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Why the double if you lose (martingale) strategy for roulette doesn't work

Updated on November 25, 2014
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Cruncher is the pseudonym of an actuary working in London with experience in insurance, pensions and investments.

The name "roulette" comes from the French for "little wheel", which basically what it is.

It started in France but quickly spread throughout Europe and North America. Today it is most associated with the casinos of Monte Carlo and Las Vegas.


Everyone wants to beat the casino. It's fun. It's money. It's the ultimate way to beat the system. But the truth is very few people do beat the casino over the long term. And the thinking you can when you can't is just making the casino owners richer.

If you want to gamble for fun with money you can afford that's fine, but don't kid yourself you can make money at it without hard work, knowledge and steely nerves.

Trouble is, most people have a theory about how they would beat the casino. And quite a few of them, if you get them drunk will tell you all about it. Sometimes twice. On the same night. And most of the time it is the old "double if you lose" strategy (sometimes called the martingale strategy) for roulette.

Trouble is, is doesn't work. Here's why.

The classic roulette wheel
The classic roulette wheel | Source

The house edge

On an American wheel the house edge is 2/38ths which is just over 5%.

On a European wheel it is 1/37th, nearly 3%.

How roulette works

First we need to understand the game of roulette.

Roulette is a game of pure chance. Winning depends on where that little ball ends up when the croupier spins the wheel. On the standard European (or single zero) wheel there are 37 slots. On the American (or double zero) wheel there are 38. But your winnings are calculated as if there were 36 slots. Yes, that is correct. The house "takes" the zeros, so the house always has an edge.

This edge means that the longer you play the longer you should expect to lose on average. But even if it was a fair game - so that the expected winnings for both sides were zero - the chances are you will still lose if you play long enough. Mathematics tells us that in a repeated game like this when you be up a little or down a little, then the winner is almost always the player with the biggest bankroll.

I won't got into detail but to understand why think about this very simple example.

Let's say you play a coin tossing game with your friend. You have $2 and they have $1. Heads they give a dollar, tails you give them one. The game goes on until one player wins. How many times do you win the game? It's clearly more than half, because half the time you win on the first throw. In fact, if you do the maths, you would win two thirds of the time.

A fair coin
A fair coin | Source

The martingale strategy - "double or quit"

"What about my 'double or quit' strategy"? says the bore in the bar? "Sure you might lose if you pick randomly, but this is a strategy!". Sorry, bar bore. It doesn't work.

It does sound plausible. If every time you lose you double up, then when you win, you will have covered your losses and made a profit. Here the house's edge isn't a problem because your payout is always double your stake. That means that you will always be ahead by your original stake at some point - assuming you have enough money to start with.

But that is a very big assumption. Remember the coin tossing game with your friend? The casino has a lot more money than you. If it doesn't, why are you wasting your time trying to beat it? Just set up your own casino!

But if the casino has more money than you, they can always wait for you to go bankrupt trying this strategy. You can't wait for them to go bankrupt.

To put it even simpler: however much money you have there is always a chance that you will never win a single spin and lose the lot. It may be a small chance but it is a chance.

In other words you haven't beaten the casino at all you have just reshaped the game. You have changed it from a game with a high chance of a small loss and a chance of a big win to a game where you win small amounts most of the time but when you lose you lose everything. Is that really worth it?

This is not a good plan to make money from the casino. Because one day you'll be at a party and the bar bore won't be there. "Oh didn't you hear?" your host explains "he went bankrupt playing roulette."

Source

Can you make money from gambling? Yes, if it involves skill, like Poker or card counting does. Or betting on events (like sports or politics) when you have more information or make better use of it than the rest of the gamblers in the market. But you can't make money from roulette. Unless you run a casino.

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