# Labouchère system

The Labouchere system is a cancellation system. It is a progressive betting system where you increase the bet after each loss, much like the Martingale. Unlike the Martingale, you are unlikely to come up against the house limit though as the progression is not very aggressive.

You start with an arbitrary set of numbers. Say, 1-2-3-4. The first bet is the sum of the first and last number. In this case, its 5. If the bet wins, you cross off the 1 and 4 and repeat. If it loses, then you add the last bet to the sequence and start again. You use this system generally on even money bets.

Below is an example.

 Bet Line Units Result Net Profit 1-2-3-4 5 loss -4 1-2-3-4-5 6 Loss -10 1-2-3-4-5-6 7 Loss -17 1-2-3-4-5-6-7 8 win -12 2-3-4-5-6 8 loss -12 2-3-4-5-6-8 10 win -2 3-4-5-6 9 win 7

In the example, if the line is cleared they’d be a profit of 10 units. You can see though, that after a run of losses, there will be some big bets needed to get back on track. The best way to play this system is with short sequences with low bets. For example.

 Safe Risky 1-1 1-2-3-4-5 1-3 4-3-10-9-7-2 1-2-1 2-2-4-7-8-7

Below shows the behaviour of the labourchere system with a simple 1,2,3,4 sequence after 10000 spins with an initial bankroll of £1000.

They had a good run getting up to £3000 before losing it all. It got back up to £5263.5 but they 1) went bankrupt before that point 2) lost it all again anyway.

With a bigger sequence such as 1,2,3,4,5,6,7 the behaviour looks like

You can be up in the short term but still, the house edge eventually wears you down and you end up losing lots of money.