 50% of the time and loses 80 cents the other 50% of the time. They earn $1.10 for every dollar they invest. The 10% advantage is called the house edge. It represents the percentage of odds that are stacked against the player and in favor of the casino.

That’s Not Much

Maybe not, but consider this: I am not the only customer the casino has. If I have been drinking, or if I am sleepy, or even just unfocused, I will probably play more than one game as well. With the amount of money I put down to play along with all of the other patrons means that the casino doesn’t have to win every time. It simply has to win against enough people to make sure it always has money.

Different games result in different house edges, and impaired judgment can even increase some of them. Additionally, the more you play, the more likely you are to lose in the long run, since the casino’s funds are always greater than yours. There is a reason the house always wins.

Should I Just Forget the Whole Thing?

Statistics are definitely not on your side. It’s one thing to go into a casino simply to have fun, and it’s another to try to win it big. Furthermore, people who understand how the game works don’t bother trying to profit from it – it’s just not a sustainable plan.