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Formula to calculate the damage gain of inevitable criticals (forced outcome oracle node)

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**Cross Platform Communication enabled with Discord.** Replies to this conversation are bridged back to **Path Of Exile 2** so website and Discord members can communicate together. Posted from Discord server: **Path Of Exile 2** Discord user: **Pip Panoma** (219894319471919104) This Discord user has not connected their TCM account yet, so TCM Administrator is posting this on their behalf. Inevitable criticals reroll hits until they crit, subtracting 30% crit damage bonus for every reroll. I calculated this with a partial sum formula. I went to Wolfram Alpha and asked it to make an infinite sum of this formula: (x\*a)(1+(b-0.3x)) where a is your crit chance and b is your crit damage. This is the expected value of the binomial distribution of your crits for x attempts, multiplied by your crit damage that is reduced by 30% for every attempt. This resulted in the partial sum of: -0.1an(1+n)(-4.5 - 5b + n) To calculate the damage take n to be your crit damage divided by 30%, since I am assuming your crit damage cannot go into the negatives. For example with 135% crit bonus I will use n=1.35/0.3=4.5 which I will round down to 4, With 21.6% crit chance the damage formula becomes thus: -0.0216\*4(1+4)(-11.25+4)= 3.132 which equals an expected 313.2% damage gain over non crits Compare this to 0.216*2.35= 0.5076 for the expected damage gain for normal crits and we can see that inevitable critical is pretty dang worth it at these values.

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