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 probability of such event in French Roulette is (18/37) 32 = 0.96886885 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. And the odds are 24,230,084,485:1. Thus this is even less likely than. For a $5 bet on the color red in roulette, for example, the expectation is -$0.263. On the average the player will lose just over a quarter for each $5 bet on red. When the wager expectation is viewed from the casino's perspective (i.e., the negative of the player's expectation) and expressed as a percentage, you have the house advantage. In Experiment 1 the probability of each outcome is always the same. The probability of landing on each color of the spinner is always one fourth. In Experiment 2, the probability of rolling each number on the die is always one sixth. In both of these experiments, the outcomes are equally likely to occur. Let's look at an experiment in which the.
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:
(1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38), that is:
The odds of winning can also be expressed in the same way. On a standard American roulette wheel, you have 37 ways to lose a single number bet and only one way to win. This means the odds of winning are 37 to 1. Since the odds of winning are lower than the payoff for the bet, the casino makes a profit in the long run.
(1/38)6 = 0.000000000332122593261671.
Roulette Color Probability Games
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(!)
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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 odds of winning can also be expressed in the same way. On a standard American roulette wheel, you have 37 ways to lose a single number bet and only one way to win. This means the odds of winning are 37 to 1. Since the odds of winning are lower than the payoff for the bet, the casino makes a profit in the long run.
(1/38)6 = 0.000000000332122593261671.
Roulette Color Probability Games
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(!)
Online casino players love free spins and in the US we get them in the form of free money casino bonuses, also known as no-deposit money. Legal and legit online casinos such as Golden Nugget and BetMGM offer free money for new players, so you should take advantage of the new player offers. Over and above no deposit required bonuses, online casinos also welcome new customers with free spins bonuses. This type of casino bonus can be offered as a no deposit option, or 'no deposit free spins', or as part of a welcome bonus. When you claim a free spins offer, you will find that they are typically tied to a specified game. Free spins no deposit bonuses are one of the most popular means of attracting new online slot players to a casino because they provide players with the opportunity to try out the casino, especially the slots, and possibly win real money payouts that they can use to enhance their bankroll. No deposit bonuses are a promotion given by online casinos to attract new players. These bonuses usually take the form of free credit, which can be used to bet on various games, or the form of several prepaid spins on certain slots. No-deposit bonuses are usually given as a gift to attract new players. Online casino no deposit bonus free spins.
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.
Roulette Color Probability Chart
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
