Short answer:

Anything that has an occurance probability of under 100% may not happen.

Long answer:

Chances of some pair of series happening can be the same, but outcomes are not the same thing as chances.

For example, I could win the lottery today and try some other numbers combination next week, - the chances of those numbers coming up would be the same, but I'd still have to be insanely lucky to win again, and it probably won't happen.

Anyway, you could follow your logic and come to the right conclusions, by either thinking it through or experimenting, or both, but you don't even do that.

You start and stop on step one: Your win rate/chance overall, or for one battle (50%).

Why don't you calculate the probability of 2 wins/losses in a row?

Or 3?

Or ..., or 8, ...?

Then you would understand why it seldom happens, etc.

You can always google "statistics" or "logic", or ask something on the forums, that's all fine.

But all of that can only inspire you or show you some direction, - you can't miss out on personally thinking stuff through, if you want to understand anything at all.