The thing is, at a tournament, if I announce that I'm activating the ability a trillion times, do I have to flip a trillion coins, or can my opponent and I just assume that I'm going to win at least 10 of those coin flips?

Rationality tells me that I have to flip all of them, because it is a random outcome and can't be assumed, but really, does an event ever become

*so*likely that we can shortcut it?