Mersenne Twister random number generator

I downloaded file from this page https://wizardofodds.com/roulette# . It contains 1 million roulette spins from the Mersenne Twister random number generator.

I started testing it against a particular area of the wheel. There was a section (between the 3700th and 3800th spin) where one section of the wheel was not hit for 37 spins. It is the section near the number 27.

27,22,36,6,6,16,00,5,32,24,22,30,23,00,13,3,33,22,4,4,33,3,7,35,00,9,36,4,9,4,14,24,7,28,11,28,15,33,27,27,19,5,6,31,00,23,17,19,30,32,11,22,19,27

This section starts with 27 then doesn't hit anything in that quarter of the wheel for 37 spins, then comes back to 27 two times, then hits 19 three times, and one 31 and then another 27.

During the period where one quarter of the wheel is not hit:

3 x 22
2 x 36
2 x 6
3 x 00
2 x 24
2 x 3
3 x 33
4 x 4
2 x 7
2 x 9
2 x 28

and the rest of the numbers were only hit once (unless I misses some)

I asked a question when I first joined this community about how likely is it that in a 1 in 4 situation that one of the four possibilities would not happen in 16 turns. The answers i received indicated it is not impossible but it shouldn't happen often. I understand that the roulette wheel is not a 1 in 4 game because of the 0 and 00 but it's close and the European wheel is even closer.

With that in mind, should I question the randomness of the RNG or continue my use of these numbers and see if this 37 spin avoidance happens again?

What quarter of the wheel are you talking about? 00 is next to 27.

The chances of something NOT happening is simply the chances of something the opposite happening, for example if you roll a die six times, the chances of NOT getting a six in at least one of those rolls is the opposite of getting a 1-5 six times in a row. So the chances of NOT rolling a six, six times in a row are (5/6)*(5/6)*(5/6)*(5/6)*(5/6)*(5/6) = .33488 or slightly better than one in three.

So taking that logic to your problem, we have a 3/4 chance per spin of the roulette wheel of not hitting that specific quarter. So if you multiply that out (3/4)^37 then the odds of and consecutive group of 37 spins not landing in a specific quarter of the wheel is 2.38373e-5 or if you divide into 1, 1/41950.

Given that there are one million randomly generated numbers in the sequence, I would expect that you should find quite a few more occurrences of 37 consecutive quarter wheel gaps.

Caveat..This is math is dredged up from my high school lessons which occurred over a millennium ago. I could be completely wrong.

Quote: scotty81

What quarter of the wheel are you talking about? 00 is next to 27.

8,10,12,18.19,25,27,29,31

Quote: s2dbaker

So taking that logic to your problem, we have a 3/4 chance per spin of the roulette wheel of not hitting that specific quarter. So if you multiply that out (3/4)^37 then the odds of and consecutive group of 37 spins not landing in a specific quarter of the wheel is 2.38373e-5 or if you divide into 1, 1/41950.

thanks. looks like the same equation the Wizard gave me.

Now I must figure out if I still made money after taking that one loss in the 12,000 spins I tested my strategy against. Then I will continue with the million spins to see what else happens.

I don't think it's quite as simple as .75 ^ 37. This is because the 1/4 wheel was not predicted in advanced; it was curve fit from the data.

Wizzard: What would be the odds of a curve fit 1/4 wheel not showing in 37 spins, assuming you only knew what 1/4 wheel it was after you looked at the data?

I'm certainly not the Wizard, but my guess as to the answer is that it is the same as the odds for a specific, pre-selected, 1/4 wheel not showing for 36 spins. My thinking is that the first of 37 spins would identify which quarter of the wheel is tested for the next 36 spins.

Warning: that's from a non-math-major.

Edit: in the above thinking, it is assumed that the four quarters are always pre-defined, but you haven't necessarily initially selected one of the four. If the question is about the probability of finding 9 adjacent numbers not showing up, without pre-defining the quarters of the wheel, that's a different question.

