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Ever since the game of roulette was invented many hopeful punters have attempted to create systems which generate consistent winnings. The aim of this site is to investigate such systems. However, its purpose is less about 'how to win at roulette', and more of an introduction to some basic ideas in Probability Theory and related topics, with roulette and roulette systems as the area of application.

Concepts and examples from Probability Theory are often presented in a particular context such as medicine, social science, business, market research, etc, which are often foreign to the beginner and/or of no interest. The student has a much better chance of understanding the ideas if they are presented in a familiar context, and almost everyone is familiar with roulette — one of the world's most popular casino games. I assume you have some mathematical knowledge, but it's modest. If you can remember most of your high school arithmetic and algebra you should be good to go (If you can't, a good site to brush up on the basics is mathisfun.com).

The tutorial sections introduce the core topics of Logic, Probability, Counting, and Statistics. Separate articles will be devoted to fleshing out the ideas, introducing new techniques, and looking at the merits of particular roulette systems. Throughout the tutorials I include problems; it's important that you attempt them (answers are provided) to check your understanding of the material. Maths is not a spectator sport — you only learn by practice.

The site is primarily an educational resource, but I do make available some software for those who like to play roulette online. These programs are for 'entertainment purposes only' and are intended primarily to enhance your understanding of the concepts introduced; Just be clear that I make no claims or guarantees with regard to winning.

Roulette Systems

What's a roulette system? For those unfamiliar with the game, roulette is very simple. A wheel with numbered compartments (more commonly referred to as 'pockets') is spun in one direction and the croupier (dealer) spins a ball around a track in the circumference in the other direction. The ball eventually loses momentum and falls into one of the pockets.

European Roulette wheel


The player can bet on a single number or range of numbers by placing chips on the layout (shown below). The blue numbered circles represent the chips and the locations of the circles indicate the various bets which can be made (the key is given in the table below in the 'Bets' column). A roulette system comprises two parts: the bet selection is what you bet on (the number or group of numbers), and the staking plan is how much you bet on them.                        

                  Roulette Layout

The payouts (what you win) and probabilities for the various bets on a European roulette wheel are given in the following table. You should familiarize yourself with this information because I'll be using it extensively throughout the site.

  Bets
Payout
Probability
(1) Single no. 35 to 1
2.7%
(2) Split (2 nos.)
17 to 1
5.4%
(3) Street (3 nos.)
11 to 1
8.1%
(4) Quad (4 nos.)
8 to 1
10.8%
(5) Line (6 nos.)
5 to 1
16.2%
(6) Dozen (12 nos.)
2 to 1
32.4%
(7) Column (12 nos.) 2 to 1 32.4%
(8) Even (18 nos.)
1 to 1
48.6%

A Winning System?

The bad news is that from a strictly mathematical point of view, there is no such thing as a winning roulette system. Casinos fix the payouts on roulette and most other casino games such that they have a small advantage (for some games, like slots, the advantage is not so small). This means that over time — assuming you continue to play — your return is likely to be less than your 'investment'.

A simple illustration will hopefully make the point clear. Suppose you and a friend agree to play a game: a coin is flipped, and if it comes down heads you pay your friend 95 cents, but if the result is tails he pays you $1. It's highly likely that your friend will object to this scheme!

This being the case, why bother with roulette at all? Why not focus on some alternative speculative activity such as sports betting or stocks & shares, where the long term expectation is not necessarily negative?

There are two possible answers to this. Advocates of roulette systems maintain that by studying the statistics of the game, the behavior of random outcomes, and by implementing appropriate money-management techniques, they are able to overcome the relatively small house advantage and secure a profitable outcome in the long run (whatever the 'long run' actually means).

There is another camp which recommends that you attack not the game itself, but the gaming device. Roulette is essentially a ball and a wheel, and the so-called 'Advantage Players' insist that it's only by exploiting the physics of the game that the house advantage can be overturned. It sounds like a sensible approach, but Casinos are well aware of this potential vulnerability and make strenuous efforts to thwart the strategy; they work hard to ensure that their roulette wheels and procedures keep outcomes as random (unpredictable) as possible.

Winning roulette system
Rather than getting involved in arguments for or against one or another point of view, I confine myself largely to mathematical considerations and empirical results. While there can be no mathematical proof of a winning system, some systems are better than others, if your objective is to maximize playing time, minimize losses, or achieve some definite profit (or loss!) target within certain constraints. Besides, systems can be fun to use, and the understanding of probability gained from creating them can be useful in other areas of life.

I will be regularly adding articles and content, so please bookmark the site!

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