Roulette Variance
Variance is the reason a 'losing' game can look like a winning one for hundreds of spins. It measures how far real results scatter around the expected value.
Understanding variance lets you read your own bankroll graph honestly. A profitable session is not proof of edge - it is often just variance in your favour.
What variance is
Variance is the average squared deviation of outcomes from the mean. Standard deviation (SD) is the square root - it has the same units as the bet (dollars).
For a single $10 bet on red on European: variance ≈ 99.93 dollars-squared, SD ≈ $10. Across n independent spins, total SD scales with √n.
Variance by bet type
Higher-payout bets have higher variance per dollar wagered. The expected value is the same, but the scatter widens dramatically.
| Bet | Per-spin SD ($10 stake) | Variance behaviour |
|---|---|---|
| Even-money (red, etc.) | ~$10 | Small - graph is smooth |
| Dozen / Column | ~$14 | Moderate |
| Six line | ~$23 | High |
| Corner | ~$28 | High |
| Single number | ~$58 | Very high - long flat sections, big spikes |
What variance looks like across N spins
Total SD scales as base SD × √n. For 100 flat $10 red bets on European, total SD ≈ $100. This means roughly 68% of sessions land within ±$100 of expected loss (which is −$27 over 100 spins).
So a result of +$50 or −$120 is unremarkable. A result of +$300 or −$400 is in the tail.
Variance by strategy
Strategy choice does change variance even though it does not change expected value.
- Flat betting: low variance, predictable graph.
- D'Alembert: low to moderate variance, smooth recovery.
- Fibonacci: moderate variance, sequence escalation widens swings.
- Martingale: low day-to-day variance but extreme tail variance when busts occur.
- Single-number flat: very high variance, sharp jumps.
- James Bond: moderate variance with one large negative on 1-12.
Why variance fools players
Variance is symmetric in the short run. Out of 100 flat sessions, roughly half will end profitable and half negative, with the average centred on the expected loss.
If you only see your own session, a profitable one feels like proof the strategy works. A losing one feels like proof it does not. Both feelings are wrong - both sessions are normal variance around the same negative expected value.
The fix: run many sessions in the tester. The aggregate result is the truth.
How variance interacts with bankroll
A larger bankroll absorbs more variance. With a $10,000 bankroll and $10 base bets, busting in 500 spins of flat red is essentially impossible (would require −1000 SD).
With a $200 bankroll and $10 base, two below-average sessions can wipe you out. The bet-size-to-bankroll ratio is the dominant predictor of survival, not the strategy choice.