Labouchere roulette system: the line method, worked through

How the Labouchere roulette system works

Grab a pen. The line is your plan, and the sum of the line is your goal for the run.

1. Write a line of small numbers. 1, 2, 3, 4 adds up to 10, so the goal is 10 units.
2. Bet the first number plus the last number on an even money chance such as red or high. Here that is 1 + 4 = 5 units.
3. If you win, cross off both numbers. The next bet uses the new first and last.
4. If you lose, write the amount you just lost at the right end of the line.
5. When one number is left, bet just that number. When every number is crossed off, you have won the goal. Write a fresh line or stop.

Each win removes two numbers and each loss adds only one, so you can lose more often than you win and still clear the line. That is the clever part. The trap is that each loss also makes the next bet bigger.

A worked Labouchere example

Three wins, two losses, 32 units staked and 10 units earned. Out of 200,000 simulated lines, each backed by 100 units, about 87% ended like this. The rest did not.

When the line runs away

A line only shrinks on wins. A cold spell stretches it and pushes every bet higher.

After ten spins the line holds eleven numbers and the next bet is 20 units, but only 12 remain. The run is over, 88 units down, chasing a 10 unit goal. Nine losses in ten spins happens only about 1.3% of the time, but in the simulation a failed line usually took ten to eighteen mixed spins and ended the same way.

Bankroll needs and the table maximum

Bets grow by adding, not doubling, so the climb is steadier than the Martingale. Steady still adds up. In the simulated lines, the typical biggest bet was 9 units, but one line in ten needed 25 units or more from a 100 unit stack, and 40 or more from a bigger one.

A bigger bankroll makes failure rarer and much more expensive. The table maximum works the same way as running out of chips: when first plus last passes the limit, the line has to be dropped and the loss taken. A 500 unit bankroll with a 50 unit maximum rarely went broke in the simulation, but it ended 100 spins down in about 54% of sessions.

The long run result and the reverse Labouchere

Across 100,000 simulated sessions (100 spin cap, 100 unit stack, European wheel), Labouchere finished ahead about 31% of the time, went bust in about 68%, and averaged a loss of about 17 units. It also put far more units into action than flat betting, around 630 per session, and lost roughly 2.7% of that. The method moves money faster; it does not change the house edge.

The reverse Labouchere flips the rules: add the stake to the line after a win, cross off two numbers after a loss. It aims for rare long winning streaks and accepts many small lost lines. Over time it loses at the same rate.

Testing the Labouchere before you try it

The tester above starts on Labouchere with a 1, 2, 3, 4 line. Give it 300 units, a base of one and a per bet limit of 50, on the European wheel, for 120 spins and 500 sessions, then run. Look at the biggest bet needed and the sample line; it often climbs in steps, then falls sharply. Try a short session of 30 spins to see why people enjoy it for a single evening.

If you play it anywhere, choose a small goal, a hard loss limit and a finish time first, and quit when either limit arrives. Compare it with the Fibonacci and Paroli, or see every method together on roulette betting systems.