Many of us have several times spent a lot of time farming rare items in wow.
Either it’s a Zul Gurub tiger or Baron’s mount and even for some hardcore grinders Hyacinth Macaw parrot (1/10000 drop rate).
The question is how many of you are actually aware the chances that you have to get your desired loot.
There are 2 parameters to approach the drop rate. The first is the chance and the second it the probability.
In the case of Baron’s mount the chance is 1% and no matter how many times you have killed him the chance of the next kill will still be 1%. Theoretically you can keep killing him forever without getting his mount ever.
On the other hand though we have the probability approach which measures the propability to get the desired loot after X tries.
The equation of the propability is: F(x) = 1 – (1 – a%)^x
Where X is the times you kill the Baron and a% is the drop rate (1% for this case).
In other words for the Baron the formula is: F(x) = 1 – (1 – 0.01)^x = 1-(0.99)^x
Here is a graph for this formula:
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As you can see less times you have killed him the higher is the probability rate. After the 180 kills the probability rate drops significally.
Here is a table with some sample values:
10 9.56%
20 18.21%
30 26.03%
40 33.10%
50 39.50%
60 45.28%
70 50.52%
80 55.25%
90 59.53%
100 63.40%
110 66.90%
120 70.06%
130 72.92%
140 75.51%
150 77.85%
160 79.97%
170 81.89%
180 83.62%
190 85.19%
200 86.60%
210 87.88%
220 89.04%
230 90.09%
Conclusions:
Before starting farming a 1% drop rate loot note that there is a 10% probability to kill it 280 times without seeing the loot.
Sources: Gambler's fallacy - Wikipedia, the free encyclopedia