Drop rates

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

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Thieving

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.

For a drop-rate of 1/20,000 (0.005%)

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 ) ^ {\dfrac{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]

There are also many online drop-rate calculators that you can use to see the math for the reward you are trying to obtain.

Good luck, and keep grinding!