How many times in a row has a little ball landed in the same pocket of a Roulette wheel, i.e. how many times has a single number occurred in a row? And how about the same color? What is the probability of these events and a potential impact on a play?
Record Occurrence of a Single Number in Roulette
The probability that any single number occurs is 1/37 in French Roulette and 1/38 in American Roulette (there are 36 numbers + zero + double zero in American Roulette). There is no doubt that it is a great coincidence when the same number comes up again and again.
The longest reliable series was registered at the hotel El San Chuan in Puerto Rico on 9 June 1959. During the course of the American Roulette, number ten occurred even six times in a row! The probability of such (successive) events is determined by a multiplication of individual events. Therefore the probability that the same number comes up six times in a row is:
- General Rules. An ordinary single- or double-zero wheel is used. Most of the layout is the same as conventional roulette. Two balls are used. Both balls must be successful for 'outside' bets to win. For example, for a bet on Red win, both balls must land in a red number. Either ball must be successful for 'inside' bets to win.
- The probability that the ball eventually ends up in one of the slots depends on how many slots there are: They are 37 (in French/European roulette) or 38 (in American roulette) colored and numbered pockets on the wheel. If you were simply betting on red, and if there were only black or red slots, then you would be winning with a 50% chance.
(1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38), that is:
There's also some handy (but not necessarily easy) information at the bottom about working out roulette probabilities, plus a little bit on the gambler's fallacy. Note: The following probabilities are for European roulette. Check out the American probabilities page if you're playing on a wheel with the double-zero. Roulette bets probability chart.
(1/38)6 = 0.000000000332122593261671.
That is a very small number indeed, roughly three billionths only. If we convert this probability into true odds that would have to be offered to us by a casino, we get the value 3,010,936,384 to one. The true (fair) odds are calculated as a reciprocal of the probability, that is 1 ÷ probability. If such a bet on a series of outcomes was possible in Roulette, we would win $3 billion for a $1 bet(!)
Crown Perth Restaurants. With premium restaurants delivering world-class fine-dining experiences and casual eateries offering a more relaxed vibe, Crown Perth is home to some of the best restaurants in Perth. So, whatever the dining occasion, we’ve got you covered. Crown casino perth dining options.
It is important to add that the above-mentioned calculation of probability deals with a multiple (successive) events, i.e. we can ask this question: What is the probability that the same number in Roulette comes up 6 times in a row?
Since it would be a different case if e.g. number 10 occurred and after that before the new spin we asked what was the probability that number ten came up again? In this case the answer would be 1/38 (in terms of American Roulette), because any number could occur with the same probability 1/38 in every new spin. That is what we call a simple event in contrast with a multiple event(s) whereas the probabilities of individual events are multiplied (→ Articles on Probability).
The true odds for a 1 to 10fold repetition of the same number are shown in the table below. It is the same mechanism as if a sporting bet company or a casino offered the odds for a victory of some home team in some football match (→ The Odds Determination and Calculation).
| The Same Number Comes Up in a Row | True Odds to One in FRENCH Roulette | True Odds to One in AMERICAN Roulette |
|---|---|---|
| 37 | 38 | |
2˟ | 1,369 | 1,444 |
| 50,653 | 54,872 | |
4˟ | 1,874,161 | 2,085,136 |
| 69,343,957 | 79,235,168 | |
6˟ | 2,565,726,409 | 3,010,936,384 |
| 94,931,877,133 | 114,415,582,592 | |
8˟ | 3,512,479,453,921 | 4,347,792,138,496 |
| 129,961,739,795,077 | 165,216,101,262,848 | |
10˟ | 4,808,584,372,417,850 | 6,278,211,847,988,230 |
The odds are reciprocal values of the probabilities – the higher they are, the lower the probabilities are. The case of the above-mentioned record series is marked green. Consider also the difference that is made by one extra number in American Roulette (the double zero).
Record Repetition of the Same Color in Roulette
There are no exceptions that the same color appeared more than 20 times in a row in practice. The record was registered in 1943, when red color came up 32 times in a row! The probability of such event in French Roulette is (18/37)32 = 0.000000000096886885 with the corresponding odds 10,321,314,387:1.
The probability of the 32fold repetition of the same color in American Roulette is much more lower: (18/38)32 = 0.00000000004127100756 and the odds are 24,230,084,485:1. Thus this is even less likely than occurrence of a single number six times in a row. Again it is clearly demonstrated what kind of importance (a negative one for players) has just one extra number in American Roulette.
Family guy games for free. Now imagine that you used the Martingale betting strategy (→ see the first test of the Martingale system), whereas the next bet is doubled if your bet loses..
→ Testing & Simulations of Roulette Bets & Strategies
Wizard Recommends
- €1500 Welcome Bonus
- €100 + 300 Free Spins
- 100% Welcome Bonus
On This Page
Introduction
Roulette is one of the easiest games to play and understand in the casino. As usual the easier a game is to understand the greater the house edge, and roulette is no exception. If you are looking for a easy to understand and slow paced table game, and are willing to sacrifice on the house edge, then you may like roulette. If you want something more stimulating or with a decent return I would suggest looking at other games.
