roulette and standard deviation

We know that standard deviation(sd) is a measure of fluctuation away from the mean.
Good or bad luck go between +/- 3 sd.
When we want to test if a system we use is a winning system we must test samples and count the sd number.
Supose we have data and test +3sd in case we play the 2nd dozen after a previous 1st dozen, and 3rd dozen after the 2nd, you play every spin on the next dozen. It is an hypotetical example.
On a singlezero european wheel we have -2.7%
We have got a 3000 sample. We tested this sample and someone who played 1st dozen after a 2nd dozen had a luck of +3sd
As we found it out after studying the 3000 sample our +3sd we realize that is not the same to pick a dozen at the beginning than scanning which was the best performer. So, this +3sd surely has some added fluctuation(type error 1). My first idea is to substract from 1 to 1.5 sd from the 3 to eliminate regular fluctuation. So, our actual sd number might be 1.5 to 2.
We take our 3000 sample and divide it by 1000 to count their sd in each of the smaller samples. We had +1.8 +1.5 and +2.1sd on each of the 3
The whole data(3000) +3sd on a 12 number play. The same data cut in 3 yielded lower sd on each as expected.

We make a new test , same dozen after dizen to play. We are picking our play beforehand.

We collect the first 1000 trials.

Any player who has played our choice reached +2 sd. The chance to be random seems to be 1/20(95%)

What does it mean?
What is the chance of this last test to be random?
What is the difference between +2sd in 1000 and 2sd in 500 or 5000 trials?
What if next 1000-spin- test yields +2sd?

I apprecciate any answer

Ybot

Quote: ybot

We know that standard deviation(sd) is a measure of fluctuation away from the mean.
Good or bad luck go between +/- 3 sd.

This assumes a normal distribution. You need to play for a while before your results start to look normal. For some games you must play for a very, very, very long time.

I am actually starting to believe that standard deviation and variance are very misleading measures for certain games.

Also, even with a normal distribution, 1% of results are outside +/- 3 sd. 1% is not really that few. In a large casino, several people will be outside this range at any one time.

Quote: ybot

What is the chance of this last test to be random?

You do not have enough information to answer this question. The likelihood of an event is not, on its own, any indication of whether the result was fairly/randomly generated.

For example, the chances of winning a lottery might be 1 in 100 million. Suppose Bob X won the lottery last week. His chances of winning were only 1 in 100 million. So, what are the chances that the lottery was fixed? You can't answer that question; you don't have enough information.

Quote: AxiomOfChoice

This assumes a normal distribution. You need to play for a while before your results start to look normal. For some games you must play for a very, very, very long time.

I am actually starting to believe that standard deviation and variance are very misleading measures for certain games.

Also, even with a normal distribution, 1% of results are outside +/- 3 sd. 1% is not really that few. In a large casino, several people will be outside this range at any one time.

Some players might be +/- 3sd but the chance is the remains of 99.73% and half of these to each side(+/-)
Hard to win or lose to rate beyond +/- 3sd.

Quote: AxiomOfChoice

You do not have enough information to answer this question. The likelihood of an event is not, on its own, any indication of whether the result was fairly/randomly generated.

For example, the chances of winning a lottery might be 1 in 100 million. Suppose Bob X won the lottery last week. His chances of winning were only 1 in 100 million. So, what are the chances that the lottery was fixed? You can't answer that question; you don't have enough information.

Basically, when you pick a way to play and it gets +2sd it can be random 1/20 on these same sample size. With 3sd the chance of random is 3/1000.

Our goal is to determine a kind of signature to a dozen after a dozen. We had our prior +3sd on 3000 and 2sd on the next 1000.
This gives us some % of confidence
Supose we take a 3rd 1000-sample, and get +2sd. Does it add more confidence?

When do we be 99.99% confident that playing one dozens after the other became a winning game out of random?

Quote: ybot

Basically, when you pick a way to play and it gets +2sd it can be random 1/20 on these same sample size. With 3sd the chance of random is 3/1000.

No, that is backwards.

Suppose I sit down at a video poker machine, and on my first hand I get a royal flush (probability = 1 / 40,000). Does that mean that I can say that there is a 39,999 / 40,000 chance that the machine was rigged in my favor? Of course not.

