Genie Rarity

When a genie levels it is given a random amount of bonus points every 10 levels to be put in stats. These bonus points are called lucky points. The number of lucky points your genie gains every ten levels is given at the following rates:

As you can see it is not an even distribution so will likely be either high or low.

Genie Rarity
Obviously getting a 100/100 lucky point genie is super rare but how hard is it? How about getting just 99/100?

The answer to these questions can be calculated from the above distribution. For example, to get a 100/100 genie requires getting 10 lucky points (19% chance), 10 times in a row which is a chance of 1 in 16,310,377. The chance to get 99/100 comes from the 10 different ways of getting 10 lucky points 9 times and 9 lucky points once.

These calculations get more and more complex for more arbitrary lucky point combinations, like 57/70. Fortunately the following table takes care of all of that already.

Genie Rarity Index
The Genie Rarity Index (GRI) is a measure of how hard it is to make a genie with a specified number of lucky points or better. For example a GRI of 4.0 means that 1 in 4 genies at a given level will have that many lucky points or better. The worst genie with the minimum possible number of lucky points will have a GRI of 1 since 100% of genies will be able to meet or beat that genie. A very average genie would have a GRI of 2 with about 50% of possible genies coming out worse at that point and the other 50% coming out better. The best genies have large GRIs. A GRI of 1,000 means only 1 in 1,000 genies ever get that good (or better).

To use this table lookup the row corresponding to the lucky points on the left with the column corresponding to the genie level at the top.

For example, a genie with lucky points of 68 / 80 has a GRI of 217. Only 1 in 217 genies ever gets that good. You would need about 651 mirages to make that many genies which would cost around 6.5 million coins. Using the GRI like this is a great way to judge the worth of a genie.