Streaks: how often they happen, and why the next spin doesn’t care
The exact chance of a run of one colour at roulette in the spins you play. Long runs are common over an evening; none of them changes the colour of the next spin.
Your wheel and your time
Pick the wheel, the run you have in mind and how long you play. The number of spins is the pace times the hours.
Double-zero wheel · runs of the same colour · 3 hours · Las Vegas Strip rating table: 38 spins an hour.
Chance of at least one run of 8 or more of the same colour in 3 hours (114 spins): 25%, in about 1 session of every 4.
The longest run of the same colour in 114 spins: in half of such sessions it is 6 or longer; in 8 of 10 it is between 5 and 9.
After 8 reds in a row, the next spin is red 18 times in 38 (47.37%), exactly as after any other spin. A run is common; it does not make the next colour any more or less likely.
| A run of the same colour of | Happens at least once in 114 spins |
|---|---|
| 5 or more | 96%in all but 1 of every 24 sessions |
| 6 or more | 75%in about 8 of 10 sessions |
| 7 or more | 47%in about 5 of 10 sessions |
| 8 or more | 25%in about 1 session of every 4 |
| 9 or more | 13%in about 1 session of every 8 |
| 10 or more | 6%in about 1 session of every 16 |
| 11 or more | 3%in about 1 session of every 34 |
| 12 or more | 1%in about 1 session of every 72 |
| 13 or more | 0.7%in about 1 session of every 153 |
Worked out exactly, spin by spin, from the pockets of the wheel (see “Show the model”): how it’s worked out.
Why the next spin doesn’t care
A long run feels as if it must end, and a colour that has not come up for a while feels due. Neither is true: the wheel has no memory, and each spin is independent of every spin before it.
Each spin is independent
Roulette balls and dice simply have no memory. Every spin in roulette and every toss in craps is independent of all past events.
The Gambler's Fallacy is the mistaken belief that if an independent event has not happened in a long time, then it becomes overdue and more likely. It is also equally incorrect that if an outcome has happened a disproportionate number of times lately, compared to statistical expectations, then it becomes overheated and less likely to occur the next time.
Wizard of Odds · Hot numbers in roulette: myths and facts · read
Both things hold at once. Over 114 spins, a run of six or more of one colour happens in 75% of sessions on a double-zero wheel. The chance that the next spin continues a run you are watching is still 18 in 38 for red on a double-zero wheel (18 in 37 on a single-zero one), the same as for any other spin.
Waiting for a run and then betting the other way changes nothing: every bet keeps the same house edge. What doubling after a loss does: How long will it last?
Wheels at casinos we list
The wheel sets the chance of red on every spin. These casinos name their wheel on their own website.
| Casino | Wheel, as the casino names it | Red on one spin |
|---|---|---|
| Caesars Windsor | Double zero Source
Caesars Windsor: roulette wheel choosing from 1 to 36, with a 0 and 00 caesars.com/caesars-windsor/casino · checked | 18 in 38 |
| Cascades Casino North Bay | Double zero Source
Cascades Casino North Bay: roulette wheel • Double Zero Roulette | 18 in 38 |
| Elements Casino Flamboro | Double zero Source
Elements Casino Flamboro: roulette wheel Double Zero Roulette | 18 in 38 |
| Elements Casino Flamboro | Triple zero Source
Elements Casino Flamboro: roulette wheel Triple Zero Roulette | 18 in 39 |
| Fallsview Casino Resort | Double zero Source
Fallsview Casino Resort: roulette wheel Double Zero Table | 18 in 38 |
| Fallsview Casino Resort | Single zero Source
Fallsview Casino Resort: roulette wheel Blackjack, baccarat and single zero roulette are offered in the Salon Privé. fallsviewcasinoresort.com/playing/table-games.html · checked | 18 in 37 |
| Fallsview Casino Resort | Triple zero Source
Fallsview Casino Resort: roulette wheel Triple Zero Table | 18 in 39 |
| Great Canadian Casino Resort Toronto | Triple zero Source
Great Canadian Casino Resort Toronto: roulette wheel Triple Zero Roulette | 18 in 39 |
| McPhillips Station Casinoelectronic terminals | Double zero Source
McPhillips Station Casino: roulette wheel MINISTAR ROULETTE 00 STADIUM GAMING | 18 in 38 |
| Parq Casino | Double zero | 18 in 38 |
| South Beach Casino & Resort | Single zero Source
South Beach Casino & Resort: roulette wheel table games featuring single-zero roulette southbeachcasino.ca/gaming · checked | 18 in 37 |
Only casinos whose own page names the wheel in words (“Double Zero”, “single-zero”, “0 and 00”). A game name such as “American Roulette” is not counted as a wheel stated.
