The Martingale System: Why Doubling Up Fails, With the Numbers
The Martingale system tells you to double your bet after every loss and return to your base stake after every win. The first win in any losing streak recovers all previous losses plus one base unit of profit. On paper it looks risk-free. In practice it converts many small wins into an occasional very large loss, and the maths shows the expected result is exactly the same as flat betting: you lose the house edge on every dollar wagered.
This page works through the system on a European roulette wheel with A$ figures. It belongs to our casino tips and strategy section; for the roulette-specific version see Martingale in roulette.
How the Martingale Works
- Choose an even-money bet, such as red or black on roulette, or Player in baccarat.
- Bet one base unit, for example A$5.
- If you lose, double the bet: A$10, then A$20, A$40 and so on.
- When you win, you are A$5 ahead for the sequence. Go back to A$5.
On European roulette, red wins 18 of 37 spins (48.65%) and loses 19 of 37 (51.35%), because the green zero counts against every outside bet.
The Bet Sequence and Bankroll You Need
| Loss number | Next bet | Total lost so far | Probability of this many losses in a row |
|---|---|---|---|
| 1 | A$10 | A$5 | 51.35% |
| 2 | A$20 | A$15 | 26.37% |
| 3 | A$40 | A$35 | 13.54% |
| 4 | A$80 | A$75 | 6.95% |
| 5 | A$160 | A$155 | 3.57% |
| 6 | A$320 | A$315 | 1.83% |
| 7 | A$640 | A$635 | 0.94% |
| 8 | A$1,280 | A$1,275 | 0.48% |
| 9 | A$2,560 | A$2,555 | 0.25% |
| 10 | A$5,120 | A$5,115 | 0.13% |
The probabilities are (19/37) raised to the number of losses. After ten straight losses the next bet is A$5,120 to win A$5. A lot of live roulette tables cap outside bets well below that, and most players’ balances run out far earlier. Either limit ends the progression and locks in the full loss.
Worked Example: A$635 Bankroll, A$5 Base Bet
Suppose you bring A$635. That covers exactly seven bets: A$5 + A$10 + A$20 + A$40 + A$80 + A$160 + A$320 = A$635. Each sequence ends in one of two ways:
- Win A$5 if any of the seven bets wins. Probability 1 – (19/37)^7 = 99.06%.
- Lose A$635 if all seven lose. Probability (19/37)^7 = 0.94%, about 1 in 106.
Expected result per sequence: 0.9906 x A$5 – 0.0094 x A$635 = A$4.95 – A$5.98 = -A$1.03.
The average amount bet per sequence is about A$37.97 (most sequences end on the first or second spin, but a few run long). A$1.03 divided by A$37.97 is 2.70%, which is exactly the house edge of European roulette. The doubling did nothing to the cost. It only rearranged when the losses arrive.
What Happens Over a Session
Say your goal is to win A$500, which means completing 100 successful sequences. The chance of getting through 100 sequences without a single seven-loss streak is 0.9906^100, or about 38.8%. So roughly 61% of players who try this plan hit the wipe-out before reaching the target.
| Sequences played | Profit if no wipe-out | Chance of at least one A$635 loss |
|---|---|---|
| 10 | A$50 | 9.0% |
| 25 | A$125 | 21.1% |
| 50 | A$250 | 37.7% |
| 100 | A$500 | 61.2% |
| 200 | A$1,000 | 84.9% |
This is why Martingale feels like it works. Most short sessions end in a small profit. The losses are rare, but each one wipes out about 127 winning sequences.
Does a Bigger Bankroll Fix It?
A bigger bankroll makes the wipe-out rarer, not cheaper on average. With ten steps covered (A$5,115), the bust chance per sequence drops to 0.13%, but each bust now costs A$5,115 to protect a A$5 profit. The expected loss is still 2.70% of everything wagered. You are risking a large amount to win a tiny one, and the price of that trade is set by the zero on the wheel.
Why No Doubling System Can Win
Every individual bet on European roulette returns 97.30% on average. A sequence of bets is just a sum of those bets. If each part has a negative expected value, the total does too, regardless of how the stakes are arranged. In probability theory this is the optional stopping theorem: no rule about when to raise, lower or stop betting changes the expectation of a game with fixed odds. It applies equally to the Reverse Martingale, Grand Martingale, D’Alembert, Fibonacci and Labouchere, which we compare on the betting systems page.
Martingale With Casino Bonuses
Using Martingale to clear a bonus is risky for a separate reason. Most bonus terms set a maximum bet while wagering, often in the A$5 to A$10 range, and many list doubling or “low-risk” betting patterns as irregular play. Breaching either rule can void the bonus and any winnings. Even-money roulette bets also often contribute little or nothing towards wagering requirements.
If You Still Want to Try It
- Write the full sequence down before you start and decide where it stops. A stop at step 5 (A$155 lost) is a planned loss, not a failure of nerve.
- Use a European or French table, never American. On a double-zero wheel the edge is 5.26% and the probability of seven straight losses rises to about 1.12%.
- Check the table maximum for outside bets before your first spin.
- Count the cost in advance using the house edge: total wagered x 2.70%.
- Do not raise the base bet after a wipe-out to “win it back”. That is chasing losses, covered in common casino mistakes.
Frequently Asked Questions
It produces frequent small wins and occasional large losses. The expected result is the same as flat betting: a loss equal to the house edge on every dollar wagered, 2.70% on European roulette.
To cover n losses in a row you need the base bet x (2^n – 1). For a A$5 base bet, seven steps need A$635 and ten steps need A$5,115.
On European roulette the probability is (19/37)^10, about 0.13% or 1 in 784 sequences. Over hundreds of sequences that becomes likely.
You can use it with real money, but bonus terms often ban doubling patterns and set a maximum bet while wagering. Breaking those rules can void a bonus.
No. Doubling after wins changes the pattern to frequent small losses and rare large wins, but the expected loss is still the house edge on the total amount bet.
Betting systems do not reduce the cost of gambling. Play only if you are 18+ and contact Gambling Help Online on 1800 858 858 if you need support.