Roulette and Probability Theory: Math That Gets Interesting

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Any game of chance is based on probabilities, and the inventors of these games were pretty keen on math. Keep that in mind when you start playing them, or you’re going to be very disappointed! Because it is a business, after all! These guys invented methods for making money using probability theory. In short, every single game of chance has its house edge, which is the casino’s advantage over a player in the long run. For most casino games, including slots, the house edge is between 1% and 10% on average. For American Roulette, it’s 5.26%, and for the European variation, it’s 2.7%.

There’s a massive difference between winning at the casino and beating the casino. If, for example, you bet a hundred dollars on a particular number and win, you’ll instantly get $3,500. It’s a decent win, but you didn’t beat the casino with it! All gains and losses at each particular wheel even out to 5.26% in the long run. The good thing about roulette is that you can play without knowing anything about it whatsoever. That will do for an hour or so; but afterwards, you might want to know exactly how it works! So this is what we’re going to help you with now.

Bets in Roulette

Let’s take American Roulette as an example, and figure out how well the bets pay. The American wheel consists of 38 slots, with different numbers on each of them. There are numbers from 1 to 36, zero, and double zero. The house edge is based on 0 and 00 slots, because if you didn’t bet on those ones specifically, you would end up losing your bet if the ball stops on either of them. All bets in roulette are separated by Inside bets and Outside bets. Outside bets are the ones where you get 2 to 1 or 1 to 1 payouts. All the others are Inside bets. So let’s see how this works.

• One number: If you bet on one particular number, your odds of hitting it are 2.63%, and the payoff is 35 to 1.
• Split (two numbers): By betting on two numbers, you get a 5.26% chance of winning and a 17 to 1 payoff.
• Street (three numbers): 7.89% probability of winning, and 11 to 1 payoff.
• Corner (four numbers): This one is also known as a square bet or quarter bet (10.53% probability and 8 to 1 payoff).
• First five (five numbers). This one is a bit tricky and is often called a sucker bet. It has a 13.16% chance to win and pays 6 to 1. The numbers are 0, 00, 1, 2, and 3.
• Six line (six numbers): You bet on six numbers, get a 15.79% chance to win, and a 5 to 1 payoff.
• Dozen bet: A roulette wheel has 36 numbers except for 0 and 00, and by making a dozen bet, you bet on any of the three dozens (1 to 12, 13 to 24, and 25 to 36). It pays out 2 to 1 and has a 31.58% probability of winning.
• Column bet: This bet is essentially the same as a dozen bet, as you get the same payoff (2 to 1) and an equal winning probability (31.58%); but you bet not on dozens but on the columns of the roulette layout.
• High or Low (1 to 18 or 19 to 36): You bet on all numbers from 1 to 18, which is called low, or from 19 to 36, which is called high. This bet pays even money (1 to 1) and has a 47.37% probability of winning.
• Odd or Even: You bet either on all even numbers or all odd numbers. The bet pays even money (1 to 1) and has a 47.37% chance of winning.
• Red or Black: Precisely the same thing regarding odds and payoff as odd/even and high/low bets: 47.37% chance to win and 1 to 1 payoff. You either bet on all red slots or all black slots.

All these bets have a 5.26% house edge, except for the First Five bet, which has a 7.89% house edge. This one is a sucker bet, which means that if you’re betting on First Five, you obviously have no idea what you’re doing! So if you’re going to play some roulette for real money, remember that the First Five bet is the least advantageous one.

Some rules might alter the house edge, but this is not something all casinos do. A half-back rule, for example, means that whenever you make an even money bet (red/black, odd/even, or high/low) and the ball hits zero or double zero, you lose only half of your bet. This rule decreases the house edge on even money bets to 2.63%, which is the level of European Roulette, and it’s mostly used in Atlantic City.

Odds and Payouts in Different Types of Roulette

The difference between European and American roulettes is that the first one doesn’t have “00” hole, increasing player’s odds. The comparison between the two kinds can be put in the following way:

As you can see here, the odds in European Roulette are a little bit higher. When you play live or online roulette for real money, you should definitely make sure the wheel is not biased. This is true of real live wheels, as well as the online software of the websites you play at. Only visit venues with a good reputation and online casinos with high ranks and feedbacks. When you play online roulette, real money bets are made; and if the website is a part of a scam, you may lose it all from your account. Yet another reason for you to be careful!

Many gamblers refer to different kinds of strategies like Martingale, Reverse Martingale or All-In systems which are believed to increase the odds and lower the house edge. Using these progressions only helps you to organize your bets in order to get the best results. Most often, if you want to reclaim the loss of your original wager you will have to hit either a winning or a losing streak.

However, every strategy has its drawbacks. The Martingale system will make you double your bet every time you lose, and it will drain your bankroll at the speed of light! Reverse Martingale has 86.5% odds of winning and its profits are really low. The 1-3-2-6 system is one of the most basic ones, and it helps players last a long time in the game. Nevertheless, this exact approach won’t make you earn much; and for the maximum effect, you would have to win 4 times in a row!

Any kind of progression theory is of doubtful value when it comes to roulette. If you hit a losing streak any one of them will be just useless. So, in those cases where one of them doesn’t work, switch to another one straight away!

Can You Use Probability Theory to Develop a Betting Strategy?

Let’s make this clear here. When people google “probability theory” plus some game of chance name, or “roulette probability,” they’re usually looking for a betting strategy.

This is okay with some card games, like Blackjack, where you can count the cards and increase your chances; but Roulette is entirely random, and there is no way of beating Roulette with math. Each and every spin of the wheel is random, and no one knows where the ball will stop. So even if the ball lands on the black ten times in a row, it has an equal possibility of hitting either red or black for the eleventh time! And anyone who states the opposite is either a liar or a simpleton.

So if you actually want some good advice, here it is. Quit while you’re ahead, and don’t try and bet more than you can afford. And don’t ever trust a betting strategy, especially if the person following it claims that it works for roulette.

It’s Still About Luck!

Now this may come as something of a disappointment to you, but you can only win at Roulette if you’re lucky. That’s the only way it works, and there is no other way; unless of course, you’ve somehow had the good fortune to come across some old, worn-out, or flawed roulette wheel. We’re all aware of the one single betting strategy that helps in Roulette: it’s called “common sense!” The best way for you to win (or at least not to lose too much!) is to make even money bets because with them, you win more often. You may bet on a particular number too, but we recommend doing so not just when you’re feeling lucky, but also when you’re feeling extremely lucky!