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The math of roulette

Red and black roulette odds

Red and black each cover 18 numbers. The win chance is 48.65% on a European wheel, 47.37% on an American wheel and 46.15% on a triple-zero wheel.

48.65%

Chance of red on European roulette

18 / 37 • Standard payout 1:1

Why it is not 50/50

The green zero pockets sit outside both colors. On a single-zero wheel, a red bet wins on 18 pockets and loses on 19. On double zero it loses on 20. A 1:1 payout does not make the probability exactly one half.

A winning color bet pays 1:1

Under standard settlement, a $10 winning color bet earns $10 profit and returns $20 including the stake. The zero outcome loses the full stake unless a specific half-loss or other rule applies.

Betting on both colors

With $10 on red and $10 on black, a colored outcome returns $20 against $20 staked, so net profit is zero. A zero loses both bets. On a European wheel, the chance of an overall profit is 0%, even though one ticket wins on 36 of 37 pockets.

A streak does not change the next spin

After ten reds, the next fair European spin still has an 18/37 chance of red. The chance of ten specified future reds is (18/37)^10. Those are different questions; use the probability guide for the full distinction.

Red or black odds on each wheel

Chance of red (or black) by wheel type
WheelWinning pocketsLosing pocketsChance of redHouse edge
European181948.65%2.70%
American182047.37%5.26%
Triple zero182146.15%7.69%

The odds of black are identical, because each color has exactly 18 numbers. The chance of hitting black on roulette is 48.65% on a single-zero wheel.

Red or black several times in a row

For a color chosen in advance, the chance of n wins in a row is (18/37)^n on a European wheel. The table covers the next n spins as one fixed block.

Chance of one chosen color on every one of the next n spins
SpinsEuropeanAmericanTriple zeroEuropean, about
223.67%22.44%21.30%1 in 4
311.51%10.63%9.83%1 in 9
45.60%5.03%4.54%1 in 18
52.72%2.38%2.09%1 in 37
61.33%1.13%0.9666%1 in 75
70.6449%0.5351%0.4461%1 in 155
80.3137%0.2535%0.2059%1 in 319
90.1526%0.1201%0.09503%1 in 655
100.07425%0.05687%0.04386%1 in 1,347

Use the roulette probability guide for losing streaks and either-color runs, or enter your own number of spins in the roulette odds calculator.

Odd, even, low and high have the same odds

Red, black, odd, even, 1–18 and 19–36 are the six even-money bets. Each covers 18 numbers, pays 1:1 and has the same 48.65% European chance. Zero is neither odd nor even for these bets.

Combining conditions on one outcome is different: a number that is both black and odd covers only 8 pockets, so the chance is 8/37. The roulette bets guide explains overlapping bets.

Which numbers are red and which are black

Red (18)
1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36
Black (18)
2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35
Green
0 on European, 0 and 00 on American, 0, 00 and 000 on triple zero

Calculation method and sources