Note: I adjusted the rates. You can contact me and let know your ideas. Note 2: There is a chance to get 2 influence bonuses at the same time. I didn't do it because it would be too complicated.
When performed 1 times, the chance to get one bonus is %5
When performed 10 times, the chance to get one bonus is %40
When performed 100 times, the chance to get one bonus is %99
When performed 300 times, the chance to get one bonus is %99