So ... I was trying to work out the CDF[Erl] of a pool getting 150 blocks a month, for 3 months, with mean difficulty of 1.25 (luck of 80%)
I can't get a reasonable result at the wolfram site it keeps telling me it's 1, so yeah I guess that means it should be ever so rare http://www.wolframalpha.com/input/?i=CDF%5BErlangDistribution%5B450%2C+450%5D%2C++1.25%5D
Using my own code I get the same effective answer
cdf_gamma_Q is 0.999997 (and cdf_gamma_P is 2.7091e-06)
So that's like saying (in my non technical words) the chance of doing that badly or worse is like 1 chance in 369,126?
What am I doing wrong?
(and then it would be even worse with a higher number of blocks ...)
I get different results - a lower tail CDF of 0.9999996 and an upper tail CDF of 4.07395×10^-7, which is the same as the result I get from wolfram alpha. That's actually more improbable than that which you got.
Intuitively, these results seem correct. Are you sure there have been 450 blocks, and did you get the correct difficulties, and
if all that's correct does it seem like the pool is publishing accurate d1eq shares per round?