Labouchere Dice Strategy

The line is your contract for the session. Every number on it represents base units of target profit, and the system's bookkeeping guarantees (more on the guarantee below) that if you ever cross the whole line off, you have won exactly the line's original sum.

Construction choices set your risk before the first roll:

• 1-2-3-4 (sum 10): the standard beginner line used in all the simulations on this page.
• 1-1-1-1-1 (sum 5): flatter and gentler; opening bets are 2 units instead of 5, and bad patches escalate more slowly.
• 2-4-6-8 (sum 20): the same shape scaled up; every stress number in this guide doubles with it.

Play at 49.5% win chance for the 2x payout, since the crossing off arithmetic assumes even money. The opening bet on 1-2-3-4 is first plus last: 1 + 4 = 5 units. A line is not a bankroll; it is a target. The money required to defend a 10 unit target is vastly larger than 10 units, which is the detail that separates people who have read about Labouchere from people who have simulated it.

Worked example with 1-2-3-4:

1. Bet 5 (1 + 4). Lose. Line becomes 1-2-3-4-5. Down 5.
2. Bet 6 (1 + 5). Win. Cross off the 1 and the 5: line is now 2-3-4. Having lost 5 then won 6, you sit at +1, with 9 units of line left to clear.
3. Bet 6 (2 + 4). Win. Line is just 3.
4. Bet 3 (single number stakes itself). Win. Line empty: session target of 10 units banked.

The asymmetry that powers the whole system: a win removes two numbers, a loss adds only one. Starting from four numbers, if W is your wins and L your losses, the line empties when 2W = 4 + L. You need barely more than one win for every two losses, and 49.5% clears that bar comfortably most of the time. That is why completion rates look so spectacular and why the system feels like it cannot lose.

The same asymmetry writes the horror story. Every loss appends a number at least as large as the biggest already there, so consecutive losses do not just lengthen the line, they steepen it. The stake, always first plus last, ratchets with every setback while the promised reward stays frozen at the original 10.

This is bookkeeping, not magic, and the invariant is worth seeing once. At any moment define your position as: profit so far plus the sum of numbers still on the line. Check each move against it:

• Win of (first + last): profit rises by first plus last, the line's sum falls by first plus last. Position unchanged.
• Loss of (first + last): profit falls by the stake, the line gains a new number equal to that same stake. Position unchanged.

The position never moves. It starts at 0 profit plus 10 on the line, so it is always 10. The moment the line is empty, all 10 of it must be sitting in the profit column. Elegant, airtight, and completely silent on the only question that matters: what happens to sessions where the line never empties.

Because the invariant also reads in reverse: a long line is not bad luck you can wait out, it is your deficit, itemized. When the line reads 4-5-6-8-9-13-17, its 62 unit sum minus the 10 unit target says you are exactly 52 units underwater, and the system's only advice is to keep staking ends that now start at 21 units. The guarantee of +10 on completion is real. It just is not a guarantee of completion, and it never touches the underlying expectation: every roll still loses 1% of its stake on average, whatever the notebook says.

Simulation settings: line 1-2-3-4, 49.5% win chance, 2x payout, 1,000 unit bankroll, line abandoned only when the next bet exceeds the remaining roll. Results across 30,000 lines:

Read the last row twice. A 98.7% win rate at +10 units per win still averages out negative, because each failure hands back nearly two years' worth of Tuesday night profits at once. On average turnover of 162 units per line, minus 1.39 units is minus 0.9%, converging on the house edge as the abandoned-line truncation washes out over longer runs.

The 363 unit peak bet deserves attention too: that line began by wagering 5. Nothing about a bad Labouchere run announces itself early; the line quietly steepens for a dozen rolls and is suddenly staking a third of your bankroll on a coin flip to win the original 10. Table max bets, which we list for every site in our best bitcoin dice sites comparison, will sometimes end the line for you before the bankroll does.

Line splitting is the classic rescue: when a line grows past 8 or 10 numbers, split it into two shorter lines and clear them separately. This halves the near term stakes but doubles the wins still owed; it converts one steep cliff into two long slopes and mostly protects your discipline rather than your expectation.

Length caps are honest stop-losses in disguise: abandon any line that reaches, say, 12 numbers and book the loss. Since a 12 number line from a 1-2-3-4 start means the session is deeply underwater, the cap simply names the moment you stop. Naming it in advance is the entire value; our stop-loss and take-profit guide covers how to place these thresholds so a bad line cannot become a bad month.

Reverse Labouchere flips the rules: cross numbers off after losses, append after wins. Losing streaks now shrink the line cheaply while winning streaks build a longer, richer line staked with house money. It behaves like paroli stretched over a notebook: many small completed lines lost, occasional big lines banked, identical minus 1% of turnover.

Whatever variant you choose, size the base so the simulated worst cases survive: with 1-2-3-4 behaving as above, a bankroll of 100x the line total is the floor, not a luxury.