Quote:
Bummer_Duck said:
I totally agree that 8 smiths is too small of sample. I believe I stated 14+ earlier, but perhaps not.
|
Here calculations are getting more complicated.
Probability of 14 smiths missing one of the paths is 80.8%.
Quote:
Bummer_Duck said:
In my current game, I will be recruiting my 15th drawf this year, and I am still missing representation of 2 magic paths. 3 paths represent 71.4% of the mages, with 3, 3, and 4 mages per magic path, respectively (3 magic paths have 1 representative each). This is the widest distribution of paths I can remember in all my tests. So...turn those equations around for me. How likely is it that in each game or test, that ~3 paths would represent +71% of the mages?
|
It seems to be even more complicated to calculate (Probability that 10 or more smiths out of 14 will be concentrated in 3 paths). It seems to be around 40-45%, but I had to drop the tail of the sequence, so I'm not sure about accuracy. I will try to calculate it precisely later.
Quote:
Bummer_Duck said:
shouldn't it approach 3/8? or 37.5% the larger the sample is? What am I missing here?
|
You mean number of mages concentrated in 3 paths should approach 37.5% of total number of mages? - No it should not, what are you saying would effectively mean that the equal number of mages in each path, which is very unlikely event. On the large samples peak of probability will probably be somewhere in 45-60% range (that's very rough estimate, I will try to calculate it precisely some time later)