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The math of roulette

Roulette odds calculator

Choose a wheel and a bet to calculate win probability, net profit and expected value. The calculator uses standard payouts and fair, independent spins.

Set your assumptions

Your result

48.65%

Chance of winning this bet

Net profit if it wins
$10.00
Total return if it wins
$20.00
Expected net per spin
−$0.2703
House edge
2.70%

Hypothetical stakes. Standard payouts only. A calculation does not predict the next spin.

Read the single-bet result

The displayed net win excludes your returned stake. Total return includes it. A $10 red bet at 1:1 produces $10 net profit and a $20 total return if it wins. Expected value combines both winning and losing outcomes.

Calculate multiple bets together

When bets overlap, count every wheel pocket once and settle every selected wager on that outcome. A pocket can win one bet and lose another. Probability of any winning ticket is not necessarily probability of an overall profit.

Calculate a sequence of spins

Use a fixed event such as red or one chosen number and a number of future spins. All, none and at least once describe that event across the specified block. They do not calculate a run anywhere within a longer session.

What the calculator includes

Standard single-, double- and triple-zero wheels are supported. La Partage, En Prison, multiplier games, side bets and nonstandard paytables are excluded. This is a math tool with no wagering or spin prediction.

How to calculate roulette odds

Every result in the roulette odds calculator comes from four numbers: the pocket count N, the number of winning pockets C, the net payout ratio r and your stake s.

  • Win probability = C ÷ N. A red bet on a European wheel is 18 ÷ 37 = 48.65%.
  • Odds against winning = (N − C) : C. For red that is 19:18; for one number it is 36:1.
  • Net profit if the bet wins = s × r. Total return = s × (r + 1), because the stake comes back.
  • Expected net per spin = s × (C × (r + 1) ÷ N − 1). House edge = −expected net ÷ s.

For several bets on one spin, the calculator settles every ticket on each pocket and counts the pockets that produce a profit, a break-even or a loss. For a sequence it uses p^n, (1 − p)^n and 1 − (1 − p)^n for a fixed block of independent spins.

Bets you can calculate

Standard bets in the calculator with their coverage and net payout
BetCoversNet payoutEuropean chanceAmerican chance
Straight-up1 number35:12.70%2.63%
Split2 adjacent numbers17:15.41%5.26%
Street3 numbers in a row11:18.11%7.89%
Corner4 numbers in a square8:110.81%10.53%
Six-line (double street)6 numbers, two rows5:116.22%15.79%
Dozen (1st, 2nd or 3rd 12)12 numbers2:132.43%31.58%
Column12 numbers2:132.43%31.58%
Red or black18 numbers1:148.65%47.37%
Odd or even18 numbers1:148.65%47.37%
Low (1–18) or high (19–36)18 numbers1:148.65%47.37%

Every split, street, corner and six-line on the layout is listed individually. The American first-five basket (0, 00, 1, 2, 3 at 6:1) is offered only on the 38-pocket wheel. Choosing 00 or 000 on a wheel without that pocket shows an error instead of reinterpreting it as 0.

Worked calculator examples

Example inputs and the calculator's outputs
InputsMain resultExpected net per spin
European, $10 on red48.65% chance of winning−$0.2703
European, $10 on red and $10 on black0.00% chance of an overall profit−$0.5405
American, $1 on 0 and $1 on 005.26% chance of an overall profit−$0.1053
American, $1 on the first-five basket13.16% chance of winning−$0.0789
European, red on all 10 future spins0.07425%Not applicable

These match the cases used to test the calculator. Read about our calculations for the method and checks.

Calculation method and sources