Roulette Payout Calculator
Print PageA Roulette Payout Calculator (also known as a Roulette Odds Calculator, American vs. European Roulette Payout Utility, Inside & Outside Bet Profit Analyzer, or Roulette Expected Value Calculator) computes exact net profit, total return payout (Wtotal = Wager · [Ratio + 1]), win probability percentage (P = Ncovered ÷ Ntotal), and long-term expected value (E[X]) across all bet types on Single-Zero European (37 pockets) and Double-Zero American (38 pockets) roulette wheels.
The single most important decision in roulette is choosing between a European and American wheel. Because an American roulette wheel adds a double zero (00) alongside single zero (0), the house edge nearly doubles from 2.70% on European wheels to 5.26% on American wheels across all standard bets!
Our free online Roulette Payout Calculator provides instant calculations across all inside and outside bet types:
- Straight Up Single Number Bet (35 : 1 Payout): Covers 1 number (e.g. $100 bet &implies;
$3,500 Net Profit / $3,600 Total Payout). - Split Bet (17 : 1 Payout): Covers 2 adjacent numbers (e.g. $100 bet &implies;
$1,700 Net Profit / $1,800 Total Payout). - Street Bet (11 : 1 Payout): Covers 3 consecutive numbers in a row (e.g. $100 bet &implies;
$1,100 Net Profit / $1,200 Total Payout). - Corner / Square Bet (8 : 1 Payout): Covers 4 touching numbers in a block (e.g. $100 bet &implies;
$800 Net Profit / $900 Total Payout). - Line / Six-Line Bet (5 : 1 Payout): Covers 6 numbers across 2 rows (e.g. $100 bet &implies;
$500 Net Profit / $600 Total Payout). - Dozen / Column Bet (2 : 1 Payout): Covers 12 numbers (1-12, 13-24, 25-36, or columns) (e.g. $100 bet &implies;
$200 Net Profit / $300 Total Payout). - Even-Money Outside Bet (1 : 1 Payout): Covers 18 numbers (Red/Black, Even/Odd, 1-18/19-36) (e.g. $100 bet &implies;
$100 Net Profit / $200 Total Payout).
Master Roulette Bet Payout & Probability Reference Table
The table below displays the payout ratio, European win probability (37 pockets), American win probability (38 pockets), net profit on a $100 Wager, and expected value per bet:
| Roulette Bet Name | Numbers Covered | Payout Ratio | European Win Prob (37 Pockets) | American Win Prob (38 Pockets) | Net Profit ($100 Wager) | Total Payout ($100 Wager) |
|---|---|---|---|---|---|---|
| Straight Up (Single Number) | 1 Number | 35 : 1 | 2.70% (1 in 37) | 2.63% (1 in 38) | $3,500.00 | $3,600.00 |
| Split Bet | 2 Numbers | 17 : 1 | 5.41% | 5.26% | $1,700.00 | $1,800.00 |
| Street Bet | 3 Numbers | 11 : 1 | 8.11% | 7.89% | $1,100.00 | $1,200.00 |
| Corner / Square Bet | 4 Numbers | 8 : 1 | 10.81% | 10.53% | $800.00 | $900.00 |
| Six Line Bet | 6 Numbers | 5 : 1 | 16.22% | 15.79% | $500.00 | $600.00 |
| Dozen / Column Bet | 12 Numbers | 2 : 1 | 32.43% | 31.58% | $200.00 | $300.00 |
| Even Money (Red/Black, Even/Odd) | 18 Numbers | 1 : 1 | 48.65% | 47.37% | $100.00 | $200.00 |
| American Basket Bet (0-00-1-2-3) | 5 Numbers | 6 : 1 | N/A | 13.16% | $600.00 | $700.00 (Worst Bet: HE = 7.89%) |
Step-by-Step Straight Up & Corner Bet Calculations
To calculate the net profit, total payout, win probability, and expected value for a $100 Straight Up single number bet (35:1) and a $100 Corner bet (8:1) on a European single-zero wheel (37 pockets):
Step 1 (Straight Up Win Prob P): P = 1 ÷ 37 = 0.027027 ≈ 2.70%
Step 2 (Straight Up Net Profit): Net Profit = Wager × 35 = $100 × 35 = $3,500.00
Step 3 (Straight Up Total Payout): Total Payout = Wager + Net Profit = $100 + $3,500 = $3,600.00
Step 4 (Straight Up Expected Value E[X]): E[X] = (0.027027 × $3,500) - (0.972973 × $100) = $94.60 - $97.30 = -$2.70 per $100 wager
Step 5 (Corner Bet Win Prob P): P = 4 ÷ 37 = 0.108108 ≈ 10.81%
Step 6 (Corner Bet Net Profit): Net Profit = Wager × 8 = $100 × 8 = $800.00 ($900.00 total payout)
Thus, a winning $100 single number bet returns a $3,500 net profit ($3,600 total payout) with a 2.70% win chance, while a $100 corner bet returns an $800 net profit ($900 total payout) with a 10.81% win chance.
American vs. European Roulette: House Edge & Odds Differences
Below is a comparative reference chart detailing the core mathematical differences between European and American wheels:
| Wheel Metric Feature | European Single-Zero Roulette | American Double-Zero Roulette |
|---|---|---|
| Total Pocket Count | 37 pockets (1 to 36 + single zero ‘0’) | 38 pockets (1 to 36 + ‘0’ + double zero ’00’) |
| Standard House Edge | 2.70% (1 / 37) | 5.26% (2 / 38) |
| Red/Black Win Probability | 48.65% (18 / 37) | 47.37% (18 / 38) |
| Expected Loss per $100 Wager | -$2.70 per $100 | -$5.26 per $100 |
History & Mathematics: 1655 Blaise Pascal to 1843 Monte Carlo
1655 Blaise Pascal & Perpetual Motion
In 1655, French mathematician Blaise Pascal invented the fundamental wheel mechanism of roulette while attempting to build a continuous-motion perpetual device. Pascal’s gaming wheel established modern probability theory alongside his correspondence with Pierre de Fermat.
1843 François & Louis Blanc (Single Zero Monte Carlo)
In 1843, French brothers François and Louis Blanc introduced the single-zero roulette wheel in Bad Homburg and later Monte Carlo, removing double zero to cut house edge in half (from 5.26% to 2.70%) and attracting gamblers across Europe.
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Frequently Asked Questions (FAQ)
What does a single number pay in roulette?
A single number (Straight Up bet) pays 35 to 1. A winning $100 bet returns a $3,500 net profit ($3,600 total payout).
Is European or American roulette better?
European roulette is significantly better. European wheels have a 2.70% house edge, whereas American wheels have a 5.26% house edge.
What is the worst bet in roulette?
The worst bet is the American 5-Number Basket Bet (0-00-1-2-3), which has a massive 7.89% house edge.