- #1

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- TL;DR Summary
- This Q was asked in a chat room: Find the number of pulls (draws from the distribution) required to have a 50% chance of getting a full set of event 5*s (*'s denote rarity in the game) from the Magic Tower Summon (of the Empires & Puzzles mobile game) which has 5x event 5*s each at a 0.2% drop rate. My first dilemma is binomial distribution or geometric distribution?

This Q was asked in a chat room: Find the number of pulls (draws from the distribution) required to have a 50% chance of getting a full set of event 5*s (*'s denote rarity in the game) from the Magic Tower Summon (of the Empires & Puzzles mobile game) which has 5x event 5*s each at a 0.2% drop rate.

My first dilemma is binomial distribution or geometric distribution?

I imagined that since the stated odds of pulling an event 5* is 1% but that includes 5x unique 5*s assumed weighted equally, I might have events A thru E be the pulling of the very first unique event 5* thru the fifth unique event 5*, where the associated drop rates are 1% thru 0.2% stepping down 0.2% each event after A. But since the unknown is the number of pulls (trials) don't I want to use geometric distribution? Please advise or solve this if you're inclined to (I won't take credit if you do and will cite you with permission from you of course)?

My first dilemma is binomial distribution or geometric distribution?

I imagined that since the stated odds of pulling an event 5* is 1% but that includes 5x unique 5*s assumed weighted equally, I might have events A thru E be the pulling of the very first unique event 5* thru the fifth unique event 5*, where the associated drop rates are 1% thru 0.2% stepping down 0.2% each event after A. But since the unknown is the number of pulls (trials) don't I want to use geometric distribution? Please advise or solve this if you're inclined to (I won't take credit if you do and will cite you with permission from you of course)?