Use this Roulette Risk of Ruin Calculator to estimate the chance that your bankroll goes broke before you reach a target profit. Choose European or American roulette, enter your bankroll, flat bet size, bet type, and target win, then compare your probability of ruin against your chance to hit the target.
This is a flat-betting bankroll simulator. It does not turn roulette into a positive expected value game, and it does not prove that any system can beat the wheel. It shows how bankroll depth, target profit, bet volatility, and the zero pockets affect session survival.
Even-money bets (Red/Black, Odd/Even, High/Low) are calculated with the classic gambler’s ruin formula. Dozen/Column and Straight Up bets are estimated by Monte Carlo simulation, so results may vary slightly between runs.
Risk of Ruin
RouletteHow to Use the Calculator
- Select the Wheel:
- European (Single Zero): Better for players. House edge 2.70%.
- American (Double Zero): House edge 5.26%.
- Enter Your Bankroll: Total session capital you are willing to risk.
- Set Your Bet Size: Flat bet amount per spin. Bankroll depth (in units) is shown beneath the inputs.
- Choose Bet Type: Even-money (1:1), Dozen/Column (2:1), or Straight Up (35:1). Higher payouts come with higher volatility.
- Set Your Target Win: Your “walk away” profit number. Without a target, long-run risk of ruin in a -EV game is 100%.
- Read the Output: The calculator shows your probability of ruin and your chance of reaching the target before going broke.
What This Calculator Assumes
- You use a fixed flat bet size every spin (no progression systems).
- You stop when your bankroll reaches the target profit or when you can no longer afford your unit bet.
- European roulette uses 37 pockets: 18 wins and 19 losses on even-money bets.
- American roulette uses 38 pockets: 18 wins and 20 losses on even-money bets.
- The session ends as ruined when your bankroll drops below your bet size — not just when it hits zero.
- Dozen/Column and Straight Up results use Monte Carlo simulation (10,000 sessions). Numbers may vary by ±0.5–1 percentage point between runs.
- The calculator does not model table limits, Martingale or other progressions, French La Partage, En Prison, or side rules.
Roulette Risk of Ruin Formula for Even-Money Bets
For Red/Black, Odd/Even, or High/Low bets, the calculator uses the classic gambler’s ruin formula because each spin either wins one unit or loses one unit.
p = probability of winning one spin
q = probability of losing one spin (1 − p)
n = starting bankroll in betting units
z = total bankroll target in units (start + target win)
Chance to reach target = (1 − (q/p)^n) / (1 − (q/p)^z)
Risk of ruin = 1 − Chance to reach targetIn European roulette, even-money bets win on 18 pockets and lose on 19, so q/p ≈ 1.056. In American roulette, they lose on 20 pockets, so q/p ≈ 1.111. That small change compounds across many spins and produces noticeably higher long-run risk on the American wheel.
For Dozen/Column and Straight Up bets, the calculator uses Monte Carlo simulation because the +2/−1 and +35/−1 step sizes don’t fit the simple gambler’s ruin formula cleanly.
Real-World Examples
Example 1: Small Target on an Even-Money Bet
You have $100, bet $5 on Red, and want to win $20.
- Bankroll depth: 20 betting units.
- Target: +4 units.
- European wheel: approximately 27% risk of ruin.
- American wheel: approximately 37% risk of ruin.
The target is modest, but the risk is not near zero. The zero pocket gives the casino a mathematical edge on every spin, and roughly 1 in 4 sessions ends with the bankroll gone before the target is reached — even with a relatively small profit goal.
Example 2: Aggressive Straight Up Bet
You have $100, bet $5 on Number 17, aiming to win $500.
- Bankroll depth: 20 units.
- Target: +100 units.
- European wheel: approximately 86% risk of ruin.
- American wheel: approximately 87% risk of ruin.
Each Straight Up win pays 35 units. To reach +100 units of profit, you need many hits to compensate for the long stretches of losing spins between them. With only 20 units of bankroll, most sessions end before you hit enough numbers.
Example 3: The American Wheel “Tax”
Same setup as Example 1, but switch from European to American roulette: $100 bankroll, $5 on Red, target $20.
- European wheel: ~27% risk of ruin.
- American wheel: ~37% risk of ruin.
- Difference: +10 percentage points just from adding the second zero pocket.
The extra “00” acts as a tax on every spin, accelerating the drain on the bankroll. If a European wheel is available, choose it.
Risk of Ruin by Target Profit
A reference table for $100 bankroll, $5 even-money bet (20 units of bankroll), varying target profit. Numbers are computed analytically.
| Target Win | Target Units | European RoR | American RoR |
|---|---|---|---|
| $20 | +4 | 27% | 37% |
| $50 | +10 | 52% | 68% |
| $100 (double up) | +20 | 75% | 89% |
| $200 | +40 | 92% | 99% |
| $500 | +100 | ~100% | ~100% |
The pattern is consistent across all bankroll sizes: doubling your bankroll is statistically harder than winning a small profit, and the American wheel makes every target meaningfully worse than the European wheel.
Why Risk of Ruin Stays Above Zero on Roulette
Roulette has negative expected value on every standard bet (House edge 2.70% European / 5.26% American). That means even a generous bankroll cannot drive risk of ruin to zero on a meaningful target — it can only reduce it. The longer the session, the more the house edge compresses your survival probability.
If you continue playing indefinitely with no target, the long-run probability of ruin approaches 100%. A clear stop-win and a bankroll deep relative to that target are what make session survival mathematically possible — not bet selection or system play.
Frequently Asked Questions (FAQ)
What is roulette risk of ruin?
Roulette risk of ruin is the probability that your bankroll falls below the amount needed to continue betting before you reach your target profit. It depends on wheel type, bet size, bankroll depth, target win, and bet volatility.
Why is American roulette riskier than European roulette?
European roulette has one zero, so an even-money bet wins on 18 pockets and loses on 19. American roulette has 0 and 00, so the same bet wins on 18 pockets and loses on 20. That extra losing pocket increases the house edge from 2.70% to 5.26% and raises long-term bankroll pressure significantly.
Does a smaller bet size reduce risk of ruin?
Usually yes for a fixed bankroll and target. Smaller bets give you more betting units, which makes short losing streaks less likely to wipe you out before variance has time to even out. However, smaller bets also require more spins to reach the target, so the house edge has more spins to work against you.
Does Martingale lower roulette risk of ruin?
No. Martingale changes the shape of risk rather than removing it. It produces many small wins and rare large losses. Bankroll size, table limits, and the cumulative effect of the house edge mean Martingale does not reduce long-run risk of ruin — it usually concentrates risk into rare catastrophic losses.
Why is Straight Up risk different from Red/Black?
Both bets have the same house edge on the same wheel, but the volatility is very different. Straight Up wins rarely (1 in 37 or 38) but pays 35:1; Red/Black wins almost half the time but pays only 1:1. With the same bankroll and target, Straight Up has a much wider distribution of outcomes — including a much higher probability of busting before any win lands.
Is this calculator exact?
Even-money roulette risk is calculated analytically using the gambler’s ruin formula and is mathematically exact for the assumed flat-betting model. Dozen/Column and Straight Up results use Monte Carlo simulation (10,000 sessions), so the displayed result may vary by roughly ±0.5–1 percentage point between runs.