Probability - How does it work?!

Shouldn't it even itself out to 50/50 over the full 100? Whereby 50 heads in a row is equally likely as 50 tails in a row, or heads-tails-heads-tails-heads-tails etc or any other combo as you say?

Over 100 coin tosses, there are 2^100 possible distinct sequences, and they're all equally likely (ie, 1 in 2^100 chance of each).
However, some outcomes can be reached by more than one sequence, so they're more likely to occur.
For example, there is only one way to get either all 100 heads or all tails, so those outcomes are vanishingly unlikely (2^100 has something like 30 zeroes).
However, take the outcome 1 head and 99 tails ... there are 100 sequences that give you the outcome, so it's 100 times more likely to come up.
The outcome 50 heads and 50 tails can be accomplished so many ways, it's much more likely to occur: look up 100 choose 50.

Easiest way to work through this is to start with small numbers (<10) and write out the tree.