Here's another way of thinking about it. Think about the OP again. If the odds of 8,8,8,8,8,8 were the same in every respect as Steve's example of 4,32,0,18,16,22, then nobody could distinguish a biased wheel from a fair one!

Because if every sequence of the same length had the same probability, then a sequence of 1000 #8's would be just as likely as a 'normal' sequence. Because that's an absurd scenario, it can't be true that the odds are the same.