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With out a STRENGTH D , NOT STD O_o weapon, what are the odds of killing the following or would be neccessary to kill it

Chaos Daemon Prince of Tzeentch w/ Invisibility, Feel No Pain (4+) and it doesn't get it's cover save.
Chaos Daemon Prince of Tzeentch w/ Invisibility, Feel No pain (4+) and it does get it's cover save

Chaos Daemon Prince of Tzeentch w/ Shrouding, 2++ Rerollable, Iron Arm (T8)
Chaos Daemon Prince of Tzeentch w/ Shrouding, 2++ Rerollable, Invisbility
Chaos Daemon Prince of Tzeentch w/ 3++ Rerollable from Grimoire and Iron Arm
Same but w/ 2++ Rerollable from Shrouding, It will not Die , Feel No Pain (4+)


I'm just trying to figure out odds right now and unsure where to start on this , mathematically. you don't have to do the equations, I'll do that, just unsure which equation to use.

Kill with what exactly?

I am assuming a BS4 S7 weapon vs T5 and no 3+ save from armour.

Hollismason wrote:
Chaos Daemon Prince of Tzeentch w/ Invisibility, Feel No Pain (4+) and it doesn't get it's cover save.

~4%

Hollismason wrote:
Chaos Daemon Prince of Tzeentch w/ Invisibility, Feel No pain (4+) and it does get it's cover save

~3%

Hollismason wrote:
Chaos Daemon Prince of Tzeentch w/ Shrouding, 2++ Rerollable, Iron Arm (T8)

0.62%

Hollismason wrote:
Chaos Daemon Prince of Tzeentch w/ Shrouding, 2++ Rerollable, Invisbility

0.39%

Hollismason wrote:
Chaos Daemon Prince of Tzeentch w/ 3++ Rerollable from Grimoire and Iron Arm

~5%

Hollismason wrote:
Same but w/ 2++ Rerollable from Shrouding, It will not Die , Feel No Pain (4+)

0.31% BTW IWND has no effect on the chance for shooting to wound (you regain wounds later after all so if there are no wounds...)

Hollismason wrote:
I'm just trying to figure out odds right now and unsure where to start on this , mathematically. you don't have to do the equations, I'll do that, just unsure which equation to use.

https://docs.google.com/spreadsheets/d/1D1XfuhXXioKlY9s3ITJY_qcSwmdIAbu7lHo3Mb5ya2Q/edit?usp=sharing
Have fun.