Hi Kav,

"random" is a difficult word to define and is the source of many pointless arguments on the forums. For me (I and I believe it's the only fruitful definition) "random" just means unknown. What's random for me may not be random for you, so in a way it's subjective.

The runs test just tests to see if a sample is Normally distributed with regard to the number of runs (does it follow the bell curve). The random aspect concerns the independence or regularity of the outcomes in the sample. In fact, it doesn't even test for non-regularity, because the number of runs could be within the "belly" of the bell curve and yet the outcomes could still be regular.

The runs test is known as a test for "randomness" in the literature (

https://en.wikipedia.org/wiki/Wald%E2%80%93Wolfowitz_runs_test) but to be precise it's really a test which compares the number of runs in a sample with what they "should" be according to the bell curve.

I do emphasise that if a sample "fails" the test (that is, the hypothesis of non-randomness is not disproved at some level) then this isn't necessarily an indication of randomness - it could just just be, and in fact is much more likely to be in Roulette, an unusual event which occurs once every 20 or 100 samples, or whatever.

If we believe that the result of each spin is totally independent, then every possible spin sequence is equally probable.

This means that this sequence: 5,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,......

is equally probable with this sequence: 36,30,1,1,4,9,17,17,4,30,30,36,18,22,6,7.....

Then on what grounds is it possible to evaluate a spin sequence and give a verdict on its randomness?

Every possible sequence of a given length has the same probability, but not in every respect. With respect to the order of outcomes, they are identical because the probabilities are both 1/37 x 1/37 x 1/37 ...

But in other respects they don't have the same probability. In the first sequence the number of runs is highly unlikely. Same for even money sequences. RRRRR has the same probability as RR B R B as a sequence, i.e. 1/2 x 1/2 x 1/2 x 1/2 x 1/2, but not in terms of the number of reds and blacks. The first sequence is relatively rare because it consists only of R.

So you have to look at the way the outcomes are distributed, not just the "raw" probabilities.

In your post, what you did is that you looked in past spins (400 zeros) to evaluate the next spins. In **principle** this is "gambler's fallacy".

If one says that a wheel that consistently shows black numbers is not random, then one basically adopts a gambler's fallacy approach.

Merely looking at past spins isn't the gambler's fallacy. A biased wheel player also does this. Is he committing the gambler's fallacy?

If someone were to say "there have been 15 reds in a row and because outcomes are equally likely it means that black must come up soon", that *would* be the gambler's fallacy. Without an explicit argument which involves a contradiction you can't say that just using past spins to predict future spins is the GF.