Roulette Probability Calculator
Exact probabilities, expected values, and session simulations for European, American, and French roulette.
Roulette Variant
Select Bet Type
Inside Bets
Outside Bets
Bet on a single number (including 0, 00)
Straight (Single Number)
Bet on a single number (including 0, 00)
Detailed Analysis
Session Simulation
Uses deterministic seeded random generator for reproducible results.
European vs American Impact
European (single zero): house edge 2.70%. For every $100 wagered, expected loss is $2.70.
American (double zero): house edge 5.26%. For every $100 wagered, expected loss is $5.26 — nearly double.
French (La Partage): effective house edge on even-money bets drops to ~1.35%. The lowest in standard roulette.
Bet Type Comparison (European)
| Bet Type | Win Prob | Payout | EV per $ | House Edge |
|---|---|---|---|---|
| Straight (Single Number)1 winning | 2.703% | 35:1 | -$0.03 | 2.703% |
| Split (Two Numbers)2 winning | 5.405% | 17:1 | -$0.03 | 2.703% |
| Street (Three Numbers)3 winning | 8.108% | 11:1 | -$0.03 | 2.703% |
| Corner (Four Numbers)4 winning | 10.811% | 8:1 | -$0.03 | 2.703% |
| Six Line (Six Numbers)6 winning | 16.216% | 5:1 | -$0.03 | 2.703% |
| Dozen (12 Numbers)12 winning | 32.432% | 2:1 | -$0.03 | 2.703% |
| Column (12 Numbers)12 winning | 32.432% | 2:1 | -$0.03 | 2.703% |
| Red or Black18 winning | 48.649% | 1:1 | -$0.03 | 2.703% |
| Odd or Even18 winning | 48.649% | 1:1 | -$0.03 | 2.703% |
| High or Low18 winning | 48.649% | 1:1 | -$0.03 | 2.703% |
Understanding Roulette Mathematics
The House Edge Cannot Be Beaten
Every bet type in roulette carries the same house edge for a given variant. In European roulette, the house edge is approximately 2.70% (1/37). In American roulette with the additional 00 pocket, the house edge doubles to approximately 5.26% (2/38). No betting strategy or pattern can overcome this mathematical disadvantage.
Expected Value is Always Negative
The expected value (EV) represents the average outcome per unit wagered over many trials. In roulette, EV is always negative, meaning players can expect to lose money over time. For European roulette, the EV per unit is approximately -$0.027, meaning for every $100 wagered, the expected loss is $2.70.
Variance vs. House Edge
While the house edge determines long-term outcomes, variance describes short-term fluctuations. Bets with higher payouts (like straight numbers) have higher variance — you may win big occasionally but lose more consistently. Lower payout bets (like red/black) have lower variance with more frequent but smaller wins.
The Law of Large Numbers
In the short term, luck can produce winning sessions. However, the law of large numbers dictates that as the number of trials increases, observed results converge toward the expected value. Over thousands of spins, the house edge becomes undeniable, and losses approach the theoretical expectation.
Educational Note: This calculator demonstrates that all roulette bets have negative expected value. There are no winning strategies. Understanding probability mathematics should inform responsible decision-making.
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