The query q and denominator q being the same letter is really confusing !!

Why is this in the easy section? lol

I managed to solve the problem on the Project Euler webpage. However my solution are decimals like: 0.33333333333 for the example given here (with 1 as input). How is it possible to recover the rational expression (fraction of integer a/b) from my result to then express it in the weird modulo formulation as asked in the problem statement? I'm confused

Maybe I'm a fool but I am completely lost on how the answer is 1/3.

On each turn Player 2 selects the number, T , of coin tosses that maximises the probability of her winning. How do we get this value of T, now?