Setting probabilities but with a weird setup (a fishing mini-game plugin within Minecraft)

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Hi, I run a Minecraft server, and I'm currently configuring the rarities of a fishing mini-game plugin. I know the probabilities I want each "rarity" to have, but this plugin calculates it them in a strange way, and I'm not sure how to account for that in my calculation. Here's what I want and how it works.

I would like to have the following hit-rates:
Common— 70%
Uncommon— 20%
Rare— 8%
Extremely Rare— 2%

Here is how the plugin calculates rarity. When it rolls for a caught fish, it starts in the Common tier. It will have a x% chance to spit out a Common fish and a y% chance to move to the next rarity bucket, Uncommon. Then the plugin rolls the Uncommon bucket— a% chance to spit out an Uncommon fish with b% chance to move to the Rare bucket.

The plugin allows me to set rarity by picking the odds of rolling each bucket in the previous tier.
Uncommon (% in Common roll): ___
Rare (% in Uncommon roll): ___
Extremely Rare(% in Rare roll): ___

How do I go about finding the values to input to get my desired roll-rates? Any help would be appreciated— thank you!!

 

[Dr.Peterson]

Hi, I run a Minecraft server, and I'm currently configuring the rarities of a fishing mini-game plugin. I know the probabilities I want each "rarity" to have, but this plugin calculates it them in a strange way, and I'm not sure how to account for that in my calculation. Here's what I want and how it works.

I would like to have the following hit-rates:
Common— 70%
Uncommon— 20%
Rare— 8%
Extremely Rare— 2%

Here is how the plugin calculates rarity. When it rolls for a caught fish, it starts in the Common tier. It will have a x% chance to spit out a Common fish and a y% chance to move to the next rarity bucket, Uncommon. Then the plugin rolls the Uncommon bucket— a% chance to spit out an Uncommon fish with b% chance to move to the Rare bucket.

The plugin allows me to set rarity by picking the odds of rolling each bucket in the previous tier.
Uncommon (% in Common roll): ___
Rare (% in Uncommon roll): ___
Extremely Rare(% in Rare roll): ___

How do I go about finding the values to input to get my desired roll-rates? Any help would be appreciated— thank you!!

Seems simple enough to me. It's a matter of conditional probability.

You want P(Common) to be 70%. Then P(not Common) = 100% - 70% = 30%.

Next, you want P(Uncommon | not Common) to be 20/30 = 67% (rounded). If it doesn't have to be rounded to the nearest percent, enter as close as you can to 2/3. This way, P(Uncommon) = P(not Common)*P(Uncommon | not Common) = 30%*67% = 20%. This leaves 10% for the last two categories.

Next, you want P(Rare | not Common or Uncommon) to be 8/10 = 80%. Then P(Rare) = P(not Common or Uncommon)*P(Rare | not Common or Uncommon) = 10%*80% = 8%. This leaves 2% for Extremely Rare.