How the Labouchère System Works—and Why It Cannot Beat Roulette

The Labouchère system sets your next stake from a line of numbers: after a win, remove the numbers at both ends; after a loss, append the lost stake. It is a staking progression, not a way to predict outcomes. It does not change roulette’s spin probabilities, payouts or house edge.

If you complete a classic cycle with net 1:1 payouts, your net profit equals the sum of the starting line. But completion is not guaranteed: your bankroll may run out, or the next stake may exceed the table maximum. Correct cancellation arithmetic is not evidence of an advantage over the casino.

Rules: How to Calculate the Stake and Update the Line

Your next stake is the sum of the first and last numbers in the line. If only one number remains, stake that amount; if the line is empty, the cycle is complete.

Follow these rules:

1. Write a starting line of positive numbers. Their sum is the target net profit for a completed classic cycle.
2. Add the first and last numbers to calculate the next stake.
3. After a full win with a net 1:1 payout, remove both end numbers. If there was only one number, remove it.
4. After a full loss, append the amount lost to the end of the line.
5. Before placing another bet, check your available bankroll and the table limit.

An even-money bet (net 1:1 payout) earns net profit equal to the stake on a win. A winning $4 stake returns the original stake plus$4 profit. “Even-money” does not mean a 50% probability of winning.

The classic rules are described in the Labouchère system paper, version 2 dated 27 August 2018. Results from models without funding limits should not be treated as estimates of success in a finite gambling session.

Why “One Third of Bets Must Win” Is Not a Success Rule

The proportion of winning bets alone does not determine whether you can complete the line or finish with a profit. Wins and losses occur at different stake sizes, and your ability to continue depends on their order, your remaining bankroll and the table maximum.

A loss adds one entry; a win removes two, or one when it is the last entry. This produces count identities for a path that has already completed. Those identities are bookkeeping, not probabilities of future completion.

They do not establish a useful “one-third” success threshold, expected number of spins, expected profit or session success rate. Nor does a losing streak make the next win more likely.

Worked Example: A $10 Target and Five 2s

For a $10 target, start with `2,2,2,2,2`. The initial stake is$4. Here, one unit equals $1, so each entry of `2` represents$2.

This example assumes a standard outside roulette bet with net 1:1 profit on a full win, the full stake lost on zero, independent spins with equally likely pockets, and no fees or chip rounding. The cumulative result is net profit or loss—not the remaining bankroll.

After the first loss, append 4. The endpoints become 2 and 4, making the next stake $6. Winning that bet removes those endpoints, leaving four 2s and a cumulative profit of +$2.

Next, losing $4 appends `4`; winning$6 removes the outer 2 and 4; winning $4 leaves a single `2`; and winning the final$2 completes the cycle.

The result of this specified path is +$10. It does not show how likely the path is or promise that you can repeat it.

Roulette Variants: Zero Rules, Payouts and Expected Value

The Labouchère system does not change the house edge in European or American roulette. The treatment of zero affects the expected value (EV) of the underlying bet, so check the table rules before applying any staking progression.

For standard outside even-money bets, such as red or black, the comparison is:

Standard roulette payouts and zero treatment appear in these undated operator rules. Double-zero rules are documented in the RWS double-zero roulette rules, version 2, published by the regulator. La Partage is described in these undated operator French roulette rules. These sources describe their respective games, not universal rules for every table.

La Partage applies only to eligible even-money bets at tables that offer it. On zero, you lose half the stake. That creates a third outcome, which does not fit the classic full-win/full-loss ledger unchanged. Neither cancelling both endpoints nor appending the full stake correctly records that partial loss.

RTP is not the probability of winning a spin or session. It is the long-run expected return ratio relative to turnover. Likewise, the house edge is not the probability of losing a particular session.

How Does the Progression Affect Expected Results?

The progression changes stake sizes, not the expected value per dollar wagered under unchanged game rules. Each new bet still faces the same house edge.

For $1,000 in turnover, the expected loss is approximately:

• European roulette: $27.03.
• American roulette: $52.63.
• Eligible French La Partage bets: $13.51.

