The same 12 pockets can produce different balances when the wager sizes change. This worked example uses an explicitly chosen input sequence. It is an arithmetic demonstration, not a random sample or a measured prediction of future play.
Declare the experiment
Start each system with 100 practice units on a fair single-zero wheel. Bet on red. Flat betting keeps the stake at one unit. Martingale starts at one, doubles after each loss and resets after a win. Stop before a requested stake exceeds either the wallet or a 64-unit table maximum.
The predetermined pocket sequence is 7, 20, 0, 32, 14, 21, 3, 5, 11, 36, 30, 18. Both systems read the same result at the same spin index. Zero loses the red bet in full.
Scroll to compare all columns
| Spin | Flat stake | Flat balance | Martingale stake | Martingale balance | |
|---|---|---|---|---|---|
| 1 | 7 | 1 | 101 | 1 | 101 |
| 2 | 20 | 1 | 100 | 1 | 100 |
| 3 | 0 | 1 | 99 | 2 | 98 |
| 4 | 32 | 1 | 100 | 4 | 102 |
| 5 | 14 | 1 | 101 | 1 | 103 |
| 6 | 21 | 1 | 102 | 1 | 104 |
| 7 | 3 | 1 | 103 | 1 | 105 |
| 8 | 5 | 1 | 104 | 1 | 106 |
| 9 | 11 | 1 | 103 | 1 | 105 |
| 10 | 36 | 1 | 104 | 2 | 107 |
| 11 | 30 | 1 | 105 | 1 | 108 |
| 12 | 18 | 1 | 106 | 1 | 109 |
What actually differs
Flat betting wagers 12 units in total and earns six. Martingale wagers 17 and earns nine. Its largest wager is four, compared with flat betting’s one. Neither reaches the budget or table limit on this chosen sequence.
The final balance alone leaves out the larger exposure. The four-unit recovery bet on spin four earns more than the flat bet because more units are at risk on that spin. If that pocket had been black or zero, the same larger wager would have produced a larger loss.
Why this path cannot rank the systems
The input contains nine red results and three losses for red. It was selected to make the changing stakes readable. It is not evidence that either system has a positive expected return or that Martingale usually ends ahead. Choosing a favorable trace and calling it a success-rate test would misrepresent the experiment.
A repeated comparison needs independent fair input streams, enough trials, predeclared stops and the full distribution including stopped runs. The methodology guide sets out those requirements. The high-win-rate analysis instead enumerates a complete finite cycle, including its uncommon large loss. Use the strategy simulator to inspect another bounded run.
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.