Labouchère

How does the Labouchère system work?

Decide how much you want to win, say 10 unitsmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full →, and write it as a line of numbers that add up to it: 1 2 3 4. Each bet is the first number plus the last: 1 + 4 = 5. Win, and cross off both ends; the line is now 2 3. Lose, and write the stake at the end: 1 2 3 4 5. Keep going until the line is empty, which means you have won 10 units, or until you cannot afford the next bet. It works like a to-do list on which every job done removes two items and every job failed adds a bigger one at the bottom.

Why does the line usually clear?

Each win removes two numbers; each loss adds one. The line shrinks whenever wins are more than half as frequent as losses, which on even money (48.6%) they usually are. Most lines clear. That is the appeal and the trap: the sessions in which the line does not clear are the ones in which losses have outnumbered wins by two to one for a while, and by then the numbers on the line, and the stakes, have grown large.

Does the Labouchère system work?

No. Most lines clear, and the ones that do not cost more than the cleared ones won. Starting from 1 2 3 4, a run of eight losses produces the line 1 2 3 4 5 6 7 8 9 10 11 12 and a next bet of 13 units, with 68 units already lost. At $10 a unit that is a $130 bet and $680 down. Eight even-money losses in a row has probabilitymathProbabilityChance of an outcome, from 0 to 1 or 0% to 100%. One number: 1/37 = 2.70%.Read full → (19/37)⁸ ≈ 0.5% from any starting point, and a 200-spin session offers many starting points. Unlike MartingalestrategyMartingaleProgression that doubles the bet after each loss. See the Strategy section for what it does and does not do.Read full →, a single win does not fix it; you need the line to clear, which takes several more wins than losses.

How much money does a short line need behind it?

The shortest common line, 1 2 3, wins 6 units. We simulated two million such lines on redbetRedEven-money bet on the 18 red numbers. French: rouge.Read full → on a European wheel with no table maximum and recorded the most money each line ever needed: the losses so far plus the next bet. Half the lines never needed more than 9 units. One in ten needed more than 79 and one in fifty more than 490, and to finish 99 lines in 100 a player needs about 1,050 units behind a 6-unit target. Even with no zerowheelZeroThe single green pocket that no even-money, dozen or column bet covers; the source of the house edge. Also: single zero, 0.Read full →, in a fair gamemathFair gameA game in which neither side has an edge: every bet has an expected value of zero.Read full →, it would take about 700. With less behind it the line is sometimes lost, and one lost line costs more than many finished lines have won.

Roulette Table Limits

Are there other versions?

Reverse LabouchèrestrategyLabouchèreCancellation system: write a line of numbers, bet the sum of the two ends, cross them off after a win, add the lost stake after a loss.Read full → adds after a win and crosses off after a loss, turning it into a positive progressionstrategyProgressionAny rule that changes the stake based on previous results. Negative progressions raise it after losses, positive after wins.Read full → with a built-in stop. Splitting a long line into two shorter ones (“1 2 3 4 5 6” into “1 2 3” and “4 5 6”) lowers the stakes and doubles the number of lines to clear. Starting with a single number is just flat bettingstrategyFlat bettingWagering the same amount every spin. The baseline every progression is compared against.Read full → with a target.

Flat Betting

Did the reverse Labouchère beat the casino at Nice?

In the reverse version a win adds the stake to the end of the line and a loss crosses off both ends. A line that empties has cost its total, 10 units for 1 2 3 4; a line that keeps winning grows its bets until the next one would pass the table maximum, and then the player banks the profit and starts again. It is the Labouchère turned inside out: many small losing lines and a rare large win. Norman Leigh’s book Thirteen Against the Bank (1976) tells how his team used it on all six even chances at Nice in 1966, and a later retelling claims that 96 of 100 practice sessions won (Goldman, 2007). That is backwards. In our simulation most sessions lose and a few win big, and the higher the maximum, the rarer and larger the wins. The cost is the same 1.35% of turnovermoneyTurnoverThe total amount wagered over a session or period, counting re-bet winnings. Also: handle, action.Read full → with la partageruleLa partageFrench rule: when zero hits, half of an even-money stake is returned. Halves the house edge on those bets to 1.35%.Read full → whatever the maximum.

Famous Roulette PlayersLa Partage

Who was Labouchère?

Henry Labouchère (1831–1912), journalist, theater owner and Liberal MP, popularized the system in London society and is said to have used it at Monte Carlo. The cancellation method predates him. It has never been shown to change the expected lossmathExpected lossExpected value times total amount wagered; the average amount lost over a session or a period.Read full →, which is the sum of the stakes divided by 37.

Monte Carlo Roulette

Simulator · Labouchère

2,000 sessions of even-money bets from a $1,000 bankroll.

Base bet $10 · table limit $500 · 100 spins per session

Questions