European versus American roulette: the risk distribution
Paired-seed simulation of 20,000 sessions per wheel showing how a second zero changes terminal bankroll, drawdown, and ruin risk.
Adding double zero changes more than a label. We sent the same 20,000 session seeds through a European and an American wheel, flat-betting $10 on red for at most 1,000 spins. Pairing the seeds reduces noise in the comparison: the generator starts from the same state while the wheel geometry changes.
Configuration
- Master seed
0x6d2b7a7f- Sessions
- 20,000 per wheel
- Session
- $1,000 bankroll; $10 red; 1,000-spin cap
- Stopping
- Stop at zero or after the final scheduled spin
The second zero compounds
| Wheel | House edge | Mean terminal | 10th–90th percentile | Ruin | P90 drawdown |
|---|---|---|---|---|---|
| european | 2.703% | $727.70 | $320–$1,140 | 1.57% | $810 |
| american | 5.263% | $478.32 | $40–$880 | 9.29% | $1,010 |
The theoretical loss on a complete 1,000-spin schedule is $270.27on the European wheel and $526.32 on the American wheel. Simulation means were close. Early bankruptcy slightly changes total action because ruined sessions cannot place the remaining bets. The more useful comparison is the shape: American-wheel ruin was about 5.9 times as frequent under this bankroll and horizon.
Limitations
This is one flat even-money strategy. En prison and la partage rules are not modeled, and casino table limits do not matter for a fixed $10 bet. A different starting bankroll or horizon changes the ruin rate. It cannot change the expected loss per unit wagered under the stated wheel rules.