On my 2nd trip to Las Vegas, I took a buddy of mine with me. Said buddy loved roulette, and he loved coming up with betting systems on the backs of napkins. He’d get really excited about these betting systems, too.

The next morning, we’d hit the casino, and he’d lose more money than he intended.

On the 3rd day of our trip, he’d lost all the money he brought with him. I had to pay for his meals for the rest of the trip, and he couldn’t even afford to pay me his half of the cab fare back to the airport.

I’m not telling you this story to scare you away from betting systems. They can be a fun way to approach a casino game.

But they don’t change the odds in your favor.

This post is part of a series of posts I’m writing in the “what is gambling” series. In these posts, I try to confront what is essential about various gambling activities and phenomena.

What about betting systems make them “betting systems” as opposed to “advantage strategies,” for example?

My goal is to explain these concepts in detail but in simple language that anyone can understand.

I make no judgments about whether you should gamble or not.

I do think that if you’re going to gamble, you should understand what you’re doing any why.

After reading this post that describes what betting systems are, you can make a decision for yourself whether this is the way you want to play roulette or slot machines or whatever game tickles your fancy.

## How a Betting System Works

A betting system is a structured way of placing bets at a casino game that’s supposed to help you win more often and/or lose less often. Betting systems always involve raising and/or lowering the sizes of your bets based on what’s happened on your previous bet.

Some betting systems have you raise the size of your bet when you’ve been losing. Other betting systems have you raise the size of your bet when you’ve been winning. All betting systems provide guidelines for when you should change the size of your bet and by how much.

**All betting systems for casino games share a simple flaw:**

They don’t change the probability of winning the bet.

They also don’t account for the fact that every bet is an independent event. What happened on the previous roll of the dice or spin of the wheel has no effect on what’s going to happen on the next spin of the wheel.

To understand betting systems and why they don’t work in the long run, you must understand something about probability and casino games in general.

## How Probability Works

Casino games are all based on probability. That’s the branch of math that deals with how likely an event is to happen or not happen.

Probability is also that description itself. It’s always a number between 0 and 1, but it can be expressed in different ways.

An event with a probability of 1 will always happen.

An event with a probability of 0 will never happen.

The probability that something will happen added to the probability that it won’t happen will always equal 1, too.

**Let’s start with a simple probability example from roulette (which coincidentally is the game which most betting systems target):**

You’re betting on black, which is an even money bet. That means it pays off at even odds, 1 to 1. If you bet $100 on black and lose, you lose $100. If you bet $100 on black and win, you win $100.

But the odds of winning a bet on black aren’t even, although they sort of seem to be.

That’s because of the layout of the roulette wheel.

A roulette wheel has 38 numbers on it. 18 of those numbers are red, and 18 of them are black.

But 2 of them are green.

The probability of an event happening is the number of ways it can happen divided by the total number of possible events.

In roulette, you have 38 possible events. Only 18 of those possible events are black.

This means that the probability of winning a bet on black is 18/38, or 9/19. That’s almost 50%, but not quite.

Those 2 green numbers represent the house’s mathematical edge over the player, because those numbers are the reason you don’t have a 50% probability of winning. (You actually have a 47.37% probability of winning.

If you bet on black every time, you’d win $100 on 18 of those spins, for $1800 in winnings. You’d lose $100 on 20 of those spins, for $2000 in losses.

That’s a net loss of $200.

Average that over 38 bets, and you’re looking at an average loss of $5.26 per spin.

That’s 5.26% of $100, so we say that roulette has a house edge of 5.26%.

But gambling system lovers don’t get this.

Which brings me to the most popular betting system of all time:

## The Martingale System – How It Works and What It’s Good For

The most famous and easiest betting system to use is the Martingale System. It has its pros and cons, for sure. Most gambling writers are pro-Martingale or anti-Martingale.

I’m Martingale-neutral, and I’ll explain why after I explain how the system works.

As long as you continue this progression, you’ll eventually win and show a profit of one unit.

This system is mostly used on games which have an almost 50% chance of winning even money. The most popular use of the Martingale, in fact, is at the roulette table, which has multiple even-money bets available.

**Here’s an example of the Martingale System in action:**

You bet $10 on black and lose. You double the size of your bet to $20 and bet on black again. You lose again. On your 3rd bet, you bet $40, and lose again.

You’ve now lost 3 times in a row: $10, $20, and $40, for a total of $70 in losses.

You double the size of your last bet ($40), so you’re now betting $80. You win this bet, so you’ve recouped your $70 in losses, and you have a $10 profit besides.

Seems foolproof, doesn’t it?

## Reasons Why the Martingale Doesn’t Work

Did you know that if you start with a penny and double it every day for a month, you’ll wind up with a million dollars?

You can do the math for yourself, but I assure you, it’s true.

This is the principle behind compound interest.

In the example above, we lost 3 times in a row before having to make an $80 bet.

I tried this at a casino one night on a date, in fact, I’d brought $400 to gamble with, and we were betting $5 per spin on the wheel. My date was impressed with how it was going.

Until we lost several times in a row, and she had to put up a bet of $160.

**Here’s what the Martingale progression looks like after just a handful of losing bets:**

- $5
- $10
- $20
- $40
- $80
- $160
- $320
- $640

**I’ll stop there, because I want to point a couple things out:**

**First**, I only brought $400 to gamble with. If I lost 6 times in a row, I wouldn’t have enough money to place the next bet in the progression.

**Second**, the casino has a maximum bet at the roulette table of $500. If I lost 7 times in a row, I wouldn’t be able to place the next bet just because the casino wouldn’t let me.

