@ !luck: I warned you at the top that it was long and technical and not directly about poker. I didn't know how much to illustrate the terms and I thought at least a couple of examples would be helpful.

@ Imthenewfish: I was trying to find a rational way to get that 10k number to show up. Many new players don't understand why the long term is so long.

@ Icanhastreebet: Yes, absolutely! BUT that's not the question we're asking.
That question is: Can this stat be 0%?
Our question is: What range of values for this stat would I expect to get if I collected this same sample size again?

@ daven: There is NEVER the chance that a frequency can be less than 0% or greater than 100%. If the error range of the CI for a stat includes numbers which are "not allowed", that indicates that not enough data has been collected, and our estimate of the "actual" stat is not reliable.

My main point here is to illustrate that a small sample size gives unreliable data and there IS a way to determine how big a sample size needs to be before the data becomes reliable. The number 10k hands gets thrown around a lot and I was trying to show a mathematical justification for why.