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Same even money bet result in a row probability. How unlikely is it to see the same colour 2 or more times in a row? What's the probability of the results of 5 spins of the roulette wheel being red? The following chart highlights the probabilities of the same colour appearing over a certain number of spins of the roulette wheel. The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the erroneous belief that if a particular event occurs more frequently than normal during the past it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. On any given spin on a European roulette wheel, the chance that the current spin is the first of nine reds in a row is (18/37)^9 = 0.001526, which is approximately 1 in 655. This merely means that statistically speaking, over a very large number of spins, you should expect a string of nine reds in a row per 655 spins.

Here it is... from your 'parent' site....an answer given to a question....
What would be the odds of having a red number turn up 18 times in a row on Roulette. - Doug Jeffrey from Eugene, USA
(18/38)18 =~ 1 in 693745. Nov. 11, 2001
how can you apply a forward prediction like that???... but then not be theoretically allowed to intercept at the 12 in a row point and bet against a 1 in 693745 chance?? Please explain

If you 'jump in' after 12 red spins in a row, the probability of there being a streak of 18 reds (where the last 12 spins are the first 12 of the streak) is much higher, calculated as follows:
(1/1)^12 * (18/38)^6 = 0.011296 = 1 in 88.525125

Roulette Odds Of 5 Reds In A Row 5

The original question was referring to 18 future spins. If 12 have already occurred, then it is only a question of 6 future spins.
The first 12 were red, so the probability of those spins being red is 100%, not the 18/38 per spin that it was before their outcomes became known. The probability of the 6 unknown future spins being red is still 18/38 per spin.

and...if you look at this situation after it has happened... 18 spins..18 reds...are you then allowed to look back and say...what happened there was a one in half million...or whatever that figure is...of happening?????

You could look back at the last 18 reds and say 'That particular sequence had a 1 in 693,745 chance of occurring' ... but you can also say the exact same thing about any 18-spin sequence where no numbers were green.
Just keep in mind that it has no bearing whatsoever on what will happen on future spins. The past does not matter.

Roulette Odds Of 5 Reds In A Row 3

JB...thanks for your help on this...I'm keen on a reply on the last point....what yu said in your last reply....unfortunately has me believing....that you can legitimately expect to win....if you jump in at 12 reds...and bet the next 6 blacks....based on a theory that 18 reds in a row is a one in approx half million chance!........and on those 6 bets you stake it small to win small....over and over......in 20 000 spins...you'll risk $50.....to win $30.......might you win significantly more often than you lose?

Regardless of when you 'jump in', your odds for the next spin are always the same:
red: 18/38
black: 18/38
zero: 2/38
In the long run, you will always lose 5.26% of whatever you bet, regardless of when you bet. (Assuming double-zero roulette)

I see that....Let me ask you this question JB....does it confuse you at all that you can look back on a sequence and accurately say those 18 spins in a row being even was a 1 in half million chance.......but .......that said......you cannot jump in at 12 evens in row and bet against that sequence of 18 happening.....does that confuse you just a little...or is it clear to you....it might be a state of mind thing that I just cannot grasp....

It doesn't confuse me, because the past does not affect the future when you're talking about random, independent events such as spins of a roulette wheel.

Roulette Odds Of 5 Reds In A Row 4

Let's attack this from another direction.
Assume that somewhere there is a casino that has a jackpot bet for 18 Red/Black/Odd/Even/High/Low in a row.
Do you think that the casino would let you place your bet after 12 in a row had already hit?

Roulette Odds Of 5 Reds In A Row Seating

Remember: For every gambler that looked at the display at the roulette table and said 'Look honey. Red came out 12 times in a row! We should bet on black,' there was another sucker that said 'Look honey. Red came out 11 times in a row! We should bet on black.'