[BruceZ]

[ QUOTE ]
I am too lazy to compute your intervals (I actuallly would have to look up how to do it, because I forgot). Anyhow, here is a basic summary:

n = 2000 (sets of 100 hands)
m = 1.6 (mean big bets won per 100 hands)
s = 15.6 (standard devitions in big bets per 100 hands)

95% CI = m +/- 1.96 (s/sqrt(n))

So 95% of the time your next sample set of hands will be between [0.91 - 2.28] big blinds per hour.

[/ QUOTE ]

That is the correct 95% confidence interval, but it is big bets per 100 hands, not big blinds per hour, and it doesn't mean that 95% of the time his next sample set of hands will be in that interval. For that to be the case, his win rate would need to be known exactly. What it means is that if his win rate were 1.6 bb/100 hands, then his results would fall in this interval 95% of the time. Most people are misled about the meaning of confidence intervals.

Also, the OP cannot compute the probability that his results will fall in various intervals unless he assumes a particular win rate.