Roulette Odds Calculator
Calculate exact hit probabilities, payout odds, total return, and expected casino house edge for inside and outside bets across European, American, and French roulette wheels.
Click any pocket on the roulette grid on the right to select your Straight Up number.
Calculated Mathematical Output
Status: Calculated (Deterministic)Comprehensive Roulette Bet Comparison Matrix
Direct mathematical comparison of payouts, hit frequencies, and house edges across European (37-pocket) and American (38-pocket) wheels.
| Bet Name | Pockets | Standard Payout | European Hit Prob. | American Hit Prob. | House Edge (EU / US) |
|---|---|---|---|---|---|
| Straight Up | 1 | 35 : 1 | 2.70% (1/37) | 2.63% (1/38) | 2.70% / 5.26% |
| Split | 2 | 17 : 1 | 5.41% (2/37) | 5.26% (2/38) | 2.70% / 5.26% |
| Street | 3 | 11 : 1 | 8.11% (3/37) | 7.89% (3/38) | 2.70% / 5.26% |
| Corner | 4 | 8 : 1 | 10.81% (4/37) | 10.53% (4/38) | 2.70% / 5.26% |
| Six Line | 6 | 5 : 1 | 16.22% (6/37) | 15.79% (6/38) | 2.70% / 5.26% |
| Top Line / Basket | 5 | 6 : 1 | N/A (US only) | 13.16% (5/38) | 7.89% (Worst) |
| Dozen / Column | 12 | 2 : 1 | 32.43% (12/37) | 31.58% (12/38) | 2.70% / 5.26% |
| Even-Money (Red/Black) | 18 | 1 : 1 | 48.65% (18/37) | 47.37% (18/38) | 2.70%* / 5.26% |
*If French roulette La Partage rules are enabled, even-money house edge drops to 1.35%.
How Roulette Odds Are Calculated
Roulette operates on deterministic combinatorial probability. Because standard wheels are unweighted and perfectly symmetrical, every pocket has an identical probability of receiving the ball on any given spin.
For instance, a single-number straight-up bet on a European wheel ($W = 37$) covers $N = 1$ pocket. The hit probability is $1 / 37 = 0.027027...$ or $2.70\%$. On an American wheel ($W = 38$), the identical wager yields $1 / 38 = 0.026315...$ or $2.63\%$.
Payout Odds vs. Winning Probability
A frequent area of confusion in casino mathematics is the difference between payout odds and event probability:
- Payout Odds (e.g., 35:1): Defines the casino's monetary reward ratio. A 35:1 payout means winning a 1-unit wager returns 35 units in profit plus the original 1-unit stake (36 units total return).
- True Odds / Probability (e.g., 36 to 1): Defines the actual physical chance of losing vs. winning. On a 37-pocket wheel, there are 36 losing pockets for every 1 winning pocket.
The Source of Casino House Edge
The casino advantage stems entirely from paying out at 35 to 1 on a wager that actually has 36 to 1 true odds (European) or 37 to 1 true odds (American). The casino holds back the extra pocket's mathematical equivalent as its fee.
Roulette Inside Bet Odds & Structures
Inside bets are placed directly on the numbered grid or their intersecting boundary lines. They cover fewer numbers and offer higher payout multipliers.
Outside Bets & Why 0 and 00 Matter
Outside bets are placed on boxes surrounding the number grid. They cover large sectors of the wheel:
Even-Money Bets (Red/Black, Odd/Even, 1-18/19-36): Pay 1:1. These bets cover 18 pockets. On a European wheel, $18 / 37 = 48.65\%$. On an American wheel, $18 / 38 = 47.37\%$.
Column & Dozen Bets: Pay 2:1. These bets cover 12 pockets. European probability is $12 / 37 = 32.43\%$. American probability is $12 / 38 = 31.58\%$.
House Edge & Expected Value Formula
The Expected Value ($EV$) per 1-unit wager is calculated by summing the probability-weighted profit and loss outcomes:
European Straight-Up Example:
$P(\text{win}) = 1/37$, $\text{Payout} = 35$, $P(\text{loss}) = 36/37$
$EV = (1/37 \times 35) - (36/37 \times 1) = 35/37 - 36/37 = -1/37 \approx -0.027027$ ($-2.70\%$).
Therefore, the casino house edge is exactly $2.70\%$.
Can Roulette Odds Predict the Next Spin?
The Gambler's Fallacy & Independent Events
In a standard random wheel spin, every spin is completely independent of past outcomes. The roulette wheel has no memory.
If Red has landed 10 times in a row, the probability of Red on the 11th spin is still exactly 48.65% on a European wheel. Black is NOT "due" to hit.
For 5 consecutive European reds: $(18/37)^5 = (0.486485)^5 \approx 2.72\%$
How We Calculate and Validate Roulette Probabilities
Adzvelo validates all mathematical calculations against standard combinatorial models and published gaming literature (including Wizard of Odds roulette frameworks).
Frequently Asked Questions (FAQ)
Roulette probabilities describe exact mathematical expectations over time. They cannot predict or guarantee individual spin results. Betting systems (such as Martingale or Fibonacci) do not alter the underlying casino house advantage. Play responsibly and within set financial limits.
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