Show the model
One spin of each wheel: how many pockets are red, black and green.
| Wheel | Red, and black | Green (zeros) | Source |
|---|---|---|---|
| Double zero38 pockets | 18 of 3847.37% each | 2 of 385.26% | Source
Roulette, double zero: pockets Worked out: red and black each win on 18 of 38 pockets (the source’s 47.37% on double zero is 18 of 38); the other 2 are green. A U.S. roulette wheel consists of 38 numbered slots: numbers 1 to 36, a zero, and a double zero. … The following table displays the available bets, the win (on a "to one" basis), and the probability of winning under U.S. rules. Table “Double-Zero Roulette”, row “Red”, column “Pays / Probability Win”: 1 / 47.37% |
| Single zero37 pockets | 18 of 3748.65% each | 1 of 372.70% | Source
Roulette, single zero: pockets Worked out: red and black each win on 18 of 37 pockets (the source’s 47.37% on double zero is 18 of 38); the other 1 are green. What most call "European roulette" is roulette played on a 37-number wheel, with one zero only. The pays are the same as in American roulette. A U.S. roulette wheel consists of 38 numbered slots: numbers 1 to 36, a zero, and a double zero. Table “Double-Zero Roulette”, row “Red”, column “Pays / Probability Win”: 1 / 47.37% |
| Triple zero39 pockets | 18 of 3946.15% each | 3 of 397.69% | Source
Roulette, triple zero: pockets Worked out: red and black each win on 18 of 39 pockets (the source’s 47.37% on double zero is 18 of 38); the other 3 are green. Triple-Zero Roulette is roulette played on a 39-number wheel. The wheel has the same numbers and colors as a double-zero wheel, plus a 39th place on the wheel. … Much like zero and double-zero, all even money bets lose if the ball lands in green. A U.S. roulette wheel consists of 38 numbered slots: numbers 1 to 36, a zero, and a double zero. Table “Double-Zero Roulette”, row “Red”, column “Pays / Probability Win”: 1 / 47.37% |
How it’s worked out
Exact, spin by spin. The page tracks the length of the current run after every spin: a spin of the same colour adds one, the other colour starts a new run of one, a green pocket ends the run. The chance of reaching the run length you picked at least once is added up over every possible sequence of spins. No simulation and no shortcut formula.
A check you can do by hand. For 100 tosses of a fair coin, the chance of four heads in a row somewhere is 97.27%: likely, not certain.
Assumptions. A fair wheel, every spin independent, the pace times the hours rounded to whole spins. “Runs of the same colour” counts red runs and black runs; “red only” counts red runs.
Pace. The Las Vegas Strip rating table is the table a major Las Vegas Strip casino uses to rate players; by number of players, Jim Kilby, Casino Operations Management; both as published by Wizard of Odds (sources on How long will it last?). Electronic terminals keep their own pace.
Precision. Chances are rounded to whole percents; below 1% to one figure.
If it stops being fun
If gambling stops being entertainment, help is available. 19+ in most of Canada; 18+ in Alberta, Manitoba and Quebec.
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