This is just a random thought that came to my mind.

What is the fraction of even numbers in decimal expansion of $\pi$ and $e$?

Is there any research on this and it’s possible generalisations?

Edit: I checked the first 100 digits and found number of even digits in $\pi$ and $e$ to be $50$ and $58$ respectively.

Is there any reason we should believe that the fraction should converge to exactly $50$%?