Why You Shouldn’t Go to Casinos (3 Statistical Concepts)
By: Tomi Mester
Tags: Gambling, Data Science, Bias, Editors Pick, Statistics

Why You Shouldn’t Go to Casinos (3 Statistical Concepts)

The house always wins. We all know this phrase. But this is more than a phrase. This is a simple, mathematically proven fact. And you’ll only have to know three statistical concepts to see why the house always wins. Tomi Mester Sep 21, 2020·7 min read

Photo by Kay on Unsplash

You are at the casino. The roulette wheel is spinning and the ball is bouncing. Bounce, bounce, bounce, you smile: “it’s red!” And then it bounces one more. No, it’s black! You lose everything again and go home with empty pockets.

Well, I hope you won’t — because you don’t go to casinos, you don’t buy scratch tickets, you don’t play the lottery or any gambling game in general.

Why? Because these games are designed to make you lose money.

And in this article I’ll tell you why. (Check out the podcast or video version of it, too!)

The house always wins. We all know this phrase. But this is more than a phrase. This is a simple, mathematically proven fact. And you’ll only have to know three statistical concepts to see why the house always wins.

These three statistical concepts come up often in data science projects, too. So if you are wondering why I’m talking about gambling on a data science channel, rest assured, you’ll be able to take advantage of this knowledge in your data science career, too.

Anyways, three statistical concepts.

These are:

survivorship bias

expected value

and the hot-hand fallacy

Let’s start with the first one.

Survivorship bias

Everyone loves good stories! A good story sticks.

And I bet that you, too, have a friend — or a friend of a friend — who won big on a sports bet, or came home with 10,000 bucks from Vegas or won the dream trip to Malta on a scratch ticket… So won something big.

The trick is that in gambling the good stories are always the ones that end with winning big. It makes sense. My grandma never talks about how she played the family numbers on the lottery last week and won nothing, again, for the 200th time. But she never forgets to mention when she won $6000 on it in 2003.

Why is that?

Because losing is boring. It’s everyday. It happens with everyone. Winning is exciting, it’s a fun-to-tell story, even after years.

The story of winning big survives the filter of boredom.

This is why this statistical concept is called survivorship bias. In this case, the story of winning is the thing that survives. And why is it a bias?

Because what happens here?

My brain hears a winning story. That’s one datapoint. Then it hears another one, then another one, then another one. Sometimes it hears losing stories, too… but by far not as many as there are in reality. So my poor brain will have a disproportionately big sample size of winning stories and a relatively small number of losing stories. And it unconsciously creates false statistics from the skewed data — and so it thinks that I have a much bigger chance to win than I have for real.

This is how my silly brain works. Well, okay, the bad news is that it’s not just my brain, it’s yours, too. In fact, it’s everyone’s brain: this is how humans are created. We instinctively believe that we have a bigger chance to win in games than we do. Because of survivorship bias.

Oh, and of course, almost all casinos and online betting companies amplify this effect as much as they can.

Anyways, if there wasn’t survivorship bias, we’d see our chances at gambling more rationally and probably none of us would ever go to the casinos. So if you hear a good winning story, you should always remember that’s not the full picture… and that on the full scale, the house always wins.

I keep saying this, by the way: the house always wins. But I haven’t yet explained the math behind it. So let’s continue with that and head over to the second statistical concept.

Expected value

Here, I won’t go into the details of the expected value calculation itself. But check out this article to learn more: Expected Value Formula.

But, let’s get back and let me talk a little bit about expected value.

Expected value shows what result you would get on average if you made the very same bet infinite times.

I know, this sounds a bit tricky, so let me give you a very simple example to bring this home.

Flipping a coin.

Flipping a coin is usually a fair game. When you flip a coin, there’s 50%-50% for tails or heads. Let’s say that you bet and when it’s tails you double your money, if it’s heads you lose your money. If you do this over and over again several times, let’s say for 1,000 rounds, your wins and losses will balance each other out. Your average profit will be 0 dollars. That means that the expected value of this game is exactly $0.

expected value — coin flip simulation (Image by author)

In roulette, there’s a pretty similar bet to flipping a coin. That’s betting red versus black. But in roulette your winning chances are a tiny bit lower compared to flipping a coin. When you put $10 on black, your expected value is not 0. It’s minus $0.27 per round. Again, I won’t go into the math here, check out the article I mentioned. But the point is that in every round you play, you lose an average of 27 cents. It seems like a very small amount of money. But over 1,000 rounds, it adds up and your losses will be around $270.

expected value — roulette simulation (Image by author)

I mean sure, expected value is a theoretical value, but it always shows itself in the long term. In other words: the more you play, the more you lose.

The point is: roulette is a game where the expected value is negative — because the probabilities in it are designed in a way that you’ll lose in the long term. And it’s not that big of a secret, that every single game in a casino is designed with a negative expected value.

And that’s why the house always wins.

So that was the second statistical concept, expected value.

Let’s talk about the third statistical concept:

Hot hand fallacy

This is another bias and it explains why people don’t get out of a game when they are in a winning series.

First off, you have to know that probability is tricky. It works in a way that’s really hard to interpret for the human brain. There are events that are extremely unlikely to happen. Like the chance that you’ll get 10 heads in a row when flipping a coin. The probability of that is less than 0.1%. Still, in a big enough sample size, let’s say when you toss the coin 100,000 times, it’ll inevitably happen, even multiple times.

And the same thing can happen to you. If you play 1,000 rounds of roulette for instance, it’s actually pretty likely that you’ll have lucky runs.

expected value — roulette simulation — there are lucky runs! (Image by author)

And when one’s in the middle of a lucky run, it’s easy to feel that she has a hot hand. So she raises the bar, plays with bigger bets — in the hope of getting the most out of these winning series. But the thing is that these winning series are nothing else but blind luck, and statistically speaking it happens to everyone every now or then.

In gambling, there’s no such thing as a hot hand. In the casino, just as fast as you win something, that’s how fast you can lose it.”. Again, you can’t get out of the law of statistics — and the more you play, the bigger the chance you’ll lose. Remember, the house always wins. So don’t fall for the hot hand fallacy. If you go to the casino and play (against common sense) and you win (against the odds), the best thing you can do is get out immediately and be happy for being lucky!

Conclusion

So why shouldn’t you go to casinos?

Because of 3 simple statistical concepts:

survivorship bias

expected value

and hot-hand fallacy

And don’t get me wrong, it’s your choice whether you gamble or not. I get it. It’s fun to play sometimes, it’s fun to get lucky and it’s fun to win.

I just wanted you to understand the math behind gambling — and to give you a more realistic picture of your chances and about why the house always wins.

Tomi Mester, data36.com