One difference between roulette and all other table games is that roulette chips have no value denomination printed on them. This actually is the true definition of a chip, one which indicates its value is technically called a check. The roulette table comes with six to eight sets of different colored chips, each set consisting of 300 chips. When a player purchases chips he gets his own color and the value of each chip is the buy-in divided by the number of chips received. The dealer will place a token on top of the dealer's stack of that color of chips to indicate the value.
Mit blackjack team total winnings. How much did the MIT blackjack team make per person and in total? Did the founders make more? The team lasted for decades and there was a lot of turnover on the team. The team was as small about 78 counters, or sometimes bigger than 30 counters.
American Rules
A U.S. roulette wheel consists of 38 numbered slots: numbers 1 to 36, a zero, and a double zero. The betting layout consists of every individual number as well as a host of 'outside' bets on combinations of numbers. After the players make their bets, the dealer spins the wheel and a ball and after several seconds the ball will land in one of the numbered slots.
The following table displays the available bets, the win (on a 'to one' basis), and the probability of winning under U.S. rules. All casinos in the U.S. follow these rules except for in Atlantic City. The house edge on all bets is 1/19, or 5.26%, except for the 0-00-1-2-3 combination, which carries a house edge of 7.89%.
Double-Zero Roulette
| Bet | Pays | Probability Win | House Edge |
|---|---|---|---|
| Red | 1 | 47.37% | 5.26% |
| Black | 1 | 47.37% | 5.26% |
| Odd | 1 | 47.37% | 5.26% |
| Even | 1 | 47.37% | 5.26% |
| 1 to 18 | 1 | 47.37% | 5.26% |
| 19 to 36 | 1 | 47.37% | 5.26% |
| 1 to 12 | 2 | 31.58% | 5.26% |
| 13 to 24 | 2 | 31.58% | 5.26% |
| 25 to 36 | 2 | 31.58% | 5.26% |
| Six line (6 numbers) | 5 | 15.79% | 5.26% |
| First five (5 numbers) | 6 | 13.16% | 7.89% |
| Corner (4 numbers) | 8 | 10.53% | 5.26% |
| Street (3 numbers) | 11 | 7.89% | 5.26% |
| Split (2 numbers) | 17 | 5.26% | 5.26% |
| Any one number | 35 | 2.63% | 5.26% |
European Rules
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. However, with one zero the house edge is cut to 1/37, or 2.70%, on all bets.
The term European roulette is somewhat of a misnomer because you can find single-zero roulette all over the world. In fact, it is the standard outside the United States. Even in the United States you can find single-zero roulette in some high-limit rooms.
Atlantic City Rules
In Atlantic City, any all even money bets (red, black,odd, even, 1-18, 19-36) follow a variation of the European half-back rule (see below). If the ball lands in 0 or 00, then the player will lose only half of any even money bet. This lowers the house edge to 2.63% on these bets. This rule does not apply on single zero wheels.
French Rules
French roulette is played on a single wheel and also features a favorable 'en prison' or half-back rule. Under the 'half-back' rule, if the player makes any even money bet (red, black, odd, even, 1-18, 19-36), and the ball lands in zero, then the player gets half the bet back, known as 'la partage' in French.
The term French roulette is also somewhat of a misnomer because the 'la partage' rule can sometimes be found in casinos outside of France, including some high-limit rooms in Las Vegas.
Rather than lose half, the player sometimes may also choose to imprison the bet. If an imprisoned bet wins on the next spin it is released and the player gets it back, without winnings. What is subject to casino rules is what happens to an imprisoned bet if the ball lands in zero again on the next spin. At some casinos the bet loses, and at others it would become double imprisoned. If a double-imprisoned bet bet won on the next spin, it would move up a level, and become single-imprisoned again. If it lost, then if would become triple-imprisoned if the casino allowed it, otherwise it would lose.
The following table shows the probability of a win, push, and loss under every imprisonment variation I'm aware of.
Imprisonment Odds
| Imprisonment | Win | Push | Loss | Expected Value |
|---|---|---|---|---|
| Single | 0.48648649 | 0.01314828 | 0.50036523 | -0.01387874 |
| Double | 0.48648649 | 0.01332346 | 0.50019005 | -0.01370356 |
| Triple | 0.48648649 | 0.01332583 | 0.50018768 | -0.01370120 |
| Infinite | 0.48648649 | 0.01332586 | 0.50018765 | -0.01370117 |
| French | 0.48648649 | 0.01351351 | 0.50000000 | -0.01351351 |
When given the choice to lose half or face imprisonment, the expected value is the same under French rules. Otherwise the expected loss is less losing half.
Triple-Zero Roulette
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. This 39th place will always be green and often the Logo of the casino where the game is located, for example an apple at the New York New York. The game premiered at the Venetian in Las Vegas in September, 2016.
