Article — Roulette Payout Calculator
Roulette Payout Calculator: every bet type, both wheels
A roulette payout calculator returns your potential winnings, win probability, expected value, and the house edge for any combination of bet type, bet amount, and wheel. European wheels have 37 pockets and a 2.70% house edge. American wheels add a second zero pocket, raising the edge to 5.26%. Both numbers come from the wheel design and apply to all standard bet types.
Roulette is one of the simpler casino games mathematically. Every bet has a single clean probability and a clean payout multiplier. The casino's edge sits in the gap between the two: the 35-to-1 payout on a single number is slightly worse than the true odds of 36-to-1 (European) or 37-to-1 (American), and the difference is exactly the house cut.
What is a roulette payout calculator
A roulette payout calculator converts bet inputs (type, amount, wheel) into outcome inputs (payout if win, probability of winning, expected long-run result). It is useful for two distinct audiences: casual players who want to know what they would win on a specific bet, and probability students who want to verify the published house edge numbers for themselves.
The math is unchanged since the late 1800s. The European wheel layout was standardized in 1842 by the Blanc brothers in Bad Homburg, Germany; the American 00 wheel migrated to New Orleans casinos around the same time. Modern online roulette uses the same payouts and probabilities — only the random-number generation method differs from a physical wheel.
Blaise Pascal invented a primitive roulette wheel in 1655 while trying to build a perpetual motion machine. The wheel was a failed engineering project that found a second life as a gambling device. Modern roulette is a direct descendant, with the zero pocket added later to give the house an edge.
Roulette bet types and payouts
Roulette offers 10 standard bet types, grouped into "inside" (specific number combinations) and "outside" (broad categories). Payouts are stated "to one" — a 35:1 bet returns 35 times the stake in winnings, plus the stake itself.
- Straight (1 pocket): 35:1 payout. Win probability 1/37 European, 1/38 American.
- Split (2 pockets): 17:1 payout. Two adjacent numbers.
- Street (3 pockets): 11:1 payout. A row of three numbers.
- Corner (4 pockets): 8:1 payout. A 2×2 block of numbers.
- Line (6 pockets): 5:1 payout. Two adjacent rows.
- Column (12 pockets): 2:1 payout. One of three vertical columns.
- Dozen (12 pockets): 2:1 payout. 1-12, 13-24, or 25-36.
- Red / Black (18 pockets): 1:1 payout. Even-money outside bet.
- Odd / Even (18 pockets): 1:1 payout. Excludes zero.
- High / Low (18 pockets): 1:1 payout. 1-18 or 19-36.
Roulette house edge explained
The house edge is the gap between the true probability and the payout. On a European wheel, a single-number bet has a true probability of 1 in 37. A "fair" payout would be 36 to 1. Casinos pay 35 to 1, keeping 1 unit out of every 37 wagered. That 1/37 fraction equals 2.70%.
Two key facts about the edge:
European 1/37 = 2.70%American 2/38 = 5.26%Edge is constant same for every bet typeFive-number (US only) 3/38 = 7.89%The same edge applies to every standard bet type. Whether you play single numbers or red/black, the casino keeps 2.7 cents per dollar wagered (European) or 5.26 cents per dollar (American), over the long run. The bets differ in variance — single-number bets produce a wide range of short-run outcomes; even-money bets stay closer to expectation — but the long-run expected loss per dollar wagered is identical.
European vs. American roulette
The difference between European and American roulette is exactly one pocket. European has 37 pockets: numbers 1 through 36 plus a single green 0. American has 38: the same numbers, plus 0 and 00.
That single extra pocket doubles the house edge, from 2.70% to 5.26%. The math is intuitive: with one zero, the casino captures 1 in 37 wagered units. With two zeros, it captures 2 in 38. The fraction 2/38 simplifies to 1/19, and 1/19 is roughly twice 1/37.
If you have the choice, the European wheel is strictly better. Many US casinos offer both, sometimes with a "single zero" table that costs more to play at but returns much better expected value over time.
Roulette expected value and variance
Expected value is the average outcome per bet, computed by weighting each possible result by its probability. For a $100 straight bet on European roulette: with probability 1/37 you win $3,500 in profit; with probability 36/37 you lose $100. EV = (1/37)($3,500) + (36/37)(-$100) = $94.59 - $97.30 = -$2.70.
Variance is the spread of outcomes around the mean. Straight bets have high variance — mostly you lose, occasionally you win big. Even-money bets have low variance — you win or lose small amounts more frequently. Same expected loss per dollar, but radically different feel at the table.
Treat roulette as paid entertainment, not investment. Decide a budget you can lose, play at a comfortable pace, and walk away when you hit your limit or your time is up. The math guarantees that the longer you play, the closer your actual loss approaches the expected loss.
Roulette betting systems myth
Every roulette betting system — Martingale, D'Alembert, Fibonacci, Labouchere, Reverse Martingale — fails the same way. Each spin is independent. The wheel does not remember whether the last spin was red or black, and it does not know how many times you have lost in a row.
The Martingale system (double your bet after every loss) is the most famous. It works in principle except for two real-world constraints: table betting limits and finite bankrolls. A typical $5 minimum, $500 maximum table forces you to walk after 7 consecutive losses (5, 10, 20, 40, 80, 160, 320, then 640 is over the cap). Seven consecutive losses on red/black occur once every 1 in 106 sessions of 7 spins — not a rare event.
"Red came up 8 times in a row, black is due." False. The wheel has no memory. The probability of black on spin 9 is exactly 18/37 (European) or 18/38 (American), the same as on spin 1. Streak intuition is a known cognitive bias and the basis of countless lost bankrolls.
La Partage and En Prison rules
Two European table rules cut the house edge in half on even-money bets. La Partage refunds half the stake when the ball lands on zero — so red/black, odd/even, and high/low effectively only lose half their value to the zero pocket. The edge for these bets drops from 2.70% to 1.35%.
En Prison is a variant that holds (imprisons) the stake for one more spin instead of refunding half. If the next spin wins, the stake is returned with no winnings. If it loses, the stake is lost. The expected value is the same as La Partage: 1.35% edge on even-money bets.
Common roulette payout mistakes
The most common mistake is conflating "win probability" with "house edge." Red/black wins 48.65% of the time on a European wheel — that is a probability, not the casino's cut. The cut is the gap between 48.65% and 50% (the fair-coin baseline), and equals 1.35% per spin: same 2.70% / 2 because the zero pocket loses on either side of the bet.
The second mistake is misreading payout odds. "35 to 1" means you receive 35 units in winnings plus your stake back. "35 for 1" would mean 35 units total including your stake — an inferior payout. Always read whether it says "to" or "for." Casinos use "to 1" universally.