Re: confidence of being better?
The key variable is the standard deviation. It's hard to guess without knowing the styles of the players, but say it's 10 BB/100 hands. In that case, after a million hands, the better player is expected to be up by 1,000 BB, with a standard deviation of 1,000 BB. There's about 5 chances in 6 that he's ahead.
After 4 million hands, the better player is expected to be up 4,000 BB, with a standard deviation of 2,000. Two standard deviations is conventionally considered to be significant; so I guess that's a reasonable answer.
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