“Beating” roulette: testing the reverse Labouchère betting system

6 min readAug 9, 2020

A quick introduction

Recently, I came across this book written by a man who claimed to have a roulette-beating betting system that actually worked. The summary of the book alone was enough to get me hooked:

In the summer of 1966, Norman Leigh took a team to the Casino Municipale in Nice with the express intention of systematically winning large sums of money at roulette. Two weeks later, his team was banned from every casino in France — not because they had cheated or behaved badly, but simply because they had won — methodically and consistently.

Cool, right? The book lived up to expectations and was funny yet interesting in equal parts from start to end. His system was simple yet seemingly very effective, the hardest part instead seeming to be picking the 12 people who he could trust to put it into action.

Yet the book got me thinking — does this system actually work? In this article I put the system to the test!

French roulette

There are plenty of sources out there to explain the rules of roulette and I’ll skip over the French translations, but here are the main bits:

A French roulette wheel has numbers from 0 to 36, and the chances of the ball landing in any of the 37 slots is the same
There are 6 “50:50” bets which pay out 1:1 (if I bet £5, I’d win £5 plus my initial £5 bet back)
These 50:50 bets are red, black, high (numbers 19–36), low (numbers 1–18), odd, and even. None of these win if it lands on 0
If the ball lands on 0, you can do 2 things with 50:50 bets — lose half of your bet, or keep the bet there for the next spin and if you win you get your original bet back but with no additional winnings

To illustrate the last point let’s run through an example of the wheel landing on 0 twice, and what these 2 choices would mean:

Scenario 1 - lose half of your bet
Spin A: £5 bet on red, ball lands on 0, lose £2.50
Spin B: £5 bet on red, ball lands on 0, lose £2.50Total - lost £5 on £10 betsScenario 2 - keep bet for next spin
Spin A: £5 bet on red, ball lands on 0, next spin lands on black, lose £5
Spin B: £5 bet on red, ball lands on 0, next spin lands on red, recover £5 stakeTotal - lost £5 on £10 bets

Neither choice particularly matters in the long run, and we can assume you will lose 50% of your bet when the ball lands on 0 for a 50:50 bet.

So, 2.7% (1/37) of the time a 0 will turn up meaning a 50:50 bet wouldn’t win, and in these cases (on average) you lose 50% of your bet. Overall, this means that the casino will win 1.35% (2.7%/2) of the time on 50:50 bets.

For example, if we both started with £50 and I played only red, but you played only black, then the casino would win £1.35 of our money over time (assuming we always bet the same amounts).

Norman Leigh’s system relied just on these 50:50 bets, so if the casino always has an edge of 1.35% — then just how does this system work?

A bit sceptical?

You’re not alone, giving benefit of the doubt that the story is true — I wanted to dig a bit deeper and see for myself.

The reverse Labouchère system itself is deceptively simple:

Start with a sequence of numbers — 1,2,3, and 4
Add the first and last numbers together, in this case — 5, this will be your stake (eg. £5) [If your sequence only has 1 number left, then just use that number only!]
Put the stake on any 50:50 bet — in Leigh’s system he had 6 people covering all 50:50 bets at the same roulette table!
If you win, add your stake onto the end of your sequence — eg. 1,2,3,4,5
If you lost, cross out the first and last numbers in your sequence — eg. 2,3,4
If your sequence is now empty due to step 5, or if step 4 causes your next stake to be above the maximum bet allowed by the table, go back to step 1 — otherwise, go back to step 2 and repeat!

A quick example:

Start with 1,2,3,4, bet £5 on red
Red comes up, my sequence is now 1,2,3,4,5, bet 1+5=£6 again on red
Black comes up, my sequence is now 2,3,4, bet 2+4=£6 again on red

Step 7, profit? Photo by Sharon McCutcheon on Unsplash

This system effectively limits your losses as in each sequence you are only putting up £10 of your own money (1+2+3+4), but if you win any of the casino’s money you use it to increase your own bets — meaning that you are betting the casino’s own money against itself.

It makes a certain level of sense, you limit the amount you lose and take advantage of winning streaks. But you know what they say, the house always wins.

Judging it for ourselves

Photo by Tingey Injury Law Firm on Unsplash

Putting aside tales of beating the roulette wheel, does this system hold up?

Wheel of fortune

First, we need to be able to model a roulette wheel’s outcomes from numbers 0 to 36 for any given number of spins. To do this we can use some simple Python code.

We can now test this:

The system

Next, we need to be able to test our reverse Labouchère system, everything is in the below code — but to summarise:

Loop through all roulette outcomes given by the above code
Calculate stake to bet
See if you win/lose/get zero, and update your sequence & money you have accordingly
The print_only argument just allows you to either show detail for one Labouchère run (see detail at each step), or just the summary of spin number & total money you have if you want to plot multiple Labouchère runs against one another

Using print_only = True, we can take this for a test run

But rather than just keep hitting refresh on an individual run, how about we try multiple runs? What if we simulated Norman Leigh’s team of tireless roulette players betting on spin after spin, day after day?

My team

Imagine 100 people, starting each session with £1,000, betting on 500 spins of the roulette wheel. Assume in this case that the roulette table never runs out of money!

We can use this code to see the results — on the x axis is the spin number, and on the y axis is the total funds in £. Each line represents a different player.

A rather worrying trend down and to the right is confirmed by the final line of code — on average the 100 players took home £933.38, a loss of £66.62.

Final thoughts

Despite the tales from the book I couldn’t systematically recreate the success of Norman Leigh and his team of thirteen, if the casino wins over time (see trend down & to the right above) then maybe he was fortunate enough to make the most of short term wins before the casino ate back into his profits.

Ironically, his team being banned from casinos in France after a very short winning streak may have actually contributed to some of their success.

What do you think? Would there be anything you would do differently?

My conclusion in all of this is if Leigh’s stories are true, then he is the exception rather than the rule — and as far as I still see it:

The house always wins