The Martingale is the oldest betting system there is. You bet on red. If you lose, you double your bet. When you finally win, you get back everything you lost plus your original stake, then start again.
It feels unbeatable because it usually works. Most sequences end in a small win. The problem is the sequence that doesn't.
The numbers
Start at $5 on a European wheel with a $500 table limit. After seven losses in a row you've bet $5, $10, $20, $40, $80, $160 and $320, a total of $635. The next bet would be $640, which is over the limit. The sequence is dead.
Seven losses in a row on red happens about once every 106 sequences. So you win $5 roughly 105 times, about $525, then lose $635 in one go. Do the maths and you're behind.
Why no system can work
Every bet on the wheel has the same 2.70% house edge. A betting system only changes the size and order of your bets. It can't change the edge on any of them, so it can't change the average. What it does change is how losses arrive: rarely, and all at once.
That's true of every progression: Martingale, reverse Martingale, Fibonacci, D'Alembert, Labouchère. They reshuffle when you lose. They can't stop it.
See what roulette costs at your stake on the roulette calculator.
Sources
- Wizard of Odds: Roulette basics