How (not) to beat the roulette - the martingale strategy

Edit: The Code is already uploaded you can find that in our Stuff section or just clicking here.

Who hasn't ever been sent an e-mail or found an advert on a website which assured that you could win as much money as desired only by playing roulette at online casinos? If you have ever tried, I'm sure that you won't get any richer - almost always it'll be the other way round. But why does this happen?

A roulette

It is said that it was French mathematician Blaise Pascal who invented the first roulette, which had 36 numbers in it - 1 to 36. At this time, there are two layouts for roulettes which are used in casinos - French and American ones, which have 37 and 38 numbers respectively. Whilst the first one added a 0 to the roulette, the Americans also added a 00 square. The basics of this game are fairly simple: each turn, the player will bet for an odd (1, 3, 5, 7, 9...) or even (2, 4, 6, 8, 10...) number. Should he have been right, he will get twice the money he betted, but if he was wrong, the player will have lost his bet. Watch out: zeroes aren't counted as even numbers; instead, they mean that the player will have lost his bet regardless of having chosen odd or even numbers.

The martingale system involves placing a minimum bet, which will be placed again if we won the bet. Each time that we lose, we will double our previous bet, so as to recover the previous losses and get, again, more money. This really sounds like an exciting opportunity to earn some cash quickly, but before rushing to online casinos and spending all your money, I strongly advise you to go on reading this article and find out why this method does not work.

Another roulette - note the green-coloured 0 box

There are 18 odd numbers in a roulette, 18 even ones and one or two zeroes, depending on which version of the game you are playing. This means that you have a 18/37 or 18/38 chance of winning each time you try, which is slightly less than 50%. This makes losing money more probable than earning it. However, this doesn't prove the strategy wrong, but hang on - we are not finished just yet.

In order to make the strategy work, you will need unlimited money. And how come that? It's this simple: most people don't believe that they could lose ten times in a row, but, once they have played long enough, they WILL. The probability of losing ten times in a row is 1 out of 2¹⁰, that is, 1/1024. And while this looks a really low chance, you need to understand what it means: once you have played 1024 hands, it's extremely probable that you have will lost 10 consecutive ones, which means that you would have to bet 1024 times the minimum bet in the next hand. But do you have that much money? Probably not.

A real-life casino

We need to pay attention to the fact that each time that we win a hand, we will only earn as much money as our minimum bet is -for example, if we had €1000 and our minimum bet was €1, we could get €1000, then €1001, €1002, and so goes on. But, unlike our profits, our losses could grow sharply, which would mean that, once we reach a certain point, we wouldn't be able to go on playing, simply because we won't have enough money to double our previous bet. If we had played 1024 hands, we could only have had as much as €2024 - but normally it won't be as much as that, because we will have already lost several hands. Ten consecutive losses would mean that we would need to bet €1, €2, €4, ..., €1024, which would mean a total loss of €2047 - and that's more money than we had!

To sum up, if you ever want to get richer by playing roulette, just DON'T. Apart from the martingale system, there are other methods which promise you success but, in the end, the only person they give money to is the casino's owner. So you might want to stay away from this.

By the way, I have written a program which simulates a roulette game, with an initial amount of €1000, a minimum bet of €1, and the American version of the roulette - that is 18/38 chance. If you are interested in it, you can ask for it in the commentaries, and I'll upload it for you. However, I can already tell you the ending - the player always ends up losing.

Edit: Daniel has been kind enough to let me upload the source file to the blog, so either he or me could give you a link soon. The program simulates a roulette game with an initial amount of €1000 and a minimum bet of €1, and creates a text file (martingale.txt) with information on the current money and bets. You can compile it yourselves - feel free to change the code if you wish.

I also invite you to ask me -this article's comments are a nice place for that - if there's something in the code that you do not understand. I've written a lot of comments in the source file, but if there is something which needs a clarification, I'll be glad to help you.