Variance in Equity over Large Samples

[Murd0c]

I was wondering what type of variance in expected equity could be expected between a large group of people, say 1 million, over a large sample size of hands of NLHE, say 1 million hands. What kind of % difference would there be of expected equity between the "Luckiest" person and the "Unluckiest" person?

<.1%? 1%? 10%?

[pna]

I'd say ~1%

[f97tosc]

Let's say they all have EV=0 and standard deviation of 20 big blinds per 100 hands.

Then they have standard deviation of 20*sqrt(1000000/100)=2000 big blinds after playing a million hands.

This suggests that the top 5% players or better are up about 2s.d.=4000 big blinds or more, the bottom players are down by the same amount. Without looking up a table for 1 in a million I think it is maybe 7 standard deviations up or so, that is the luckiest player would be up maybe 7*2000=14,000 big blinds and the unluckiest down by a comparable amount.

On the other hand, if each player made on average X big blinds per 100 hands, then the luckiest would be 10000X+14,000 compared to 10000X - 14,000 for the unluckiest player.