Labouchere System Calculator

Leave Cancellation Sequence at the default text 10,20,30,40. The engine parses those four numbers, sums them for Target Profit, and sets Opening Bet to first + last (or the only number if a singleton remains). Sum = 10+20+30+40 = $100.00. Opening Bet = 10+40 = $50.00. Numbers in Sequence = 4. The Labouchère rule: you stake the sum of the two ends; if the even-money bet wins, you cross both numbers off; if it loses, you append the amount you just lost to the right end. Goal of a completed line: win a net equal to the original sum, here $100, through a mix of wins and losses that eventually empties the list.

Worked first spin. You bet $50 even money. Win: cross off 10 and 40, list becomes 20,30, next stake 20+30=$50 again, remaining target $50. Lose: list becomes 10,20,30,40,50, next stake 10+50=$60, remaining target $150, and you are already $50 down. That asymmetry is the point people miss. One loss lengthens the line and raises the next stake; you need more than one later win to erase a loss. The calculator shows the opening snapshot, not the whole tree.

Common mistakes: typing a target as a single number and expecting a split (use 10,10,10,10 if you want four tens that still sum to 40); including zeros or words the parser will drop; thinking Opening Bet is a Martingale double. Next, replace the text with 5,10,15 and confirm target $30, opening $20; or 100 and confirm a singleton opening bet of $100 with target $100. Try 10,20,30,40,50 to see target $150, opening $60. None of those paths is plus-EV. They are different ways to schedule the same negative-edge even-money bet.

Read $100 / $50 as the line’s goal and first stake, not as a promise you will book $100. A European even-money bet still loses 19/37 of the time. A long losing cluster turns 10,20,30,40 into a tail that can demand table-max stakes, at which point the cancellation system cannot complete. Type a line you could actually finish under the table’s maximum, not a line that looks neat.

Labouchère — cancellation, split Martingale, American cancellation — is a negative progression that attacks a written list instead of a single doubling index. Henry Labouchère (1831–1912), British politician and journalist, popularised the method as a roulette staking plan: pick a sequence that sums to the profit you want from the session, bet the ends, cross off or append. Victorian and Edwardian casino literature loved it because it looks like bookkeeping rather than gambling. The bookkeeping does not remove the zero.

This calculator is for pricing a specific list before you write it on a card. System researchers compare a 10,20,30,40 line with a long flat line of ten tens: both sum to $100, but the opener is $50 versus $20. The shape of the list changes volatility and the speed of disaster, not the edge. Pit regulation still kills the plan when the appended tail exceeds the max bet.

What it does not do: play out wins and losses, compute the distribution of completion times, or include wheel type. There is no house-edge output. The parser splits on commas, spaces and semicolons and keeps positive numbers only. It will not warn you that a 200-unit opener exceeds a 100-unit max. Reverse Labouchère (append on wins, cancel on losses — a positive progression) is a different system and is not this page.

Limitations. Target Profit assumes you eventually cancel every number, which requires a win majority in a particular pattern, not in expectation. On 18/37 win rate you more often lengthen the line than shorten it. The opening bet formula matches the classic two-end rule. Mid-line you would re-sum the new ends yourself; this tool only prices the list you typed, as a snapshot.

Educational cancellation arithmetic. Not a method for extracting $100 from a roulette wheel. Not financial advice. The default 10,20,30,40 line is a $100 target with a $50 first stake, a snapshot of the list before any spin, nothing more.

Henry Labouchère’s cancellation plan attacks a written profit list rather than a single doubling index. The default sequence 10, 20, 30, 40 sums to a target of 100 dollars. Opening stake is first plus last: 10 + 40 = 50 dollars. Count of numbers in the line is 4. Victorian and Edwardian casino literature loved the method because it looks like bookkeeping. The bookkeeping does not remove the zero from a European wheel. Henry Labouchère (1831–1912), politician and journalist, popularised the split or cancellation Martingale as a roulette staking plan; crossing numbers off a profit list is older table folklore.

Cancellation dynamics are the derivation, and they should be stated as invariances rather than as software. A win deletes both ends; a loss appends the lost stake to the right. The sum of the list always equals remaining target profit plus, after losses, the extra deficit that must be recovered. Completing an empty list yields net profit equal to the original 100 if no table constraint intervened. Proof sketch for a win: removing a and b reduces the sum by a + b, which is exactly the even-money profit of staking first plus last. Loss case: one loses a + b and appends a + b, so the list sum rises by a + b, matching the new larger target. After a winning first spin on 50 the list becomes 20, 30 with remaining target 50. After a losing first spin it becomes 10, 20, 30, 40, 50, next stake 60, remaining target 150, already 50 down.

Asymmetry is the pedagogical point people miss. One loss lengthens the line and raises the next stake; more than one later win is required to erase that loss. Each spin still has expected value minus (1 / 37) times the stake on European even money. The list does not change win probability 18 / 37. Optional stopping when the list clears selects a subset of paths that look like wins and hides the fat-tailed paths that hit a maximum bet. Completion probability before ruin is less than one, and the loss when the tail explodes is larger than the 100-dollar target. A cousin of Martingale, Labouchère spreads recovery across two ends instead of one double.

Worked variants show that shape changes volatility, not edge. A flat line of ten tens also sums to 100 but opens at 20 rather than 50. A singleton 100 opens at 100 with target 100 and count 1. Extending to 10, 20, 30, 40, 50 lifts the target to 150 and the opener to 60. Reverse Labouchère, appending on wins, is a different positive progression and is not this lecture. Splitting a large appended number into two smaller ones that sum to the same amount is a common live patch after a bad loss; it does not restore plus expected value.

Assumptions: even-money payout when the line is actually played, independent spins, and the ability always to post first plus last. House edge is not beaten. Target 100, opening 50, count 4 are the sum and two-end opener of the sequence 10, 20, 30, 40 before any spin, a snapshot of Henry Labouchère cancellation, not a forecast of session profit. Table maxima kill the plan when the appended tail demands a stake the felt will not accept. Educational cancellation arithmetic, not a method for extracting 100 dollars from the wheel.