To think of it another way, consider a perfect, uniform RNG which generates integers in the range [0, 2]. You draw three numbers from this range. The only possible combinations are:

Code:

0 0 0
0 0 1
0 0 2
0 1 0
0 1 1
0 1 2 *
0 2 0
0 2 1 *
0 2 2
1 0 0
1 0 1
1 0 2 *
1 1 0
1 1 1
1 1 2
1 2 0 *
1 2 1
1 2 2
2 0 0
2 0 1 *
2 0 2
2 1 0 *
2 1 1
2 1 2
2 2 0
2 2 1
2 2 2

I've marked the combinations which have uniform frequency counts -- there are 6 of them. According to these frequencies, given three draws of random numbers in the [0,2] range, only 6/27 combinations have a perfectly uniform distribution. This means that, given a combination of three values, it's *more likely than not* that the values drawn will be NON-uniform.

In other words, if I see a perfect set of counts, I actually have reason to believe that the RNG is *not actually random,* because this is actually less likely than drawing a set with unequal counts.