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Drop rates: Difference between revisions
From Melvor Idle
→Calculating the chance of drops
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<math>P = 1 - \left ( 1 - \dfrac{1}{k} \right ) ^ {n} </math> | <math>P = 1 - \left ( 1 - \dfrac{1}{k} \right ) ^ {n} </math> | ||
If the drop-rate is low | If the drop-rate is low (which ''is'' typical for rare drops) then you can approximate this as: | ||
<math>P \approx 1 - \left ( \dfrac{1}{2.718} \right ) ^ {\left ( \dfrac{n}{k} \right )}</math> | <math>P \approx 1 - \left ( \dfrac{1}{2.718} \right ) ^ {\left ( \dfrac{n}{k} \right )}</math> | ||
For those unfamiliar with math notation, the brackets mean take the largest whole number. | |||
For example, for the {{ItemIcon|Chapeau Noir}} there is a 1 in 20,000 (k) chance of this item dropping, and 100 attempts gives a probability of: | For example, for the {{ItemIcon|Chapeau Noir}} there is a 1 in 20,000 (k) chance of this item dropping, and 100 attempts gives a probability of: | ||
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This means that you have a 0.5% chance of discovering at least one of these after 100 attempts. | This means that you have a 0.5% chance of discovering at least one of these after 100 attempts. | ||
== Calculating the number of attempts == | |||
The number of attempts (n) for a given drop-rate (k) with a certain probability (P) is given by: | |||
<math>n = \left \lceil \dfrac {ln(1 - P)} {\ln \left (\dfrac{(k - 1)}{k} \right )} \right \rceil</math> | |||
If the drop-rate is low which ''is'' typical for rare drops then you can approximate this as: | |||
<math>n \approx \left \lceil -k \cdot \ln(1 - P) \right \rceil</math> | |||
For example, for the {{ItemIcon|Chapeau Noir}} there is a 1 in 20,000 (k) chance of this item dropping, and we want a 75% chance of getting at least one, then we would need: | |||
<math>n \approx \left \lceil -20,000 \cdot \ln(1 - 0.75) \right \rceil = 27,726</math> | |||
This means that you would need 27,726 attempts to give you a 75% chance of discovering that item. | |||
There are many online [https://dropchance.app/|drop-rate calculators] that you can use to help understand drop-rates in practice. Good luck! | There are many online [https://dropchance.app/|drop-rate calculators] that you can use to help understand drop-rates in practice. Good luck! | ||