You might think it’s impossible or next to impossible to have 7 or 8 losses in a row, but it happens all the time.

And the probability doesn’t change for the next spin just because you lost on the last spin.

The probability of getting red on the next spin is 47.37%. That doesn’t change because of what happened on the previous spin.

We talked about this, remember? Roulette is a game of independent events.

## What’s Good about the Martingale System?

What the anti-Martingale system folks don’t explain to you is that if you’re playing in a short session, the Martingale System really does increase your probability of walking away a winner.

You probably won’t see big profits, but during a one-hour session at the roulette table, you’ll have about an 80% probability of walking away a small winner.

The problem is that 20% of the time, you’ll lose, and you’ll lose a lot of money because of the system’s doubling of the size of your bets.

If you’re gambling with someone who doesn’t know much about gambling, you might be able to convince them that you’re really onto something with the Martingale System. Let’s say you’re trying to impress a date who’s never been gambling at a casino before.

This might work for that.

But over time, using the Martingale System won’t make you a winner.

## What about Other Betting Systems?

No, the Martingale System isn’t the only betting system you can use. The number of betting systems available to you are practically endless, although some of them are more famous than others. The Martingale System is the most famous, but it’s by no means the only option you have.

The Paroli System is another example of a betting system, and it’s also sometimes referred to as the Reverse Martingale.

Can you figure out based on that how this betting system works?

If you guessed that you double the size of your bet after a win instead of after a loss, give yourself a pat on the back. That’s exactly how the Paroli System works.

The idea is to take advantage of winning streaks. If you win a bet, you double the size of your next bet. If you win again, you double the size of your bet again.

Once you’ve won 3 times in a row, you either quit playing or you go back to the minimum sized bet and start over again.

**Here’s an example of the Paroli System in action:**

You bet $10 on red and win. So you now bet $20 on red again, and you win again. Now you bet $40 on red again, and you win.

At this point, you’ve won $10, $20, and $40, or $70 total over 3 bets.

You can either walk away, or you can start over again at $10.

Also, anytime you lose a bet, you go back to your base bet.

So let’s say you bet $10, win, and then bet $20, and win again. On your next bet, you bet $40 and lose. On the following bet, you’d go back to a $10 bet.

This system doesn’t work, either, but it can be a fun way to play.

## Fun with Betting Systems

I read a great article once about how the probability of winning a million dollars is always ridiculously low, and that article explained that you’d have a better probability of winning a million dollars by repeatedly reinvesting your bets on the same thing over and over again.

I don’t remember the exact numbers on this, but I can explain how the math works.

When you’re trying to calculate the probability of winning multiple bets in a row, you multiply the probabilities by each other.

Let’s set a more modest goal for our winning session than $1 million and determine a winning system for that.

Let’s say we have a goal of winning $1000 at the roulette table tonight.

You’re going to bet $10 on a single number, and if you win, you’ll get paid $350.

But instead of cashing in your winnings, you’re going to bet all your winnings on that same number, too. In other words, you’ll immediately place a bet of $350 on the same number.

If you win twice in a row, your winnings will total $12,600.

What’s your probability of winning that?

The probability of winning one of those bets is 1/38.

The probability of winning 2 of those bets in a row is 1/38 X 1/38, or 1/1444.

Sure, you’re not likely to succeed in your quest to win $10,000, but you have better odds of winning $10,000 that way than you do playing a progressive slot machine.

That’s not the only way to do it, either. You could also choose even-money bets and just keep your winnings riding on it. You’d have to win more bets in a row, but you could also set a smaller win goal.

Say you wanted to win $1000 instead of $10,000.

**You could bet on black or red and hope to win a certain number of times in a row:**

- $10
- $20
- $40
- $80
- $160
- $320
- $500
- $1000

You’ll notice that I changed the bet and didn’t double it on bet #7. That’s to reflect the betting limits at the casino.

But you’ll also have some money left over, so you’ll get a 2nd chance at working your way up to $1000 if you wanted to try again.

## Loss Limits and Win Goals

Most betting system advocates are also big fans of the idea of money management. This is just a technique where you set win goals and loss limits for yourself for each session.

These are usually suggested as a percentage of your bankroll, which the advocates suggest you separate into multiple, smaller bankrolls.

A money management advocate would tell you to handle a 3-day trip to Las Vegas this way:

You have $1200 set aside to gamble with. You should set aside $400 to play with each day. You should furthermore plan on 2 gambling sessions per day—one early in the day, and another later in the day. You should have $200 set aside for each of those sessions.

Your win goal and your loss limit tell you when to quit during those sessions. Those are usually expressed as a percentage of your bankroll.

If you have a loss limit of 40%, then you’d quit during any of those sessions once you got down to $120.

If you had a win goal of 50%, then you’d quit during any of those sessions once you got up to $300.

Of course, having arbitrary stopping points for your gambling sessions does nothing toward changing the probabilities and math behind the game. You’re still going to face the same mathematical edge from the casino.

Pausing the game at various points doesn’t really change the probability or your long-term expected results.

## Conclusion

Betting systems can be fun ways to play casino games, as long as you understand they don’t change the odds of being a winner at a casino.

All casino games are negative expectation bets, and that’s just how they work.

If you enjoy the Martingale System or the Paroli System, or if you like the idea of sometimes walking away from a session as a winner, these kinds of systems might be worth trying.

I should also distinguish between a betting system and a gambling strategy. Basic strategy in blackjack isn’t the same thing as a betting system. Neither is counting cards.

Those are legitimate strategies that tilt the odds so that they’re not favoring the house as much.

Do you use betting systems now, or do you plan to in the future? Why or why not?