The martingale sounds unbeatable. Bet £5 on red. Lose, bet £10. Lose again, £20. When you finally win, you’re £5 up. Repeat until rich. The martingale calculator shows where that plan meets reality, and it’s sooner than most people think.
With a £500 bankroll and £5 starting bets, you can survive 6 losses in a row: 5, 10, 20, 40, 80 and 160, which adds up to £315. The seventh bet would be £320, and you’ve only got £185 left. Six reds in a row going against you sounds rare. On a European wheel it happens 1.83% of the time, so about once every 55 runs.
What the martingale calculator tells you
Set your aim at 100 wins, which is £500 profit at £5 a time. The chance you hit that losing streak before you get there is 84%. You’d probably win a lot of small amounts, then lose £315 in one go.
The calculator also shows the expected result per run. On European roulette it’s about −£0.87. On a fair coin with no house edge, it’s exactly zero. The doubling doesn’t create an edge. It just rearranges your losses into rare, big ones.
A bigger bankroll doesn’t save you
Bump the bankroll to £5,000 and you’d expect to be safe. But tables have a maximum bet, and on a £500 limit you can only double from £5 up to £320. After that the next bet isn’t allowed. The calculator flags when the table limit is what stops you, which is often.
That’s what table limits are partly for. They cap the size of a doubling sequence, so the casino doesn’t take on a player with a deep pocket chasing one loss.
The maths
Losses you can survive: K, where base × (2^K − 1) ≤ bankroll
and base × 2^(K−1) ≤ table limit
Chance a run busts = (chance of losing one spin)^K
Chance of a bust before your goal = 1 − (1 − bust chance)^goal
Every run either wins one starting bet or loses base × (2^K − 1). The rare big loss is bigger than all the small wins put together, by exactly the house edge.
The martingale won’t hurt you if you treat it as entertainment with a known price. Go in knowing the number above, and knowing that a long losing streak isn’t bad luck. It’s the system working as designed. For the odds on every roulette bet, use the roulette calculator.
Chasing losses is the habit the martingale is built on. If you catch yourself doing it, stop. BeGambleAware.org is free and confidential if it stops being fun.