You can calculate how many tries it takes to obtain an icon on average (not a precise value, because it depends on luck, it could take more or less than the value) and the percentage you have, to obtain an icon from the next chest you open:
• For gold chests:
n = 1÷((13-g)÷(48-a))
x = 100÷n
• For silver chests:
n = 1÷((10-s)÷(200-b))
x = 100÷n
Where:
n is the number of tries it takes to obtain an icon,
x is the percentage of obtaining an icon from the next chest,
g is the number of gold chests you have opened that contained an icon,
a is the number of gold chests you have opened,
s is the number of silver chests you have opened that contained an icon,
b is the number of silver chests you have opened.
It is clear that doing this procedure is not worth the time and energy with silver chests, since they require 4 less keys to open, give 3 less icons in total, and there are 152 more of them than gold chests. So, it would take longer to collect an icon using this strategy. It's best to just keep opening them the regular way and eventually you will get the icons. For gold chests, on the other hand, it's quite useful, since they also require more keys to open and so it would take longer to open all of them.
Music: Ahrix - Left Behind
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