No staking system changes roulette's house edge. Every system rearranges when you lose — many small wins against rare large losses, or the reverse — while the expected loss stays exactly 2.70% of total wagered (European wheel). This page shows the mechanism for the four famous systems, with the streak numbers that end them.
The streak table that breaks every progression
Even-money bets win 48.65% of spins. Losing runs are routine:
| Losing streak | Probability per 200 spins |
|---|---|
| 5 in a row | ~98% |
| 7 in a row | ~65% |
| 9 in a row | ~25% |
| 11 in a row | ~8% |
Two hundred spins is one evening of live roulette. Plan on the 7-streak; expect the 9 occasionally.
Martingale
Double after every loss; any win recovers the run plus one unit. The progression from a $5 unit: 5, 10, 20, 40, 80, 160, 320, 640... The 8th bet is $640 to chase $5, and the 9-loss streak (a 1-in-4 event per evening) requires $2,555 wagered and likely exceeds the table maximum first. Result over time: many +$5 sessions, occasional catastrophic ones, expected value unchanged.
If you want the math: each round of martingale risks bankroll B to win one unit u, succeeding with probability ≈ 1 − (0.5135)^n where n is how many doublings B affords. The win probability is high; the loss, when it lands, is the entire progression. Multiply out and the expectation equals flat-betting the same total volume: −2.70%.
Fibonacci
Bet the sequence 1, 1, 2, 3, 5, 8, 13... advancing on losses, stepping back two on wins. Gentler curve than martingale, same destination: deep streaks still demand large bets, and the slower climb just means losing runs take longer to bankrupt. Edge unchanged.
D'Alembert
Add one unit after a loss, subtract one after a win. The gentlest progression, often sold as "low risk." Accurate description: low variance, identical expected loss. It produces long mediocre sessions rather than sharp ones — a preference, not an edge.
Labouchère
Write a number line; bet the sum of the ends; cross them off on wins, append the loss on losses. Complex bookkeeping over the same arithmetic. Complexity is the product being sold — it feels like control. The wheel does not read the notebook.
What bet sizing is actually for
Variance control. Flat-betting a fixed unit (1–2% of session bankroll) keeps normal streaks survivable and sessions the length you intended — see the same framework in the blackjack bankroll guide; the math transfers directly. If you enjoy a progression as entertainment, price it honestly: martingale buys frequent small wins with rare disasters, at the same total cost as any other way of wagering the same volume.
The only lever that changes roulette's price remains table selection: French > European > American, covered in the wheel comparison.