User blog comment:Belthazar451/How To Get A Ghazt; Or, So How Does This Binomial Probability Thing Work, Anyway?/@comment-25087059-20140728204951

Very nice explanation. I discovered the same thing on my own (your article would have sped up the process a bit) when trying to understand statistical significance of data I've collected on my MSM tracking site. When I was first looking at n! / (n-k)!(k)! I was thinking "This is odd. I'll get the same result with 10 choose 7 as 10 choose 3." And then I thought of the curve and realized it made perfect sense.

We currently have 1369 attempts logged, and I wanted to calculate the statistical significance of the resultant %'s when comparing different characteristics.

For example, 2E Ethereals have been bred on Ethereal island in 10 out 132 attempts out of 982 attempts, for a rate of just under 8%.

But 9 of them resulted from 100 attempts with 10 wishing torches (9%), while the other 1 success resulted from 32 attempts with no torches (3.1%). This would obviously seem to strongly indicate that torches are effective, but the sample size is much too small to reach a clear conclusion. Even so, I would like to calculate the p-value indicating what the chances are that this result could happen randomly if torches were not at all effective. Doing so requires using the math you described above as a starting point.

The problem I quickly ran into was what you mentioned: Calculators (and computers, since I'm doing this with programming) are not good at handling the really large numbers resulting from big factorials. What I have unsuccessfully been trying to find is an online resource that can show me how to mathematically approximate the probabilities when the numbers get to be too big to calculate explicitly.

If anyone happens to have any ideas on where I could find that I'd be most appreciative.