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I understand your examples and -- I think -- the point you are trying to make. You posit that any outcome is as likely as any other. Do I have that right?

For the situation of a set number of random coin tosses.

I understand your point. Here's the thing -- go back to the coin tosser tossing fifty coins on the table. They all come up heads. What's on the other side of the coins?

Understand that I said all heads and not any combination of heads and tails. How many outcomes are there when we allow at least 30 heads? At least 40, etc. Well you can figure those out. Combinatorics 201. The answer for fifty heads out of fifty coins is easy and you've already given it. One chance in 2**50. That is, impossible. Impossible unless the toss is rigged or the coins are rigged. Assuming we saw the toss and the coins and by that would make a assumption of rigging the toss very very unlikely -- we ain't talking magical space aliens coin tossing here, just a man out of the crowd.

What's on the other side of the coins?