Roulette 'streaks'

Is it just me or do 'streaks' happen with a consistency that I wouldnt expect on something that has such a low probability?

Example:
The probability of a streak of 6 or more in european roulette is 0.013 which is approx 1.3 times per hundred spins.
Being that 1.3% is quite low, I would have thought that the variance associated with it would be quite high. I have rarely played 100 spins without seeing a streak of this size.
What is the reason for it occuring with such consistancy despite the low probability?

Because sample is not individually based. You're measuring a streak of 6 or more 95 times within 100 hands. so 1.3%*95 might as well you're seeing them all the time.

Yes i know the correct calculation is 1-(1-1.3%)^95 but the simplified version was enough to make the point.

Quote: Stats

Example:
The probability of a streak of 6 or more in european roulette is 0.013 which is approx 1.3 times per hundred spins.

This is not correct.
here is how I look at it.

You can not say that the probability of a dependent event of 6 in a row in 6 spins (p=18/37 so run of 6 = p^6) = the average over 100 spins or 1/p
p^6 is just for the very next 6 spins

1 in 75.43542 = the average number of attempts and each attempt is not one spin in length.
the average length of each attempt is 1+p+p^2+p^3+p^4+p^5 = 1.921553381
multiply those together and get 144.9532 spins for the average.

The average number of runs of at least length 6 in 100 spins = 0.653145036
that comes directly from it's distribution

Quote: Stats

Being that 1.3% is quite low, I would have thought that the variance associated with it would be quite high. I have rarely played 100 spins without seeing a streak of this size.
What is the reason for it occuring with such consistancy despite the low probability?

you are only looking at the next 6 spins.
That is why it is quite low.
The probability of at least one such run in 100 spins = 0.494937160377822
or about a coin flip

removed
silly


Sally

Quote: mustangsally

you are only looking at the next 6 spins.
That is why it is quite low.
The probability of at least one such run in 100 spins = 0.494937160377822
or about a coin flip
Sally

I see.
Even at 0.49 it seems to happen with alot more consistancy than black/red.
I would be very suprised if it went 500 spins without a streak of 6 or more, though wouldnt think twice if i viewed 5 blacks in a row if you know what I mean.

That .49 is for at least one such run
there could be 2 or more in 100 spins too
just random events unfolding

Event	Run Probability	1 in
0 runs of length 6 or more	0.50506284	1.98
at least 1 run of length 6 or more	0.494937160377822	2.02
at least 2 runs of length 6 or more	0.133755019241570	7.48
at least 3 runs of length 6 or more	0.021961798732982	45.53
at least 4 runs of length 6 or more	0.002321310968390	430.79

The variance is very high too.
the standard deviation is almost the average number of spins it takes to see 6 in a row
140.2434348
144.9532
Wild!

In 500 spins there is about a 1 in 34 chance of NO such run or greater
0 runs of length 6 or more = 0.029153937
very possible, not out of this world

Streaks are just streaky
Sally says