Random Magic Paths - is it truly random?

[atul]

Ivan Pedroso said:
Hmmmmmm, why shouldn't it approach 3/8 ?!?

Let us assume that the distribution behind the scenes is uniform. Then the observed frequencies will approach 1/8.

What you're missing here, assuming I've managed to follow the debate, is that they're talking about 3 most common random result. As there's selection based on how the randoms have turned out, the distribution is altered.

Gah, talking hard, let me give an example.

Two random numbers, x1 and x2, both with uniform distribution from zero to one. Each have an expected value of 0.5. But if you're asking what's the expected value of the _greater_ of two, that's 2/3!

Same thing told in the universal language of love (mathematics):
x1,x2 ~ U(0,1)
E(x1)=E(x2)=1/2
E(max(x1,x2))=2/3

My language or notation may be a bit off, but I hope the general idea is clear.

Of course, same applies to discrete case with magic randoms and so on, but is a bit harder to calculate.