Maushold Damage Calculations

Background and Description

Pokemon Scarlet and Violet introduced an interesting move in the newest generation. Population Bomb is a multi-hit move. However, instead of having a set distribution of the number of hits, the move instead hits continuously until it misses or hits 10 times. This nuance implies that accuracy improving effects now have a damage increase to this move.

I set out to calculate exactly how much damage this move does in expectation and also how effective certain accuracy boosting items are for it. This task uses some neat summation tricks to generalize the geometric distribution.