Labouchere system

How the Labouchere system works

The Labouchere system is also called the cancellation system. You write a short list of numbers, and that list tells you how much to bet.

It is meant for even-money bets like red or black, odd or even, high or low. Each one pays 1 to 1.

1. Write a list. The tester uses one, two, three, four.
2. Bet the first number plus the last number. With one, two, three, four, that is one plus four, so you bet five chips.
3. If you win: cross out the first and the last number.
4. If you lose: add the amount you just lost to the end of the list.
5. If only one number is left: bet that number.
6. When the list is empty: the cycle is done. You start a new list.

Every finished list wins you the sum of the starting numbers. With one, two, three, four, that is ten chips.

A short example round

Here is how one cycle can go with the list one, two, three, four.

• Bet five (one plus four). You lose. The list is now one, two, three, four, five.
• Bet six (one plus five). You win. Cross out one and five. The list is now two, three, four.
• Bet six (two plus four). You win. Cross out two and four. Only three is left.
• Bet three. You win. The list is empty.

You lost five chips once and won fifteen chips over three bets. The cycle ends ten chips up.

The problem starts when losses come in a row. Every loss makes the list longer and the next bet bigger.

What the system tester shows

The system tester on this page is already set to Labouchere. Run it and watch the bankroll line move.

For the numbers below, we ran 20,000 sessions on the European wheel with these settings:

• Bankroll: 200 chips
• Goal: win 50 chips, then stop
• Up to 300 spins per session
• Table maximum: 500 chips

The results:

• Reached the goal: 74.3% of sessions
• Ended with some profit: 74.3% of sessions
• Lost the whole bankroll: 25.7% of sessions
• Average result per session: -14.2 chips
• What the house edge predicts: -13.5 chips

Now change the settings. Try a longer list, a smaller bankroll, or the American wheel, and run it again.

Why it wins small often and loses big sometimes

Most sessions end with a small win because a few wins clear the list. Because each win crosses out two numbers and each loss adds only one, you can finish a cycle even if you lose more bets than you win.

But a long losing streak keeps adding bigger numbers to the end of the list. The bets grow until they hit the table maximum or use up your bankroll.

• Often: a small win of the size of your goal.
• Sometimes: a large loss that takes the whole bankroll.

Put together, the many small wins and the few big losses give an average of -14.2 chips. That is very close to the -13.5 chips the house edge predicts.

On the European wheel the house edge is 2.70% on every bet. Changing bet sizes does not change that. The Labouchere system only changes how you lose on average – not whether you do.

The same pattern shows up in the Martingale and Fibonacci systems. Read more in Can you beat roulette?

Reverse Labouchere

The Reverse Labouchere flips the rules. When you win, you add the amount you won to the end of the list. When you lose, you cross out the first and the last number.

This turns the pattern around: you lose small amounts often and win big sometimes, when a winning streak keeps the list growing. The average result still matches the house edge.

Want to compare more systems? Visit the roulette strategy page or try the Paroli, which also raises bets after wins.

Questions