Five strategies, the same 10,000 seed sequences
A paired comparison of Flat, Martingale, Fibonacci, D’Alembert, and Paroli under identical European-wheel outcome sequences.
Strategy comparisons are noisy when each system receives unrelated spins. This experiment pairs them: Flat, Martingale, Fibonacci, D’Alembert, and Paroli receive the same 10,000 seed sequences. Differences then come from wager sizing and stopping, not a luckier seed list.
Rules held constant
- Master seed
0x6d27738b- Wheel
- European; every system bets red
- Bankroll / unit
- $1,000 / $5
- Table maximum
- $500
Flat never changes its $5 wager. Martingale doubles after a loss. Fibonacci advances one sequence step after a loss and retreats two after a win. D’Alembert adds one unit after a loss and removes one after a win. Paroli doubles after wins, resets after a loss, and banks after three consecutive wins. A run stops if its required wager no longer fits the bankroll or table maximum.
| Strategy | Mean terminal | P10–P90 | Mean wagered | Return / wagered | Progression failure |
|---|---|---|---|---|---|
| flat | $932.53 | $790–$1,080 | $2,500 | -2.699% | 0.00% |
| martingale | $906.95 | $420–$1,635 | $3,686.25 | -2.524% | 90.08% |
| fibonacci | $857.17 | $115–$1,510 | $5,215.86 | -2.738% | 49.32% |
| dalembert | $607.05 | $20–$2,130 | $14,296.48 | -2.749% | 67.96% |
| paroli | $887.20 | $610–$1,170 | $4,232.31 | -2.665% | 0.00% |
Same edge, different exposure
Aggregate return per dollar wagered stayed near the European wheel’s −2.70% edge for every system. Terminal bankrolls differed because strategies put different amounts at risk and sometimes stopped early. D’Alembert generated the most action in this configuration and the lowest mean terminal bankroll. Martingale produced a wide distribution and broke its progression in 90.08%of 500-spin schedules. Paroli limited wager growth to a three-win cycle, so it did not hit a progression limit here; it still lost on aggregate.
Limitations
Parameter choices matter. This table compares named rules at one unit size, bankroll, cap, and horizon. It does not rank every variant of those systems. Paired seeds improve the comparison but do not turn simulated results into future predictions. The fair-wheel model contains no physical bias and no dependence between spins.