Much like zero and double-zero, all even money bets lose if the ball lands in green. The order of the numbers 1 to 36 is the same as in single-zero roulette. The 0, 00, and Logo are all consecutive, with the Logo in the middle.
There is an added bet on any green, which pays 11 to 1. The house edge on every bet is 1/13 or 7.69%.
Short Pays
I've noticed some electronic roulette games don't pay the full 35 to 1 on single-numbers bets, and/or 17 to 1 on double-number bets. Invariably, any game that short pays the player like this is going to be on a double-zero wheel as well. The following two tables show the house edge on single- and double-number bets, according to the win, assuming a double-zero wheel, and based on 'to one' odds. Be careful that on electronic games wins are often given on a 'for one' basis, meaning the original wager is not returned on a win. To convert a 'for one' odds to 'to one' odds, subtract one.
Single-Number Bets
| Win | House Edge |
|---|---|
| 35 to 1 | 5.26% |
| 34 to 1 | 7.89% |
| 33 to 1 | 10.53% |
| 32 to 1 | 13.16% |
| 31 to 1 | 15.79% |
| 30 to 1 | 18.42% |
Double-Number Bets
| Win | House Edge |
|---|---|
| 17 to 1 | 5.26% |
| 16 to 1 | 10.53% |
| 15 to 1 | 15.79% |
Best Roulette in the West
Best in Nevada: The Bellegio, Mandalay Bay, MGM Grand, Mirage, Rio, and Wynn all have European roulette, with a house edge of 1.35%. Usually such wheels are in the high-limit rooms, but the MGM and Mirage also have a European wheel in the main casino at a $25 minimum.
Best in California: It is my understanding that the only single-zero roulette in California is at the Barona casino, with a house edge of 2.70%.
The State Assembly ratified the compact on August 19, 2014.There are also signed agreements with the city of Yreka and the California Department of Transportation.The Rain Rock Casino project was planned in 2 phases. Closest casino to yreka california.
Las Vegas Rules Survey
I am proud to present my Las Vegas roulette survey at my companion site Wizard of Vegas.
Number Placement
To the casual observer, it would appear that the numbers on the wheel are not organized and seem to be distributed randomly. The only obvious patterns are that red and black numbers alternate and that usually two odd numbers alternate with two even numbers. However the distribution of numbers was carefully arranged so that the sum of the numbers for any given section of the wheel would be roughly equal to any other section of equal size. Most numbers are part of a pair, with one number between them. These pairs add to either 37 or 39.
For what it is worth, the sum of all the numbers in roulette is 666.
Wheel Tracking
Some people and books claim that roulette wheels are biased, with a heavy side and a light side. Gravity causes the numbers in the heavy side to hit more often. This, I believe, used to be true when the quality of the equipment was poor. However, modern roulette wheels are much better and very rigorously tested. Only in a casino using a very dated wheel, may you be able to find a biased one by testing many thousands of spins. Based on stories I have heard, your odds of finding such wheels are probably best in Europe.
Betting Systems
Ugh. If you think you can beat roulette with a betting system please read my section debunking betting systems. If you don't believe what I say there, here is what the Encyclopedia Britannica says under the subject of roulette:
Odds Of Ball Landing On Zero Roulette Free
The oldest and most common betting system is the Martingale or 'doubling-up' system,in which bets are doubled progressively. This probably dates back to the invention of the Roulette wheel, but every day of the week some gambler somewhere reinvents it, or some variation of it, and believes he has something new. Over the years hundreds of 'sure-fire' winning systems have been dreamed up, but regardless of what system is used, in the long run it cannot overcome the house's advantage of the 0, or 0 and 00. This house advantage is the only system that consistently wins in the long run.
'No one can possibly win at roulette unless he steals money from the table while the croupier isn't looking.' — Albert Einstein
San Diego Area Roulette
The California Constitution prohibits a ball and wheel alone to determine the outcome in roulette. In the greater San Diego area the casinos have thought of some creative ways to offer roulette anyway. Visit my page onSan Diego County roulette to see how they do it, and who offers the best odds.Ball Steering
Odds Of Ball Landing On Zero Roulette 2
I get asked a lot about whether I believe dealers can influence the spin to a certain area of the wheel. I used to be very skeptical of it. However, after considering the articles How to Win at Roulette — Part I and Part II by Arnold Snyder as well as other evidence, I think it would be easy for a colluding dealer could do a late slow spin to benefit a wheel clocking player. An extremely skillful dealer may even be able to influence the ball to a certain sector of the wheel. So, for now, I'm still straddling the fence on this one (ow!).
Organic Roulette Experiment
In March 2017, I concluded an analysis of an electronic roulette game by Interblock for ball steering away from perceived wheel clockers. For more information please see my page on the Organic Roulette Experiment.
Play for Free
Play roulette for free with this Flash game. I finally found a Flash game for my site which downloads quickly.
Written by: Michael Shackleford