So, how does it work to see if what we believe is possibly true or not and the % of error and randomness?

Quote: ybot

So, how does it work to see if what we believe is possibly true or not and the % of error and randomness?

When you observe an event, there are many different explanations of it. You need to compare the probabilities of those events. This came up on another thread.

For example, suppose you get randomly tested for a disease. The disease has no symptoms, so you have no a priori reason to believe that you are any more likely than a random person to have the disease.

Now, suppose that the test has a false positive rate of 1 / 100,000. Suppose you test positive. Does that mean that you have a 99,999/100,000 chance of having the disease? NO! You need to compare the the probability of a false positive to the a priori probability of having he disease. Suppose that only 1 in a million people have the disease. So that means that, in a sample of 1,000,000 people, there are 10 false positives and 1 person actually has the disease (assume that the false negative rate is 0, for simplicity). That means that you have a 1 / 11 chance of having the disease.

The point here is that it is not enough to know that probability of a false positive on the test -- that is not enough information to determine whether the test was accurate in your case! You also need to know the probability of the alternate explanations.

So, in order to determine the probability that the results of your tests are anything other than random luck, you need to compare it with the probability that they are somewhere else. Since we all know that no betting system exists which beats roulette, the probability that your wins were the result of your betting system is 0. That is easily proven, mathematically (it makes no sense to be using mathematics at all if you are going to ignore things that are easily proven). So, what are other possibilities? There is some small chance at a biased wheel, but certainly less than 1/20. Maybe 1 / 100,000 (I just made that number up, but it seems reasonable). So, I'd estimate that there is a 4999/5000 chance that your results are due to randomness.

I caught your explanations.

In case of a biased wheel, we make other 1000 spin test and get another +2d.
Is it easy to acomplish +3sd, then +2sd on the next 1000 and +2sd on a 3rd test?

Doesnt it mean something out of random?

No it doesn't.

Counting your individual results in terms of sds is a little strange. It makes more sense to combine all your data together. I actually wonder how you are calculating this.

The normal win rate for betting a dozen on a single-zero wheel is 12/37. What win rate do you claim to be able to achieve?

13/37 would be enough to beat the game at a nice 5.4% edge. If you got 1160 wins in 3330 bets (note that this is slightly less than 13/37), I'd say that it is worth looking into.

In 3000 trials, +3sd on 12 numbers means that they hit 1050/3000

In 1000 trials, +2sd on 12 numbers means that these 12 hit 354 times.

At 3000, +3sd means 5% edge
At 1000, +2sd means +6.20%edge

I guess my calculus are correct

So why are you wasting time posting? How come you are not at the casino right now? Use full Kelly betting and you will own the casino in a couple of months.

Let us know how that works out!

I am asking about the way to understand probability and not to fall prey of random fluctuations that in roulette, the multinomial distribution takes more data than we(me) imagine.

I thank you for your time.

To apply Kelly I need an actual edge, we still do not know if this samples are facing regular fluctuation or there are other variables that affect its fairness.

I lack of technical skills to understand it clearly

Quote: ybot

I am asking about the way to understand probability and not to fall prey of random fluctuations that in roulette, the multinomial distribution takes more data than we(me) imagine.

I thank you for your time.

To apply Kelly I need an actual edge, we still do not know if this samples are facing regular fluctuation or there are other variables that affect its fairness.

I lack of technical skills to understand it clearly

Multinomial? It's binomial. You either win or you lose.

A few thousand spins at the same bet is actually quite a lot of data (it is not very much if you are moving your bets around)

Ok, binomial.
How many trials does it take to be confident of a random fluctuation or an unfair roulette?

We have already 3000+1000+1000

Quote: ybot

Ok, binomial.
How many trials does it take to be confident of a random fluctuation or an unfair roulette?

We have already 3000+1000+1000

5000 trials is a lot of data, if you did your experiment correctly.

If you gathered the data, looked through it, and found a winning system, then your data is worthless. Start over.

If you decided beforehand what your system would be, and then did 5000 trials, it's a lot of data.

How many wins out of 5000? How did you collect your data? Did someone stand at the roulette table with a pencil and paper? (or, in front of a computer if it's online?)