Hello, dear eDomination players!

Intro
Some days ago one of the players asked - why did he make an 941 hits, but ability triggered only 78 times instead of 94?
And then I understand that people rare understand probability theory from scientific side :)
Here I come!

Some theory for quick start
Will ability activate or not - does not depend from success or fail of the last attempt. So here we have series of indepedent tests.
That means that we can calculate a probability of X ability activations through Y attempts via binomial distribution.

Most interesting
I have calculated probabilities of X successful trigger activations for 1000 attempts for Artillery ability (10% chance).
Here on picture I show only intervals with significant probabilites.



So we can make next conclusions: 

Maximum probability has, obviously, 100 trigger activations. But probability of such case is only 4,2% from 100%.
There is 99,7% chance that trigger will be activated from 73 to 128 times. It means that chance to have 72 and less or 129 and more activations is near impossible. You also can notice that right tail of our distribution fall slightly slower than left one - that because there are a more of space in comparison (from 101 to 1000 activations against from 0 to 99 activations)
You will have from 80 to 120 trigger activations with probability 97%, which is a lot too :)

Thank you for reading!