Probability - How does it work?!

I'll give it one more go... while 100 tails or heads is of equal probability to any ONE other specifically noted sequence

Agreed, 1,27 nonillion sequences available from a 100 bit system (a hectobit) all have equal probability of occurring in a genuinely random system.

this is not what people are betting about or generally referring to.

Oh yes it is.

: )

When you bet someone that 100 head/tails is near impossible or that they couldn't possibily toss a coin 100 times and get 100 heads, what we are betting upon is: that ANY ONE among the astronomic number of different random equally possible other sequences is more likely to come up when you toss the coins, than any one specific sequence that they may choose.

This is where we disagree, it's simply not that case that (and I will quote what you say to avoid colouring your idea):

ANY ONE [I]among the astronomic number of different random equally possible other sequences is more likely to come up when you toss the coins, than any one specific sequence that they may choose.[/I]

Let's try an example, here is our 100 heads:

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Can you type out (or cut and modify the above) a sequence from the other sequences more likely to occur ?

I guess what you are trying to say is that the chances of it (100Hs) not occurring is more likely than it occurring, this is true, but this equally true for all sequences.