These amounts are rounded to cents from the exact house-edge fractions. Turnover means the sum of all stakes, including money wagered again—not your starting bankroll. These are expectations under the stated model, not predictions for one session.

For more on table-rule choices, see the separate Labouchère roulette guide.

Does the Same Accounting Work for 2:1 Payouts or −110 Odds?

No. The classic line accounting assumes a full win produces net profit equal to the stake. It cannot be applied unchanged to a 2:1 payout or −110 odds.

A 2:1 bet produces net profit twice the stake, so ordinary endpoint cancellation no longer represents the same monetary balance. At −110, risking $110 earns$100 net on a win—not a net 1:1 payout. The calculator does not account for these differences or establish that the classic ledger applies to them.

Bankroll and Table Limits: When to Stop

Stop before placing the next bet if its stake exceeds your available bankroll or the table maximum. An empty line is not the only possible stopping point, and an unfinished cycle does not guarantee that losses can be recovered.

From 2,2,2,2,2, eight consecutive losses require these stakes:

$4, $6, $8, $10, $12, $14, $16, $18

The total loss is $88**, and the next required stake is **$20.

• With a starting bankroll of $100**, only **$12 remains. You cannot place the required $20 bet.
• With a $15 table maximum**, you must stop earlier: six losses total **$54, and the next required stake of $16 exceeds the maximum.

These are two constraints on one illustrative path—not a ruin probability or a bankroll recommendation. Neither $100 nor any other amount becomes “safe” because you use this system.

Calculate the next stake first, then compare it with both available funds and the table limit. If either check fails, do not place it. Reducing the stake or changing the line departs from the original cycle, so the original target profit can no longer be promised.

How to Use the Manual Labouchère Calculator

The calculator updates the line and calculates the next stake from wins and losses you record manually. It does not generate random spins or simulate roulette. Its tile labelled “Bankroll” shows manually recorded cumulative profit or loss—not actual remaining funds or a bankroll forecast.

Open the Labouchère system calculator, or use the embedded tracker:

To reproduce the screenshot states:

1. Set up the line. Enter $10** as the target, then select **“Generate Sequence”**. Check that the line contains `2,2,2,2,2` and the next stake is **$4.

English Labouchère calculator showing a 10 target, five 2s and a 4 next stake

Manually recorded calculator example, not casino outcomes: the generated $10 line starts with a$4 stake. The “Bankroll” tile tracks cumulative profit or loss, not available funds.

2. Record a full loss. Select “I Lost”. The line becomes 2,2,2,2,2,4, the next stake is $6**, and the cumulative result is **−$4.

English calculator after a recorded loss, showing five 2s followed by 4, a 6 next stake and −4 in the Bankroll tile

Manually recorded calculator example, not casino outcomes: “Bankroll” shows a cumulative loss of −$4, not the remaining bankroll.

3. Record a full win. Select “I Won”. Four 2s remain, the next stake is $4**, and the cumulative result is **$2.

English calculator after a recorded loss then win, showing four 2s, a 4 next stake and 2 in the Bankroll tile

Manually recorded calculator example, not casino outcomes: “Bankroll” shows $2 in cumulative profit, not$2 in available funds.

4. Continue recording outcomes only within the chosen full-win/full-loss model.

The tool also lets you edit the line and inspect the manually recorded results and chart. These three English screenshots were captured on 6 October 2026 from the owned workers.dev mirror. They do not document casino play or verification of the main production domain.

What Are the Calculator’s Limitations?

The tool does not calculate the probability of completing a cycle or check whether you can afford the next stake. It has no random spins, odds or probability inputs, roulette rule selector, starting-bankroll field, loss limit or table limit.

Check your actual remaining funds and permitted stake separately. The line, history and chart describe only the path you entered.

“Undo Last” does not fully reverse an entry. It removes a displayed history/chart value but does not restore the previous line or statistics. After an input mistake, reset the calculation and replay the correct results from the beginning.

Use this manual tracker to check arithmetic, not as evidence of profitability. It can show how stakes and the line change, but it cannot remove the house edge, predict outcomes or guarantee completion.