I don't think that makes 100 / 100 the most likely result if you flip a coin 200 times. It's not about 100 / 100 vs. another single possible result. It's about 100 / 100 vs. NOT 100 / 100, which includes all other possible results other than 100 / 100.

If you flip a coin 200 times, and repeat that a billion times, 100/100 will be more likely than any other ratio.

It will be a bell curve with 100/100 as the peak