The plan being simulated
The Martingale doubles the stake after every loss on an even-money bet, so that the first win recovers all earlier losses and adds one starting stake. Each series here starts with a fresh bankroll. It stops when a bet is won, or when the next stake would exceed the bankroll or the table maximum.
What the simulation shows
- In this model most series end with a gain of one starting stake, and a minority end with a loss far larger than all those gains put together.
- A series that can no longer double (bankroll or table maximum reached) ends with a loss of everything staked so far. With a starting stake of 1 and room for 8 losses, that loss is 255.
- The cumulative chart climbs in small steps and drops in cliffs. The theoretical average per series is negative. The simulated average wanders around it and, with few series, can even end above zero by chance.
The arithmetic
After k losses in a row the total lost is 2k − 1 starting stakes. A loss on red has probability 19/37, so k losses in a row have probability (19/37)k. The average result per series is the starting stake times the probability of finishing with a win, minus the loss at the limit times the probability of stopping. The house edge has not gone anywhere; see betting systems and the Martingale myth.
Raising the bankroll makes a series hit the limit less often, but the loss when it does is larger, and the average stays negative. This describes the model’s arithmetic and is not a recommendation.
If gambling stops feeling under control, see signs it is time to stop gambling.
Frequently asked questions
Can a bigger bankroll make the Martingale work?
It makes a series hit the limit less often, but the loss when it does grows even faster, and table limits still apply. The average result per series stays negative.
Why is the chart not smooth?
Each series is one small win or one large loss, so the cumulative result climbs in small steps and falls in cliffs.
