Explode - Profane Bloom - Beacon of Madness - math

Let's say I have the Occultists Profane Bloom Ascendant node and my enemy is currently cursed by me.
And lets say I am wearing the version of Beacon of Madness which explodes enemies and I am currently Mad.

Profane Bloom gives a 50% chance for killed enemies to explode if they are cursed.
Beacon of Madness gives a 40% chance for killed enemies to explode if I am currently Mad.

My question is do these percentages stack, giving me an overall 90% chance to explode an enemy, or does the game treat each instance of explode separately, rolling on a 50% chance and a 40% independently of each other.

Remember, the enemies are cursed and I am Mad when I kill them.

I worked out the math with a simply Python script. If there is a single combined 90% chance, then it's a 90% chance to explode.
If they are independent rolls, then it's ~76% chance to explode. (I rolled two d100s. if either die was within its respective range, i counted that as a single success. repeated 10k times and calculated the percentage. For fun I saw what happened if there were three rolls each at 30% [30*3=90] and it's ~72%, slightly worse than two rolls but much worse than a single roll.)

How would POE handle this, a single combined roll, or two independent rolls? I'm hoping for a single roll. Thank you --

While I don't remember a quick way to find a concrete answer, my recollection is that each explode is rolled separately.

So you can't, say, take Chieftan's "Hinekora, Death's Fury" ascendancy passive for "Enemies you Kill have 5% chance to Explode, dealing 500% of their maximum life as Fire Damage", then use something like Haemophilia or Inpulsa's Broken Heart to guarantee that monsters explode and make every monster that dies deal 500% of their life as damage to surrounding enemies.

While every monster meeting the conditions would explode in that case, there'd still only be a 5% chance for the 500% of max life explosion effect occuring.

Each explosion is calculated separately, and its damage is calculated separately. The wiki is the best place for information like this: https://www.poewiki.net/wiki/Explode

You can calculate the chance to explode using the chance to fail, instead of the chance to succeed: For a 50% explode and a 40% explode, you have an overall 1 - (1-0.5)*(1-0.4) = 0.7 = 70% chance for any given monster to explode. Of course there is a 0.5*0.4 = 0.2 = 20% chance for it to explode twice.

Explosions of the same kind stack their variable values. Different explosions don't stack, they proc separately.

These two explosions are the same, they have constant damage part (quarter of Life as Chaos Damage) and variable chance to proc.

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kahwigulum wrote:

My question is do these percentages stack, giving me an overall 90% chance to explode an enemy

This one.

if the explosions do the same thing, the percentages are added

if the explosions do different things, they are rolled separately and can happen simultaneously