Roulette Payout Calculator

What the roulette payout calculator does

This calculator shows what a roulette bet pays and what it is really worth. Pick the wheel, the type of bet, and the amount, and it gives you the payout if you win, the chance of winning, and the expected return, the average result of the bet over the long run.

That last number is the honest one, and it is always against you. Below is how the payouts work and why the wheel is built so the house comes out ahead.

How to use it

1. Choose the wheel, European with one zero or American with two.
2. Choose the bet type and enter the amount you would stake.
3. Press Calculate for the payout and the expected return, or Reset to clear it.

How the payouts are worked out

Each bet has a fixed payout, stated as a multiple of your stake. An even-money bet like red or black pays 1 to 1, so a winning stake is matched. A single-number bet, the riskiest, pays 35 to 1. The rarer the bet is to win, the more it pays when it does.

The payout the calculator shows is your winnings, the profit on top of your stake, and if you win you also keep the stake itself. So a 35 to 1 win on a single number returns your stake plus thirty-five times it. The payout scales with how many numbers your bet covers: the fewer it covers, the bigger the reward and the longer the odds.

The house edge, and where it comes from

Here is the heart of it. The payouts are set as if the wheel had only the 36 numbered pockets, but the wheel also has a green zero, and the American wheel has two. Those green pockets are what create the house edge. They lower your real chance of winning without changing what the bet pays, and that gap is the casino's built-in advantage.

Take a single-number bet. It pays 35 to 1, which would be exactly fair if there were 36 pockets, since you would win one spin in 36 and be paid 35. But there are 37 pockets on a European wheel, or 38 on an American one, so you win less often than the payout assumes. The payout is calibrated to a wheel that does not quite exist, and the difference is the edge that, over time, moves money from players to the house.

European versus American

The two wheels differ by a single pocket, and it matters more than it looks. The European wheel has one green zero, giving 37 pockets. The American wheel adds a second green pocket, a double zero, giving 38. Every payout is the same on both, so that extra pocket is pure disadvantage to the player.

The result is that the European wheel has a house edge of about 2.7 percent, while the American wheel's edge is about 5.26 percent, nearly double. If you have the choice, the European wheel loses your money roughly half as fast. The lesson is that a single green pocket doubles the cost of playing, which is a striking amount of damage from one small addition to the wheel.

Why the expected return is always negative

The expected return is the average outcome of a bet, working in both the chance of winning and the chance of losing. On a fair game it would be zero, meaning you break even in the long run. On roulette it is always below zero, no matter which bet you choose.

This is the same idea as expected value, applied to a wager. Every bet on the wheel, from red or black to a single number, carries the same negative expected return for a given wheel, about 2.7 percent of your stake on a European wheel and 5.26 percent on an American one. Different bets change how wildly the results swing, but not the long-run average, which always leans the house's way. That is why no betting system can beat roulette: the edge is baked into every single bet.

A worked example

Suppose you place 10 dollars on a single number on an American wheel. The payout is 35 to 1, so a win returns 350 dollars in winnings, plus your 10 back. But the chance of winning is only 1 in 38, about 2.63 percent.

Put those together and the expected return is about minus 0.53 dollars. On average, every 10 dollars staked this way loses about 53 cents, whatever happens on any single spin. The very same bet on a European wheel would lose about 27 cents instead, half as much, purely because that wheel has one fewer green pocket.

Entering your values

Choose the wheel and the bet type, and enter a stake greater than zero. The calculator shows the chance of winning for the selected bet, the payout as your winnings if it lands, and the expected return, which will be negative. Reading the payout and the expected return together is the point: the payout is what you might win, and the expected return is what the bet costs you on average.

Questions people ask

Does the payout include my stake?

No, it is your winnings on top of the stake. If you win, you also keep the stake, so a 35 to 1 payout returns your stake plus thirty-five times it.

What is the house edge?

The casino's built-in advantage, created by the green zero pockets. They reduce your real chance of winning while the payouts stay as if those pockets were not there.

Which wheel is better for the player?

The European wheel, with one zero and a house edge of about 2.7 percent, versus the American wheel's two zeros and about 5.26 percent. The European wheel loses your money about half as fast.

Can a betting system beat roulette?

No. Every bet has the same negative expected return, so no pattern of betting changes the long-run average. Systems alter how the results swing, not who comes out ahead.

References

A quick note on where the methods here come from. The probability and expected value behind games of chance are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook covering expected value and probability.

1. NIST/SEMATECH e-Handbook of Statistical Methods (probability and expected value). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (expected value and probability topics). https://openstax.org/details/books/introductory-statistics-2e