Poll Simulation
Pity copies are not accounted.
For Master Fairs, pity for gems is 36600 at 400 scout points.
For Arc Fairs, pity for gems 45600 at 500 scout points.
For gems and scout calculations, in algorithm the multi scouts are first pulled, and then the 300 gem single scouts until gems (scout points) deplete. Dallies are not accounted in calculations (as this would introduce unnecessary complexity.)
The scouts are modeled to be a binomial distribution and calculated using the binomial coefficient.