Earlier quoted context omitted.
Still skeptical. What happens when you have pokerbots play against each other? Do they have similar variance across 100,000 hands?
Yes. Some of the first statistical analyses of poker I came across when I was learning were based on simulations using bots run by none other than Nate Silver (he used to be a poker pro). His conclusions were in line with what I've been saying, and these simulations were using full and 6-handed tables if I remember correctly. Heads-up has even more variance.
Let's say you came out even after 100,000 hands. If I randomly divided those hands into two sets of 50,000 each, would you expect one of those sets to be up by 10% and one of those sets to be down by 10%?