Probability of getting x number of rarity type in 10x pull

A couple of days ago, I made a 10x pull during the event only to get 10 useless 3s. I was furious and gutted as I saw the gems I worked hard to accumulate for months disappear for nothing to show for them. This got me interested to work out the chances of pulling a certain number of 3s in a 10x elemental summon (71% for rare, 26.5% for epic, and 2.5% for legendary, 1.3% for HOTM). Here are some things to note based on the picture attached:

· The area under each curve should equal to 1.

· I was unlucky (about 3%) to get all 3*.

· The most likely scenario is to get 7 rare and 3 epic heroes or 8 rare and 2 epic heroes, which is already common knowledge.

· The probabilities also shows that getting more than two legendries or HTOM in one 10x is next to nothing.

Thought this was interesting to share with the community


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