Drop rates: Difference between revisions
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<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 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: | |||
Good luck! | <math>P = 1 - \left ( 1 - \dfrac{1}{20,000} \right ) ^ {100} = 0.005 = 0.5 \%</math> | ||
This means that you have a 0.5% chance of discovering at least one of these after 100 attempts. | |||
There are many online [https://dropchance.app/|drop-rate calculators] that you can use to help understand drop-rates in practice. Good luck! | |||
Revision as of 13:36, 31 March 2024
What is the chance of dropping a reward?
On many of the guides you will see the drop-rate for a particular reward given. This will typically be expressed as a fraction and a a percentage. For example, the rate of drop-rate for the 
Chapeau Noir in
is 1/20,000 (0.005%).
The drop-rate of the reward shows you probability of the item dropping, but it is not the same as the chance of the reward being given. For example, if you were to perform this action 20,000 times you might reasonably expect to get this item, however, there is only a 63% chance of this happening.
For example, the chances for the Chapeau Noir to drop at least once for a given number of attempts can be seen on this table.
| Chance of success | Number of attempts |
|---|---|
| 50% | 13,863 |
| 90% | 46,051 |
| 99% | 92,102 |
It might be surprising to learn that farming for rare items is often going to take considerably longer than you may have initially thought based on the drop-rate. Of course, you might get lucky and drop this reward on your first attempt!
So keep grinding, and see the next section for some of the math behind the probabilities of drops.
Calculating the chance of drops
The probability (P) for a given drop-rate (k) over a fixed number of attempts (n) is given by:
[math]\displaystyle{ P = 1 - \left ( 1 - \dfrac{1}{k} \right ) ^ {n} }[/math]
If the drop-rate is low, and the number of attempts high (which is typical for this game) then you can approximate this as:
[math]\displaystyle{ P \approx 1 - \left ( \dfrac{1}{2.718} \right ) ^ {\left ( \dfrac{n}{k} \right )} }[/math]
For example, for the Chapeau Noir there is a 1 in 20,000 (k) chance of this item dropping, and 100 attempts gives a probability of:
[math]\displaystyle{ P = 1 - \left ( 1 - \dfrac{1}{20,000} \right ) ^ {100} = 0.005 = 0.5 \% }[/math]
This means that you have a 0.5% chance of discovering at least one of these after 100 attempts.
There are many online calculators that you can use to help understand drop-rates in practice. Good luck!
