Finally, we may want to go back to the OP:
We get this for 100k hands (SD 100):
70% confidence interval
Approx difference
[-3.16 BB/100, 3.16 BB/100]
6.3 bb
95% confidence interval
[-6.32 BB/100, 6.32 BB/100]
12.6 bb
500k hands:
70% confidence interval
[-1.41 BB/100, 1.41 BB/100]
2.8 bb
95% confidence interval
[-2.83 BB/100, 2.83 BB/100]
5.7 bb
2M hands:
70% confidence interval
[-0.71 BB/100, 0.71 BB/100]
1.4 bb
95% confidence interval
[-1.41 BB/100, 1.41 BB/100]
2.8 bb
6.5M hands:
70% confidence interval
[-0.39 BB/100, 0.39 BB/100]
0.8bb
95% confidence interval
[-0.78 BB/100, 0.78 BB/100]
1.6bb
All in all the bots give a bit too pessimist picture. Though, for 500k hands with an expected win rate of 5bb/100 luck indeed can mean as much as the expected. Approximately you are between 2.2 and 7.8 bb/100 with 95% confidence. And even with 70% confidence you are between 3.6 and 6.4 bb/100.
At 100k hands luck is indeed expected to mean more than 5bb/100.