standard deviation question

We have got european roulette wheel data , 2000 trials

We check and see that 12 numbers of the 37 in case they were played in the last 2000 trials performed with +4 standard deviations(732/2000 for 12 numbers)

We know there is positive fluctuation in these 4 standard deviation

But, how much? 1 , 2 standard deviations?

If we substract 2 full standard deviations of the total hit of the 12 numbers at the 2000 they still are ahead

We picked these 12 hot numbers after data were taken

Could we infer these 12 numbers have any advantage and deserve being played for the next 2000 trials?

Quote: ybot

hot numbers ?

Your post really boils down to these two words. :/

There must some bounderies to consider thenm hot numbers or biased, and the least advantage (if any)you can get from them

You can't really infer anything like that. The wheel could be biased, but it could also not be. If it is biased, you still don't know the precise nature of the bias (especially if your 12 hot numbers are not adjacent). You also don't know whether the casino will balance the wheel in the time you'd want to make your next 2000 bets.

In other words, I wouldn't waste my time if I were you.

Quote: MathExtremist

You can't really infer anything like that. The wheel could be biased, but it could also not be. If it is biased, you still don't know the precise nature of the bias (especially if your 12 hot numbers are not adjacent). You also don't know whether the casino will balance the wheel in the time you'd want to make your next 2000 bets.

In other words, I wouldn't waste my time if I were you.

How does it change in case the 12 numbers where adjacent?

Casino`s leveling and balancing is another realm

Supose we collected the first 2000 in 2 days and we have got the rest of the week to play(or not) before technicians mend a possible problem

We try to use math tool to explain past events and the likelihood they repeat in the future, and how close to previous results next one would be.

Mathextremist, you as a math guy know the fact saves times and money how knowlegde saves time and money

warm regards
ybot

For what it's worth (if anything)... this is from my research notes in to biased wheels some years back:

- TO FIND BIAS NUMBERS -
Number of spins to record: Minimum 7600 (so should be about 200 occurrences of each number)

Size of the bias: 6-10%


- TO TEST BIAS NUMBERS -
Only need about 1/3 to 1/5 of the spins to confirm biased numbers (more live gathered data).


...This came from much more experienced minds than ours on the topic.

Quote: Romes

For what it's worth (if anything)... this is from my research notes in to biased wheels some years back:

- TO FIND BIAS NUMBERS -
Number of spins to record: Minimum 7600 (so should be about 200 occurrences of each number)

Size of the bias: 6-10%


- TO TEST BIAS NUMBERS -
Only need about 1/3 to 1/5 of the spins to confirm biased numbers (more live gathered data).


...This came from much more experienced minds than ours on the topic.

Can you hit me up with a link to go read how to do that? I haven't done this kind of math in more than 30 years and I don't even remember where to start reading ( hence having a hard time choosing the search parameters on Google)

Quote: Wonko33

Can you hit me up with a link to go read how to do that? I haven't done this kind of math in more than 30 years and I don't even remember where to start reading ( hence having a hard time choosing the search parameters on Google)

Sorry this was out of my Advantage Play -> Roulette folder with a document that has over time compiled notes on the subject. I gathered bits and pieces from other forums, google, GWAE radio show, and old threads in this forum. The best advice I could give you is googling "How to identify roulette wheel bias".

My notes should be fairly self explanatory though, not much math involved... Run 7600 spins on the supposed biased roulette wheel. Log the numbers, and see if any are 6-10% outside of what they should be. If each number has a 1/38 chance (given 0 and 00) then after 7600 spins each number should come up 200 times. If you have numbers coming up an additional 6-10% (an extra 12-20 times), then you possibly have a biased wheel. Next, run a smaller test to confirm carefully following those numbers.

The standard deviation number tells about how far from mean certain results come.

4 standard deviations seen after data were taken involves many fluctuation.

What if we see 6sd instead of 4 sd in this example?

Fluctuation might be up to 3sd, 6-3= +/-3sd is still a very unlikely event so face by chance

Anything outside of 3SD is abnormal.... for what it's worth. If you're seeing 5SD and 6SD, you have a bias (so long as you have a decent number of data points, aka 5000-10,000 spins).

Quote: Romes

Anything outside of 3SD is abnormal.... for what it's worth. If you're seeing 5SD and 6SD, you have a bias (so long as you have a decent number of data points, aka 5000-10,000 spins).

The question is to divide past data analized from data taken after the 12 numbers have been already chosen

In 5000 spins, findind a group or section of 12 performing +5sd does not mean that these 12 number would hit similar the next 5000

There is fluctuations working

*5sd on 12 numbers at 5000 might mean a true 2,5sd or less

We have not say these number are neighbors or not yet

You could tell me that the proper way to analize is choosing number beforehand.

The subject here is to know how many standard deviations should be substructed to be the closest to true frequencies.

It surely takes a math guy

warm regards

Quote: ybot

We have got european roulette wheel data , 2000 trials <snip>

sounds to me you need to read the paper by S.N. Ethier
"Testing for Favorable Numbers on a Roulette Wheel"
he wrote it way back in 1982 (he must have been, what, 9 years young?)
Source: Journal of the American Statistical Association, Vol. 77, No. 379 (Sep., 1982), pp. 660-665
Published by: American Statistical Association
Stable URL: http://www.jstor.org/stable/2287733 .

and also has more info in his Doctrine of Chances book
page 469
13.2 Biased Wheels


it looks real easy to understand the math, at least to me, and that speaks volumes
and looks complete too, meaning, how to find the fav # and how to bet it
i due not think S.N. Ethier is a gambler, but he knows a lot about the subject and the math
born lucky

that way only you will know and no one else (well, except me)

have fun winning!
Mully

Mully, Ethier's paper is a specific answer to Allan Wilson's challenge in his famous 1965 book

Quote: ybot

Mully, Ethier's paper is a specific answer to Allan Wilson's challenge in his famous 1965 book

i found that paper hard to read and understand, nothing new about that for me.

and his Doctrine of Chance book (out in 2010) is much easier to read, imo and it makes perfect sense to me than the paper
I think he has a different target audience in mind with the book (a college book)

Quote: mustangsally

i found that paper hard to read and understand, nothing new about that for me.

and his Doctrine of Chance book (out in 2010) is much easier to read, imo and it makes perfect sense to me than the paper
I think he has a different target audience in mind with the book (a college book)

Ethier´s paper was for graduates, Klotz´s work wasn´t