Labouchère: follow the cancellation line

Labouchère starts with a line of positive numbers. Wager the sum of its first and last numbers. After a win, remove both ends; after a loss, append the stake. If only one number remains, wager that number. Clearing the line ends the cycle.

Watch the line change

Start with 1, 2, 3, 4. Its sum is ten units, the intended profit if the cycle completes under the rules without hitting a limit.

The arithmetic completes this particular path. It does not promise that a real or simulated cycle will finish. The line can grow after repeated losses, and the required wager can exceed the available balance or table limit before enough wins arrive.

A target is not money already earned

A line represents a proposed recovery process. Unfinished lines remain real losses and exposure in the record. With a 20-unit starting wallet, the first two losses above leave nine units. A further seven-unit loss leaves two, while the next requested wager would be eight. The cycle stops with eighteen units lost and an uncleared line.

A useful comparison reports the starting line, total wagered, largest stake, ending balance and stopped cycles. Counting only completed lines leaves out exactly the difficult outcomes that matter.

Native convention and alternatives

The audited named app plan defaults to 1, 2, 3, 4, removes both ends after a profitable even-money wager and appends the current stake after a loss. It has a finite line-length safeguard. That safeguard ends the plan; it does not make the line profitable.

Compare Fibonacci for a position-based recovery rule, and Oscar’s Grind for a cycle-profit state rule. The bankroll guide explains how to record the unaffordable stop above.