[magic_man]

We frequently see posts on the low-limit forum and other places in which the poster says they have calculated a win rate of 5 BB/hr over 100 hours (or whatever), and everyone laughs and says that 100 hours is not nearly long enough to calculate valid statistics. I am confused as to why a confidence interval cannot be used to validate these numbers. For example, suppose you play 6 sessions of 10-20 with the following results:

Net # Hours
-200 6
+600 6
+300 6
+300 6
-200 6
+500 6

Your win rate here would be:
$36/hr or just over 1.5 BB/hr

Your std deviation would be:
$128/hr or just over 6 BB/hr

This is all over 36 hours of play. If we calculate a 90% confidence interval for win rate, we get:

error = 1.64 * $128 / sqrt(36)
error = $35/hr

Therefore win rate is between $1 and $71 / hr.

So we can say with at least 90% confidence that this player is at least break-even. Is there an error in this argument? It seems to me that there would be many cases where after only one or two hundred hours, you could make a 95 or 99% confidence interval to show that you were a winning player. Am I making some mistake in my understanding of the equations used here? Thanks for any input you may have.

~Magic_Man