Roulette Odds Event

To calculate the house edge in roulette, we multiply the difference between the true odds against winning and the casino odds by the probability of winning. On a double-zero wheel, the odds against winning with a Straight Up bet are 37 to 1 but the house pays only 35 to 1 which results in a house edge of 5.26%. The betting odds in roulette of hitting a single number with a straight-up bet are 37 to 1, since there are 38 numbers (1 to 36, plus 0 and 00). However, the house only pays out 35 to 1 on winning. The figures are applicable to all even-money roulette bets: black or red; even or odd; low or high (1-18 or 19-36). 1 trial (spin) - probability (odds) to win: 48.6%; odds = 1 in 2.05 - probability (odds) to lose: 51.4%; odds = 1 in 1.95 (the probability to lose is 19/37; adding zero to unfavorable cases). 2 trials (spins). Even Money Betting System. Red/Black, Odd/Even, High/Low — these are even money bets. At the very beginning of the game, the probability that the ball will stop on a red or black section is 18/37, 0.486. The probability that the zero wins is 1/37, 0.027. If Black wins, then the Red winning odds are increased like 19/37 = 0.736.

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:

(1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38), that is:

(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(!)

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?

Roulette Odds Evens Strategy

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 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.

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...

Roulette Odds Of Black

→ Testing & Simulations of Roulette Bets & Strategies

What are the longest streaks of the Even Chances?

The following statistics table shows all Even Chances (Red, Black, High, Low, Even and Odd) series (ie. sequences), including single spins, that appeared in 397271 recorded past spins of a European roulette in a brick and mortar casino. A sequence was regarded as stopped whenever a ZERO was found or, of course, the opposite outcome. When an end-of-day or end-of-file was reached, the ongoing sequence was NOT counted for, as this was regarded as an “unnatural” or “premature” ending.
Total number of spins investigated: 397271
Outcomes
Red: 395457
Black: 395454
Even: 395381
Odd: 395414
Low: 395465
High: 395305
ZERO: 10641

LEGEND (explaining the columns of the following table):
Lth: Length of sequence
NoFR: Total number of sequences of this lenght found, of Red
NoFB: Total number of sequences of this lenght found, of Black
NoFE: Total number of sequences of this lenght found, of Even
NoFO: Total number of sequences of this lenght found, of Odd
NoFL: Total number of sequences of this lenght found, of Low
NoFH: Total number of sequences of this lenght found, of High

You can also study the detailed statistics tables:

Roulette Odds One Number

Roulette Odds On 00

Thanks to the work of the late Mr. Oops.