Trust the RNG. Mersenne Twister is nifty.

There are patterns in Roulette spins, but only when looking at them in the past.

There are no patterns in Roulette spins that can be predicted into the future.

Quote: chifool55

8,10,12,18.19,25,27,29,31

Those 9 numbers are not one quarter of the wheel. it is 9/37 of the wheel or .243243. a different and smaller number than 1/4 or .250000. Now I have to redo my math formulas.

Quote: 7winner

Those 9 numbers are not one quarter of the wheel. it is 9/37 of the wheel or .243243. a different and smaller number than 1/4 or .250000. Now I have to redo my math formulas.

In my other reply:

I understand that the roulette wheel is not a 1 in 4 game because of the 0 and 00 but it's close and the European wheel is even closer.

Quote: dwheatley

Trust the RNG. Mersenne Twister is nifty.

Trust no

Continue using yes

Thanks for your vote of confidence in the MT RNG

I read the wikipedia page on it. Didn't understand a thing. It must be good.

Quote: Doc

If the question is about the probability of finding 9 adjacent numbers not showing up, without pre-defining the quarters of the wheel, that's a different question.

That's really the question. There are no defined, specific quarter wheels known in advance. In reality, there are 38 possible 9 number adjacent sections that could qualify "after the fact". The math is not simple. The only way I know of to reliably compute the answer to this question is to run a series of simulations, and then count how many actually occur.

The fact that you observed perceived "non-randomness" is not sufficient to doubt the generator. As soon as you identified the range in question, between 3700 and 3800, you took a sample of your larger sample. But this sub- sample is not a random sample of the new population i.e. the original large sample, because you selected it not at random but because it appeared to you to be questionable. Therefore the sub-sample is a judgement sample and statistical tests based on randomness do not apply. You selected this particular sub-sample because it was easy to see--there are probabily many sub-samples like the one you saw, that are not as apparent.

To test the generator you must take a random sample. You could generate a random sample by using the generator to generate n pseudo-random numbers between 1 and 1 million and select those sample items from the array of 1 million sample points you have. This is your sample, size n. Then apply a chi-square or some other test to that sample. Or you could apply the chi-square test directly to the original 1 million observations.

Quote: matilda

The fact that you observed perceived "non-randomness" ...pseudo-random... chi-square

way over my head but thanks

pseudorandom - being or involving entities (as numbers) that are selected by a definite computational process but that satisfy one or more standard tests for statistical randomness

Quote: chifool55

There was a section (between the 3700th and 3800th spin) where one section of the wheel was not hit for 37 spins.

Beware of data clumps. You could have a million people tested to see if, say, they get in a car accident when Jupiter alines with Mars. There would probably be a "clump" within that million *somewhere* suggesting there is a connection.

This is a well known thing to avoid.

Quote: matilda

But this sub- sample is not a random sample of the new population i.e. the original large sample, because you selected it not at random but because it appeared to you to be questionable. Therefore the sub-sample is a judgement sample and statistical tests based on randomness do not apply.

exactly

Quote: odiousgambit

...car accident when Jupiter alines with Mars...

...thing to avoid

I thought I was the only one that got into an accident that day :-) . By the way, did they decide to make Jupiter a planet again?

Periods like the 37 spin one will hurt when I challenge Michael Bluejay. I hope they don't come often and don't get worse. I can only tolerate about 29 spins without it hitting a quarter (or should I say 9/37 or 9/38) of the wheels. In casino play, because I am not there for 1 billion spins, it is less likely that this type of run will happen while I am there. But going up against the RNG for 1 billion is different.

Thanks to all of you for sharing your better understanding of probability.

Quote: chifool55

way over my head but thanks

pseudorandom - being or involving entities (as numbers) that are selected by a definite computational process but that satisfy one or more standard tests for statistical randomness

For clarification: All of the "random" numbers in this thread are in fact pseudo-random numbers. That is what a generator gives you.