I know this will sound like a trivial maths problem, but recently I've been playing a game in which you can pay 5 in game gems to get a Rare (R), Super Rare (SR), and Ultra Rare (UR) characters randomly. And the probability of getting said characters are 90%, 9%, and 1% respectively.
What I have calculated thus far is that each character is worth approximately 5.5, 55, and 500 gems respectively by doing the following calculation:
Average Cost = Cost of Rolling/Probability
But I have no proof that this is correct or incorrect. I thought it had something to do with expected value as taught in school, but something seems off about it.
To further complicate things, you can spend 50 gems to roll 11 times. And on top of that, occasionally you can roll spend 50 gems to roll 11 times with 1 guaranteed SR. What would then be the expected average cost for each respective rarity?
Probability has always been interesting to me, but definitely not my strong suit.