Are my odds higher predicting a $50/50$ bet with a constant or picking a random number each time? I added the last part: The context is this - casino games - more specifically dice ones. After asked for context 2 times - while I think that was not necessary. (for the curios It's a game on the o...

I am an undergraduate who has taken group and ring theory, complex analysis, and probability and measure, but no number theory. My understanding is that the RH, if true, gives that $|\pi(x) - \text{Li}(x)| \in O(\sqrt{x}\log x)$, which is essentially a square-root bound on the error, because $\sq...