Do RNGs produce random outcomes?

[kimss]

Well I for sure would like to have some input on this matter, since I lack the understanding of chaos theory, law of large numbers and such. I am however plenty skilled in software deloping, creating stats, reverse enginering and all this - but math is not my favourite subject. That doesn't mean I don't understand it, however it would be much easier for the people understanding this helping me out. I am not afraid of new words, I can google,

So the topic - do RNGs produce random numbers. I take this as a true statement, or it would have no meaning. The question becomes, what are random numbers? If you were to spot a pattern, (could mean certain numbers appear more often or less) the usual tactic would be to throw in the chaos argument, or law of large numbers. I've seen it used many times.

So let me throw a bone here, a question. Say we have 3 numbers, and the RNG would create a series of numbers. Say we generate 9 numbers, the optimal outcome would be:
1. 3 hits
2. 3 hits
3. 3 hits

If we were to get this result:
1. 1 hit
2. 4 hits
3. 4 hits

Then the argument would be, the sample size is far to small.

My question, how big sample size would we need to the last example to not be random?

[ThodorisK]

I do not understand your example. Make it more clear if you want.

[aka23]

My question, how big sample size would we need to the last example to not be random?

It depends with how much certainty we say "not random." If less than 1 in a million chance is good enough to be "not random", then we only need ~100 samples in a 1/4/4 distribution. If less than 1 in a billion chance is required, then we need ~150 samples in that distribution.

[kimss]

Let's say the task was to determine if the produced series of numbers were random, or weighted. I know you like cards, but I'm a slot's person. However talking RNG it is practically the same since we are talking shuffling the deck, or producing reel positions.

Going back to my example, we let the RNG produce 9 random numbers from 1-3. The perfect balance would be 3/9=33%, we should expect to see each number being represented 33.3% of the time the RNG comes with a number.

If the results were to look weighted, meaning that one number appears more often than the others (or less) - how many numbers would we need the RNG to produce for this not being random. Or let me rephrase, how many numbers must the RNG produce before we can state as a fact that certain numbers are weighted (which means that it is not RNG). How big must the samle size be to be sure.

Am I still unclear?

[kimss]

It depends with how much certainty we say "not random." If less than 1 in a million chance is good enough to be "not random", then we only need ~100 samples in that distribution. If less than 1 in a billion chance is required, then we need ~150 samples in that distribution.

Great! A more concrete question would then be, take a little give a little...

Backinfo:
If we have 40 possible numbers, each number should in theory then get a 100% / 40 numbers = 2,5% chance of hitting. So if we were to pull 1000 numbers from the RNG we should "excpect" a 2.5% hit on each number. So far so good.

Question:
How much could one number be below or over the 2.5%, and how many numbers do we need to produce, for this not to be random. Let me rephrase again. Say the number 1 was off, how much must it be off %, and how many numbers would we have to produce for it not be random? We are talking 1 number off here - the others leveling around 2.5%

I hope my math quiz is understandable. I don't need 100% sure numbers, but a feel of what we are talking about.

[lojo]

Kimss, I believe the weighting occurs in the program, not the RNG. Two different animals.

[aka23]

Great! A more concrete question would then be, take a little give a little...

Backinfo:
If we have 40 possible numbers, each number should in theory then get a 100% / 40 numbers = 2,5% chance of hitting. So if we were to pull 1000 numbers from the RNG we should "excpect" a 2.5% hit on each number. So far so good.

Question:
How much could one number be below or over the 2.5%, and how many numbers do we need to produce, for this not to be random. Let me rephrase again. Say the number 1 was off, how much must it be off %, and how many numbers would we have to produce for it not be random? We are talking 1 number off here - the others leveling around 2.5%

I hope my math quiz is understandable. I don't need 100% sure numbers, but a feel of what we are talking about.

It sounds like we are talking about 5 Reel Drive reel positions. For the number of hits on a particular reel position to be 5 SDs beyond the mean, the following must be true:

ABS(x - np) > 5*SQRT(np(1-p))
x = actual number of events
n = number of samples
p = chance of event
np = expected number of events
SQRT(np(1-p)) = standard deviation

Or another way of looking at it, ABS(x - np) / SQRT(np(1-p)), correspponds to the number of SDs beyond the mean the result is.

The number of samples required depends on how far the distribution is from expected. The closer the distribution is to expected, the more samples you need.

[kimss]

Man I wish I understood those formulas, however I should look more into that since it's obviously the correct way of studying the numbers. 5 Reel Drive would be a nice example, but not in this case, however I have more tricks up my sleeves!

The variations on 5 Reel Drive is pretty dramatic looking at the %, I would think everyone agrees here that they are weighted. However a more subtle change would be harder to detect, unless you are looking in the right places. This is why such a formula is of most importance and I thank you for it. I will put on my thinking cap on now and get back a little later,

Thanks again aka23!

[happygobrokey]

I do not understand your example. Make it more clear if you want.

examples be damned. you said if someone starts the thread about rng randomness, that you'd disseminate your findings with respect to this.

so disregard the example scenario.

the question: do rng's produce random results?

your contention: they do not.

your proof: i expect it to be forthcoming.

[ThodorisK]

I was writing it all night. It will be posted here.