[irchans]

The size of a 95% confidence interval is about
1/Sqrt("number of observations"). (About two Standard Deviations)


So for your first example, if you observe 6 hands played out of 10, then the confidence interval size is about 1/sqrt(10) = 32%, so you can conclude that he plays between 28% and 92% of his hands. (This is a rough estimate--better estimates are possible.)

For your second example, you saw him play 4.5 million out of 30 million hands, so 2 standard deviations is about 1/Sqrt(30000000) = 0.02%. You can conclude that the player plays between 14.98% and 15.02% of his hands with 95% confidence.

Cheers,
Irchans