Trying to get the God of Evil achievements? This guide details the god's spawn mechanics so you hopefully don't have to spend as much time on it as I did.
Guide to A God of Evil
The God of Evil is a notoriously rare spawn. So rare in fact that many people have never even seen it. There are 2 achievements related to it however, so any completionists will find themselves grinding it out. After 150+ hours I only ever had it appear once, and at that time I couldn't get the 2nd achievement, The Cruel Punishment.
Any online information I could find was vague at best and didn't seem to work for me. Needless to say it started to get on my nerves at some point.
So I did what anyone in my situation would do. I decompiled the game and went on a mission to find out the exact spawn mechanics of the God of Evil, and now I am sharing this information so you don't have to endlessly search for it.
God Spawning Mechanics
I've seen people suggest that at most 3 gods can spawn in any run. Nothing in the code seems to suggest this. Gods do however have an interval at which they can appear. After a god spawns on a floor, no other gods can spawn for 5 floors. It is worth noting that sub-scene (arena) bosses are exempt from this rule, and can always spawn.
Some gods also get disabled on lower difficulties. Most notably the God of Evil only being enabled on the highest difficulty (Chaos). Because of this we'll focus on Chaos difficulty.
Gods also seem unable to spawn on the first floor on regular runs and before floor 10 on infinite runs. Interestingly the code has a segment that prevents the God of Evil from spawning on infinite mode before floor 20. Infinite mode seems to be designated as Nightmare difficulty internally however, which would mean the God of Evil can't even spawn there to begin with.
Disregarding infinite mode, we now focus on normal mode.
All gods have a range of floors they can spawn in. For God of Evil on Chaos difficulty this is floor 15-20. I've seen nothing in the code to suggest the God of Evil actually has a lower spawn chance than the other gods. It simply takes a random pick from all gods that have their spawn conditions satisfied, which at this point would be God of Evil, God of Contract, and God of Vengeance.
Now, assuming you are on a floor in the 15-20 range, the change for an arena to spawn is 15%.
The chance for the area to then spawn a god is 50%. I'm not sure how the game treats a god you've picked before the run, so let's assume you picked none. That means 3 gods can spawn in that arena.
This compounds to:
3/10 * 1/2 * 1/3 = 2.5% chance for the God of Evil to spawn.
This is low, but not impossibly so. Especially not if you quit to main menu to prevent going down floors.
TLDR: What to Do
Play on Chaos difficulty (the highest difficulty) and grind floors 15-20 for arenas.
Do not play on infinite mode.
Note: Quit to main menu before exiting a floor to generate a new floor without actually going down.