The Use of Mathematics in Gambling

You might not realize it now, but by the time you get through this article, you’ll see that math is everywhere in gambling.

It’s in the blackjack hands you play, the toss of the dice, and every single spin on your favorite slot machine.

And while mathematics is certainly important in gambling – you can use it to make smarter, more profitable bets – we’d wager that most people who read this won’t have much use for it.

We’ll explain why a little later on.

Before we get to that, though, we want to first talk about where and how math is used in gambling. Along the way – assuming you play poker, blackjack, or bet sports – we’ll show you how you can use this info to your advantage.

Let’s get to it.

Math is everywhere in gambling. But the most common math-type thing you’ll see, hear, or experience, is probability – the likelihood that something specific is going to happen.

We’ve looked at how math is used in gambling. And we’ve looked at the different variables that affect the probability of every game you play, or situation you’re in.

However, something that gets overlooked and is VERY important to remember is that there’s variance in every game or situation you play.

ThePokerBank.com puts it well when he says:

In other words, variance is the ups and downs you experience, and it, too, is math.

Poker is a great example of variance, as anyone who’s played the game has undoubtedly experienced a “bad beat” where they got it in with the best hand but still lost the pot.

Take the AA vs KK example from above. Aces are roughly 80% to win, so when you have aces and lose every once in a while – 1 out of 5 times – that’s perfectly normal. It’s expected. Poker players call that running at expectation.

However, if you lose 4 out of 5 times, that’s not in line with what’s expected – what the odds say should happen – that’s variance.

Where people get screwed up is that variance is about the short run, which is tiny compared to statistically relevant results over TONS – hundreds of thousands or millions – of hands or rounds. It’s perfectly normal to lose multiple times with aces (vs kings) over 100 or 1,000 hands. It’s frustrating, but normal.

But the closer you get to statistical relevance, the more the aces will win, and the closer they’ll get to that 81-ish% mark.

For another example, take betting on the outcome of flipping a coin. You know that, assuming a fair coin and everything else being equal, the outcome is 50% either way.

In the short run, though, the results can look like this:

And only after enough flips will it start to even out.

Let’s look at one more example: the Daniel Rainsong Challenge from the WizardOfOdds.com.

The Wizard of Odds issued a challenge that no betting system could beat the house advantage over the course of one billion hand computer simulations. He put up $20,000 against the $2,000 of the challenger.

Daniel Rainsong thought his system could beat the house because he had shown a profit of $8,215 over 33,000 hands of casino play with a starting bet of $1.

Now, as a side note, this is where people get screwed up. They see a “small” sample size of 33,000 with $8,000 in winnings and think that this is a legit and profitable betting system. But 33,000 hands aren’t enough.

You see this all the time in poker, too. People make plays based on short-term results, even though in the long run they’re not good plays.

Anyway, back to the story….

They settled on the rules and stakes, and then hit the button on the simulator. But they didn’t get through a billion hands. In fact, they didn’t even get close.

They stopped at 168,621 blackjack hands. This was the last point the betting system showed any profit. By the time they got to 10 million hands, the bankroll fell so deep into the hole that it was obvious the system would not work in the long run.

Rainsong forfeited the challenge.

The story above shows why sample size matters, and how long it might take for variance to run its course before the actual expectations (the probability) show.

And that’s why we believe that, for most people reading this, mathematics in gambling simply don’t matter.

By this point, we’ve thrown a lot your way. We’ve talked about:

Now let’s talk about why nearly none of that will matter to most people reading this.

The reason why math won’t matter to most people is that nearly every game in the house is designed so that the player will lose.

Not only that, but (most) players know this and simply don’t care. They play these games anyway.

So, there’s not much sense in thinking about probabilities or odds, because if people truly cared about these and wanted to turn a profit, they’d never step foot in the casino in the first place.

Gambling is a form of entertainment. Most responsible people know this and go into the casino with an amount of money they’re comfortable losing, knowing that it’s the most likely outcome.

They’re fine with that so long as they’re being entertained.

Now, let’s say that you’re a little different. You still may want to play the occasional slot machine, but you’d rather be able to shift the math in your favor when/if it’s possible to do that. How would you go about doing that?

Here are some simple tips for you:

We have many resources on GamblingSites.com to show you how to accomplish each one. And for the majority of people reading this who are interested in improving the odds, this will be enough.

However, if you really want to shift the math in your favor, this is what you ought to do:

This is MUCH easier said than done. You can play poker for the rest of your life and still not be one of the best players. And you can be one of the greats, but still have so much left to learn.

That goes for all the different games or betting opportunities, too.

There are pros/cons to each, too, such as the amount of time and money you’ll need to invest to become great. You also have the challenge of finding action, as weaker poker players will want to avoid you, and many casinos and sportsbooks will not want an advantage player taking them for a ride.

But those are the challenges you accept/face if you want to shift the mathematics in gambling into your favor.

Gambling math is important – even fun for some people – but unless you’re out to make a bunch of money, it’s not going to make a huge difference in the experience you have gambling.

Most people are going to play or gamble on whatever they want, regardless of the probabilities of them winning/losing, or how profitable an opportunity it may or may not be.

But mathematics is everywhere in gambling.

And that’s something anyone can do.