I'm a stats consumer but by no means a statistician. I'm a little confused about how resampling an existing sample can bring useful information, but I get the general idea that you can generate confidence intervals based on the bootstrap distribution. Specifically, I'm wondering about the actual process of resampling a finite amount of times.
1) If we already know the frequency of observations in our sample, shouldn't we be able to use that probability to calculate what we expect the bootstrap distribution to look like with infinite resamples? Such that we don't actually need to run simulations of resampling? In a dumbed-down analogous way, we don't have to flip a coin 10000+ times to confirm that what the distribution of coin flips looks like.
2) Is there such a thing as too many bootstrap simulations? Generally more samples are a good thing, and I've read about different arguments for the minimum accepted number of bootstrap simulations. In regards to 1), perhaps there's a reason we wouldn't want to general to infinity simulations?