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 that continues until it misses or hits 10 times, which means accuracy boosts now directly scale damage.

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