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What are the odds on roulette, bet by bet
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"Odds" means two things at a roulette table. The chance that a bet wins, and the ratio the bet pays. They are never the same, and the gap between them is the only reason casinos offer the game. Here is the chance side, for every bet, in the forms people actually ask about.
Odds of winning, European wheel
| Bet | Probability | Odds against | Pays |
|---|---|---|---|
| Straight-up | 2.70% | 36 to 1 | 35 to 1 |
| Split | 5.41% | 17.5 to 1 | 17 to 1 |
| Street | 8.11% | 11.33 to 1 | 11 to 1 |
| Corner | 10.81% | 8.25 to 1 | 8 to 1 |
| Six line | 16.22% | 5.17 to 1 | 5 to 1 |
| Dozen / column | 32.43% | 2.08 to 1 | 2 to 1 |
| Even-money | 48.65% | 1.056 to 1 | 1 to 1 |
Compare the last two columns in every row. The true odds against are always a little longer than the payout. That little is 2.70% of your stake on average, every spin.
On an American wheel
Add a pocket. Straight-up 2.63%, even-money 47.37%, dozens 31.58%. The payouts stay where they were, so the gap widens to 5.26%. The five-number basket wins 13.16% of the time against a 6 to 1 payout and loses 7.89% to the house.
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Streaks
People ask about streaks because they feel meaningful. They are not, but the numbers are worth knowing so that a normal run does not look like a sign.
| Event | Chance |
|---|---|
| Red 3 times running | 11.5% |
| Red 5 times running | 2.7% |
| Red 8 times running | 0.31% |
| Red 10 times running | 0.075% |
| Losing an even-money bet 7 times running | 0.94% |
Over 200 spins, a run of eight of the same colour somewhere in the sequence turns up in roughly 47% of sessions (about 27% for one named colour). It changes nothing about spin 201.
Droughts
A number that has not hit for a long time is not due. The chance it has not hit in n spins is (36/37) to the power of n: 50 spins, about 25%; 100 spins, about 6.5%; 150 spins, about 1.7%. Those are the chances for one specific number. Across the 37 numbers on the wheel, at any given moment some number will usually be in a drought of 100 or more, by pure chance.
The odds nobody quotes
The chance of being ahead after a session. For 100 spins of £1 on red on a European wheel it is roughly 36%. For 100 spins of £1 on a single number it is around 40%, higher, because a single 35:1 hit puts you ahead, but the losing sessions are deeper. Neither figure is a strategy. Both are what the game looks like from the player's chair, which is a sequence of mostly small losses, some wins, and an average that sits quietly at minus 2.70%.
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Short answers
What are the odds of hitting a single number?
1 in 37 on a European wheel, 2.70%. In ratio form, 36 to 1 against. The bet pays 35 to 1, and that one-unit gap is the house edge.
What are the odds of red coming up five times in a row?
About 2.7% on a European wheel: 0.4865 to the power of five. It happens roughly once every 37 sequences of five spins, which over an evening is not rare at all.
What are the odds of a number not hitting in 100 spins?
About 6.5%. Each spin it misses 36 times in 37; raise 36/37 to the power of 100 and you get roughly 0.065. Long droughts on a single number are normal.