Roulette Odds: The Casino Math Behind The Game

I got my first article request over the weekend! Thank you “J”. I’m guessing you were inspired by The Roulette Strategy That Proved Einstein Wrong? The request concerned advice on a roulette strategy and “J” wanted me to conduct a mathematical analysis for the game. Well I’m going to do you one better (because I happen to be in a splendid mood) and enlighten all of you on the math behind some of the more popular casino games in a whole new series. Let’s kick things off with Roulette Odds!

By the way “J”, I won’t be conducting a simulation for your strategy because as you will realise by the end of this article, your proposed strategy is negative EV and is doomed to fail very quickly. Sorry buddy.


Roulette Odds Hotness

This article is kinda technical…
So here’s a cheap trick to keep you attentive 🙂


The Odd Illusion of Roulette Odds

When it comes to games like Roulette (and Craps, Sic Bo, etc.) they all have one thing in common – they create an illusion of ‘even money’. This leads to plenty of recreational gamblers out there thinking that their bets have a 50-50 chance. For example, I can’t begin to tell you how many people still believe that betting on Black/Red in Roulette is a 50/50 proposition.

It’s not and here’s why…

I’m using American Roulette because it’s the more common one you find in casinos these days. Why, you may ask? Simple – it makes the casinos more money! The difference between an American and European Roulette wheel is the latter contains just one ‘green zero’ while the American one contains two (‘0′ & ’00’). And in case you need it spelt out for you – this means you’re getting worse Roulette odds.

Let’s begin with your odds on the Black/Red bet. Many forget that there’s also a ‘Green’ colour where the ball can land – ‘0’ and ’00’. When that happens, your Black/Red bet goes ‘poof’. Here are the exact figures:

Total possible outcomes – 38 (36 numbers, 18 red, 18 black, and two zeros).
Which means your odds of winning a Black/Red bet = 18/38 = 47.368%

Just for the sake of idiot-proofing this article – If it were European Roulette odds the same bet would be 18/37 = 48.649%

There are plenty of bets you can place when playing Roulette – individual number(s), colour, groupings like first 12 numbers, etc. And It’s really easy to calculate the odds – simply divide your chances of winning by 38. But you may find it fascinating that regardless of what bet you make, your expected value remains exactly the same! You should know how to calculate that by now so go do the math and check it out for yourself.

You’re not going to do it are you?

The Odd EV of Roulette Odds

The answer is -0.0526 EV. This means that for every dollar you place as a bet when playing Roulette, you are losing 5.26 cents. To make things a little easier for you, here’s a table that gives you all the information you need.

Type of Bet Pays Probability of Win Casino’s Edge
Red 1 to 1 47.37% 5.26%
Black 1 to 1 47.37% 5.26%
Odd 1 to 1 47.37% 5.26%
Even 1 to 1 47.37% 5.26%
1 to 18 1 to 1 47.37% 5.26%
19 to 36 1 to 1 47.37% 5.26%
1 to 12 2 to 1 31.58% 5.26%
13 to 24 2 to 1 31.58% 5.26%
25 to 36 2 to 1 31.58% 5.26%
Split (2 numbers) 17 to 1 5.26% 5.26%
1 number 35 to 1 2.63% 5.26%

As you can see, there’s virtually no bet you can place that would give you an edge over the casino. Many have tried, and the same ‘many’ have failed. In fact the more variations or betting patterns you include in your strategy, chances are more likely than not that you are only making your odds worse. I’ve seen so many of these ‘strategies’ being advertised (which are shockingly still being purchased today!) and they all fail miserably when put through a simulation. Don’t ever fall for that! If anyone has a sure win strategy for any casino game, they wouldn’t be selling it on such a public forum – and definitely not for $99.99!


Roulette Odds Wheel

Ironically, trying to beat this game
will have you going around in circles


So far the only theory or strategy (that I’m aware of) that’s successfully beaten the game of Roulette is that of wheel bias. But it appears that loophole has been fixed. That shouldn’t stop you from trying though. I find it very exciting to work on casino strategies simply because the potential reward can be so great and there’s such a small chance of coming across a winner. Moreover, if nothing else the challenge makes for some excellent brain exercise!


Hey! Take a gamble by connecting with us on social media. Odds are you’ll love it.

Images: mammaoca2008diverkeith