Probability - How does it work?!

^^^^Yes but you're only considering a very specific example of equally probable events and the order matters.

Yep, agreed, a coin flip resulting in 100 heads is the target.

Comparing that to a series of other sequences ([99 heads and 1 tail] in one of 100 combinations) doesn't really work as a guide for probability as the original problem is searching for a specific sequence (1 sequence from 1.27n sequences) as 100 heads in a row has no variations even if we ignore the order of events.

The question as stated what is the probability of flipping 100 heads in a row? is looking for a single event not a group of events, so in that respect the order always matters, otherwise all we are saying is "hey look, these 100 sequences are 100 times more likely to occur that this 1 sequence, which is axiomatic.

Hope that makes sense !!!

If the runs were repeated infinitely many times all outcomes would occur. It's infinite! that's the basis of much of the theory, that for infinite runs all will occur.

I can't see that.

Let's keep the machinery light here - I have a perfect random number generator, switch it on and away it clicks, it produces either a 0 or a 1 every second, ignoring the cold death of the universe, a second term for the coalition or any other physical limitations (let's keep it all in an unchanging, hypothetical sempiternal universe) it keeps clicking away for an enormous amount of time, 0 after 0 after 0 after 0 after 0 after 0 after 0 after 0 after 0, nothing is broken, the machine is remotely checked without interference playing a part and all is well, it just happens to have only produces 0s so far. . .

By what mechanism would it be compelled to produce a 1 ?

S = - sum [p_i * ln(p_i)] for all i

'pips', I read 'pips', also 'sum', but I am going to stick with 'pips', how many points for 'pips' ?