Progression systems change the next stake depending on the previous result. The best known is Martingale: you double after every loss, so the first win wipes out all losses and leaves a profit equal to the original stake.
Why it seems to work
At odds of 2.00 and a 50% chance, most sequences end with a profit of 1 unit. A long losing streak is rare, so for weeks the system looks flawless.
Why the edge does not change
Every bet has its own expected value (EV). If the odds are below the fair price, each bet loses on average, whatever the stake. A sum of negative numbers stays negative. The system only changes when you lose: many small wins and one large loss.
There are practical limits too. The bookmaker caps the stake and your bankroll is finite, so the run that wrecks you is not theoretical.
Fibonacci, D’Alembert, Labouchere, Paroli
- Fibonacci: after a loss you raise the stake along 1, 1, 2, 3, 5, 8... Slower than Martingale, same logic.
- D’Alembert: +1 unit after a loss, −1 after a win. Lower risk, but still no change to EV.
- Labouchere: write a list of numbers and stake the sum of its ends. Risk grows as you lose.
- Paroli: you double after a win. You usually lose only the base stake, but you profit only when a winning streak arrives.
None of them gives a bet with negative EV a positive one. If a real edge exists, a flat stake or a fraction of Kellyi is enough, as in the bankroll lesson.