A finite Martingale cycle can finish ahead more than 99% of the time and still have a negative expected result. The reason is visible in an exact seven-step model: most completed cycles gain one unit, while the remaining outcome loses 127.
Fix the model before calculating
Use a European wheel and a red bet with full loss on zero. Start each cycle with 127 units. Wager 1, 2, 4, 8, 16, 32, 64, stopping at the first win or after seven consecutive losses. Assume the table permits every stake through 64. This is an exact finite calculation, not a Monte Carlo result.
Each step wins with probability p=18/37 and loses with q=19/37. A first win at any of the seven positions earns one unit overall: the winning profit exceeds all earlier losses by one. The only other path is seven losses, costing 1+2+4+8+16+32+64=127 units.
Scroll to compare all columns
| Cycle outcome | Probability | Net units |
|---|---|---|
| A win arrives within seven bets | 1−(19/37)^7 | +1 |
| Seven consecutive losses | (19/37)^7 | −127 |
Weight amounts by their probabilities
Expected net is 1−128×(19/37)^7, approximately−0.21 unit per cycle. The seven-loss probability is about 0.94%, so the profitable-cycle rate is about 99.06%. A small percentage of large losses outweighs the frequent one-unit gains.
These are probabilities across repeated new cycles with the same starting resources. They do not promise that a particular finite list will contain exactly that proportion of losses. The chance of an entirely loss-free series also falls as more cycles are attempted.
A reset needs actual funds
After a complete 127-unit loss, the player cannot start another identical cycle from the exhausted wallet. A theoretical comparison that replenishes 127 units each time must count those fresh funds as part of the experiment. A longer session with one shared wallet is a different model.
A table limit below 64 or a smaller starting wallet changes the stopping rule and the result distribution. Reducing the final requested stake changes the system too. These conditions should stay beside the headline percentage.
What to report beside a win rate
Record the gain on a winning cycle, loss on an unsuccessful cycle, total wagered, capital required and the frequency of each stop. For a sampled simulation, also report sample size and uncertainty rather than treating its observed percentage as exact.
Compare Martingale’s stake requirements with the matched-spin worked example. The house-edge explanation shows why arranging ordinary bets into cycles cannot erase their negative expected contribution.
Sources and scope
- Rules of Play for Table Games, Roulette. British Columbia Lottery Corporation. Double-zero standard payout table and placement. European pocket count is independently verified from native Wheel.
Publication date: not stated. Checked 2026-11-07.
- Roulette probability derivation. Amenti Labs LLC. Fair independent pockets, fixed payouts, full outside loss on zero. Formula and all supported bets regression tested.
Publication date: 2026-11-07. Checked 2026-11-07.