The Labouchere Roulette Betting System

Labouchere is another popular negative progression system (bet amounts increased after losses, decreased after wins) applied to the game of roulette. Progressions are less aggressive than Martingale but more aggressive than D’Alembert, making it a arguably a more moderate approach to roulette betting than these methods, if no more successful.

The idea behind the system is that, everything going to plan, you are able win a predetermined amount despite losing more times than you win.

The system’s invention has been credited to English aristocrat Henry Labouchère (1831-19212); a man who inherited a fortune and had both money and time to burn…are you hearing warning bells too?

The Labouchere is also referred to as the Split Martingale or Cancellation System.

How to play Labouchere

1. You begin by selecting a sequence of numbers. How many numbers, and the value of each number is up to you but the higher the values, the more you will be betting.
   The sum of these numbers is the amount you will win if all goes to plan. Write your chosen numbers down.
   example: 5 10 5 10
2. Your first bet – choose an even money roulette bet (red/black; odd/even; high/low), and bet an amount equal to the sum of the first and last numbers in your sequence.
   for our example: 5+10 = 15
3. For your next bets apply these rules:
   If the proceeding bet was a WIN: erase the 2 numbers in that sequence that combined to make that bet. Next bet equals sum of the new first and last numbers in remaining sequence
   for our example: 5 10 5 10 | next bet is 10+5 = 15
   If the proceeding bet was a LOSS: add this amount to the end of the sequence. Next bet equals sum of the new first and last numbers in sequence
   for our example: 5 10 5 10 15 | next bet is 5+15 = 20
   
4. Continue betting until all numbers in your sequence are erased, at which point your net win will equal the sum of the numbers in your sequence
   for our example: 5+10+5+10 = 30

So the aim of the game, as it were, is to completely erase your sequence.

Since a win removes two numbers from the sequence while a loss only adds one, this goal can be achieved with only half as many wins as losses. Expressed another way, a win rate (bet wins/number of bets) of a little over 1/3 will get you there. Remembering we’re playing even money bets with a odds of a win equal to 18/37 (or 18/38 for American Roulette), then on the face of it a 34% win rate seems easily achievable.

Bear in mind though, that this simple win rate analysis neglects to take into account a reasonably important part of the equation…BET AMOUNT. As you are losing bet amounts are escalating so win rate requirements aside, it is still possible to come (badly) unstuck. Consider that a win rate far lower than 33% will be good enough to have you walking away from the roulette table in the black using Martingale, and yet that system also does not guarantee success.

Hypothetical outcomes to illustrate bet methodology

Starting sequence: 5 10 5 10

Net win target: $30

Bet number	Sequence	Bet amount	Win or Loss	Net position
1st	5 10 5 10	$15	win	+$15
2nd	10 5	$15	loss	even
3rd	10 5 15	$25	loss	-$25
4th	10 5 15 25	$35	loss	-$60
5th	10 5 15 25 35	$45	loss	-$105
6th	10 5 15 25 35 45	$55	loss	-$160
7th	10 5 15 25 35 45 55	$65	win	-$9 5
8th	5 15 25 35 45	$50	win	-$45
9th	15 25 35	$50	loss	-$95
10th	15 25 35 50	$65	win	-$30
11th	25 35	$60	win	+$30

In this example,  5 wins from 11 spins is enough to reach the target.

Throw in another losing streak and bet amounts would be getting hairy, and we’d be a long way adrift of erasing the sequence.

Bet choice

The system doesn’t dictate that you stick with any particular type of even money bet during your sequence. Switching from ‘black’ to ‘red’ to odd’ to ‘even’ should in theory make no difference.

Actually, the same should be the case for Martingale, although it’s users seem to like to stick with the same bet, thinking this helps somehow.

Does Labouchere work?

Depends on your time frame I guess. More often than not you’ll erase your sequence and have a modest win. When you lose, you’ll lose big. If you pull up stumps before the big loss, or at a point when your accumulated wins are greater than the losses then you can say it has worked for you.

Play an infinite number of spins using this system and your net position should approach the games mathematical house edge – which is a net loss for you unfortunately.

Like most roulette betting systems, this one falls down in the face of that unfortunate truth that each roulette spin is an independent event with a small edge an all possible bets.

The method you choose to place those bets, however complex, cannot change this.

I’d love to know how much of his fortune Henry Labouchère lost to his system.