The Martingale gambling system tested

Can you beat the roulette wheel? This article investigates a popular system and has a built-in simulator

I once read a novel in which a sure-fire way to win at gambling was described. Called the Martingale System, its simplicity and logic were an instant hit with an impressionable teenager.

You wager on an event where the odds are 50/50. Heads or tails on the flip of a coin maybe, or odd/even on the roulette wheel. Actually roulette either/or bets aren't quite 50/50 because of the zero. It may score an automatic loss, or allow the house to keep a chunk of your stake. This is the casino's profit margin.

A European wheel has the numbers 0 – 36. American wheels add 00, which puts an additional bias in favour of the house.

In the Martingale System, you decide on a standard amount to bet and commence play.

If you win, you either place another bet or walk away with your profit. If you lose, you bet again, this time double what you just lost.

If you win this bet, you cover your losses in the previous game and make a small profit. If you lose again, you double up once more. The system tells you to keep doubling until the run of losses breaks. When you eventually win, all your losses are wiped out, you have a small profit, and you revert to your standard bet.

Here's an example betting session. The currency matters not, I'm British so I use pounds:


After the win, your next bet is £10.

Notice how a losing streak requires an exponential growth in stake. If you experience an unduly long run of losses, you will run out of money to stake further bets. In the above example, the next bet would have been £80. With a reserve of only £70 you cannot cover your full loss even if you bet £70 and win.

If you reach your limit, you can place no further bets and have sustained a large loss. Either take it on the chin, or come back another time with a larger reserve and continue where you left off.

Given a large enough pot in relation to your basic stake, wipe-out events should be rare. In general, you should make a series of small wins that add up to a good return.

And that's the Martingale deal: steady small gains offset by a smaller chance of a large loss.

Armed with that valuable nugget of gaming strategy, could you make a living just playing the Martingale system in an honest online casino?

That's tricky to answer definitively.

No matter how big your reserve in relation to your standard wager, there is always the possibility of a sequence of losses long enough to wipe you out.

If you just play the Martingale system once or twice by way of experiment, there is a fair chance that you will avoid such a calamitous event. But play it continually with the aim of making a living and sooner or later, you will encounter the killer streak.

What we really want to know is, for a given regular stake and a given reserve, how likely is it that we will be wiped out?

We could calculate the answer from probability theory. We could also set up a simulator that reports the outcome of a large number of trial games.

And that's what you will find below.

Try the Martingale simulator

WARNING: The simulator is an afternoon's hack. It seems to work properly but has not been rigorously tested. Therefore you should not interpret your experience as a guarantee of real-life behaviour. Results are written back into this page.

Suppose you hit the casino with £1,000 in your pocket and decide to make £10 bets. And we'll also suppose that you intend to play 10 games per hour in the hope of making a steady income. That would give around 1500 games per month.

So enter 10, 1000 and 1500 and press the button to run a simulation of a month's worth of roulette. The simulation stops early if you lose your reserve.

As in real life, two runs are rarely the same. You get a few very good ones, a few very bad ones and plenty of middling ones. Try it many times to get a feel for what happens. Notice how often long runs of losses occur, and how often you fail to survive (zero reserve and aborted trial).

Increase the ratio between stake and reserve and try a different number of games.

Some sets of parameters lead to frequent disasters but you can tweak the inputs until good runs are in the clear majority.

You may then be tempted to head for the casino and take a chance on applying your 'safe' parameters. That's your call, but...

Casinos have seen it all before

These outfits operate to make a profit. Many clever people have tried to beat them. Any casino that can't handle players who use systems would not have survived to do business with you.

With few exceptions, anything you do will have been seen before and the house rules stacked against it.

Beware of maximum and minimum stakes and maximum payouts which effectively limit the run of doubling and force you to reduce the ratio between reserve and stake.

William Hill's Internet casino, for example, at the time of writing has a maximum £1,500 bet on its Classic Casino roulette. Minimum outside bet (which includes all the either/or type bets we're interested in) is £5. That imposes a limit of eight straight losses with Martingale because after that, the next bet must be £2,555.

To follow an eight-loss sequence through, you would need a cash reserve of £2,555. Try £5 and £2555 in the simulator over 100 games and you will find a scary number of clean-outs and large losses (reserve greatly reduced). And it's easy to get through 100 games in an hour if you turn off the animations!

This tells us that if you were to do it for real, you might bomb out soon after you start. And if you get away with it for a while, tears are inevitable within a few hours.

Call me yellow, but for me Martingale is only OK for an occasional small fun bet. No way would I apply it regularly with serious money!

What about the law of averages?

Somebody emailed to say that the simulator and my reasoning are flawed because I do not take account the law of averages. According to my correspondent, it goes like this: say even or red comes up a few times in succession. The likelihood of the same result coming up in the next bet steadily drops. Therefore, Martingale is far safer than I am making out.

That definitely isn't true. Roulette wheels do not have a memory. Neither does a coin. Heads and tails are always equally likely no matter what happened previously. Suppose you flip 20 tails in a row. The chance of tails coming up next time is exactly the same as it was on the first occasion. There is no spring-like force of nature winding up to push the odds towards heads.

Please don't take me to task if you disagree. I have already spent enough time playing email tennis with this one. Read what the others say and you're welcome to believe what you will.

All material © 2012 Ian Sharpe. Nothing may be reproduced or made available for download elsewhere without permission.

About this site

This is the personal web site of Ian Sharpe, a software developer and writer based in Bath, United Kingdom.

Before taking up software development full time, I had a career in computer magazine publishing. My obsession with programming accidentally took me into magazines in 1986 and I worked in the industry for 16 years. Some visitors may remember me from titles such as PC Plus, PC Answers, PC Today and CPC Computing.

Most of the material here dates from that period.

There is no binding theme – it's just whatever comes into my head to publish, hence '@random'.

There used to be a lot more, but I drop items when they become outdated and do not reflect current interests.

The remainder survives while it stays popular. I may occasionally add new material.

When my magazine adventure eventually played out, I switched to what I wanted to do all those years ago. I spent five years developing software at a busy digital printing company.

Now I work freelance. My professional services site is www.iansharpe.com.

Because my personal site is mostly old material that I'm not very interested in, answering email about it is not my favourite activity. If there is a real problem (or opportunity!), my address is ian@iansharpe.com.

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