the long run and infinity

[AaronBrown]

No for two reasons.

One problem is that things are not constant. As you measure over a longer interval the effect of hand-to-hand luck declines, but the thing you are measuring keeps changing. For example, we have 80 years of good data on stock market returns, with many millions of observations, yet we can't make any kind of accurate determination of the average return on stocks.

In theory, if you had an absolutely constant win rate and standard deviation, the importance of luck would diminish with the square root of hands played. If your standard deviation was $200/100 hands, after ten billion hands the standard deviation of your average result per 100 hands would be only $0.02. But the second problem is, the standard deviation of your stack at that point would be $2 million. You learn more and more about your average win rate as you play more hands, but the dollar swings that result from luck still grow.