So, the most important question is "What is the probability to get at least 1 purple rune buying the gold chest, and what probability do I get by buying a number of bronze or silver chests for the same amount of gold?"

To get to a comparable amount of gold, we use 9000 gold (it's either gold OR keys).

Number of bronze chests for 9000 gold = 45 => Number of runes = 90

Number of silver chests for 9000 gold = 18 => Number of runes = 54

Number of gold chests for 9000 gold = 2 => 6 (But here you always get at least 1 purple, so rather it is 2 purple + 4 unknown)

Purple rune probability:

bronze: P(90) = 1 - (1 - 1/100)^90 = 59.5%

silver: P(54) = 1 - (1 - 1/50)^54 = 66,4%

gold: P(4) = 1 - (1- 1/10)^4 = 34.4% (+ 2 guaranteed purple)

This means that if you are willing to spend a lot of Gold, go for gold! If you want to spend less Gold, go for silver!

Last edited: Oct 25, 2018