Roulette Expected Loss
Expected loss is the most useful number for comparing strategies honestly. The formula is simple - total wagered × house edge - but it cuts through almost every marketing claim.
Run any strategy in the tester and the final report shows expected loss alongside actual loss. The gap between the two is just variance.
The formula
Expected loss = Total wagered × House edge
- European: house edge = 1/37 ≈ 2.7027%.
- American: house edge = 2/38 ≈ 5.263%.
- French (1:1 with La Partage): 1.35%.
- American five-number bet: 7.89%.
Why it is 'total wagered' and not 'bankroll'
A $100 bankroll wagered ten times in flat $10 bets has total wagered $100 - expected loss $2.70 on European.
The same $100 bankroll wagered through a Martingale doubling streak might see total wagered of $600 in a single cycle - expected loss $16.20.
The strategy that puts more money through the wheel has higher expected loss, even with the same starting bankroll.
Worked examples
| Strategy | Typical 200-spin wagered | European EL | American EL |
|---|---|---|---|
| Flat $10 red | $2,000 | $54.05 | $105.26 |
| $10 D'Alembert | ~$3,000 | $81.08 | $157.89 |
| $10 Fibonacci | ~$4,500 | $121.62 | $236.84 |
| $10 Martingale | ~$6,000-$10,000 | $162-$270 | $316-$526 |
| $10 Labouchere (1,2,3,4) | ~$5,000 | $135.13 | $263.15 |
| $200 James Bond | $40,000 | $1,081 | $2,105 |
The strategy with the highest expected loss is not Martingale's strategy - it's any strategy that drives total wagered up. James Bond at $200 per spin wagers more in 200 spins than most strategies do in 2,000.
Actual loss vs expected loss
Single-session actual loss varies widely around expected loss because of variance. A 200-spin flat session might end at −$5, +$30 or −$150 - all are consistent with expected loss of −$27.
Across many sessions, mean actual loss converges to expected loss. If your average across 50+ sessions is significantly different from expected loss, either (a) your sample is still small, or (b) you found a real bias somewhere - extremely rare in modern roulette.
What expected loss is not
- Not a prediction of any specific session.
- Not a maximum loss (drawdown can exceed it).
- Not a number you 'pay' upfront - it accrues across all spins.
- Not changed by any betting system.
Practical use
When evaluating any roulette strategy: ask what its average total wagered per session looks like. Multiply by 2.70% (or 5.26%). That number is the floor of what you should expect to lose, on average, over many sessions.
If a strategy claims to beat this number, it is claiming positive expected value. That requires extraordinary evidence, not screenshots.