Is my Half Orc Barbarian invulnerable to death by falling?

Question

Forgive me if I've botched any math, but here's the situation I've found myself in (assuming 4th level):

Falling damage caps out at 20d6 at terminal velocity. Kronan the Barbarian has 55 Max HP currently. (+3 CON mod, three great HP rolls at level-up.) That means that from Max HP, a fall of any height has approximately a 0.00% chance of instant lethality. And he has Relentless Endurance, so he has a 100% chance of getting up and walking after the fall if he hasn't expended it. He's also got the Bear Totem Path, which cuts non-psychic damage in half when he is raging. That means that even if he has spent his Resilience, his chance of death is about 0% as long as he was conscious and raging before he hit the ground. And he can apparently do this repeatedly as long as he manages to keep at least 1 Hit Point.

Is this correct? Is this character really capable of circumventing death by falling? Can this character willfully jump from the top of a skyscraper multiple times in succession and live to tell about it? Or have I made some mistake?

Answer 1

Yes, your Half-Orc Barbarian is nigh-invulnerable to death by falling, as a consumable resource.

Remember that your relentless endurance and your rages both recharge on a long rest. So four times per long day you can take a header off a skyscraper and be pretty sure of living.^* (At least for the moment.)

Also, your Bard and Wizard friends can do this, too. Along with five of their friends.

It's called feather fall.

Point being: you can spend your consumables on base jumping without a parachute, and they can spend theirs on doing it with a parachute. You just get a bigger adrenaline rush out of it. (And the accompanying exhaustion.)

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^{*- How sure? Assuming you start at 6HP or more it's impossible to instantly die from rage-jumping massive damage: the fall would need to do 61 damage after reduction, which is impossible for the mere 20d6 you're looking at. You may be at 0HP and looking at some death saves, the odds on which are not nearly as good**}.

^{Relentless-jumping is a little riskier on the front-end, but you do walk away. At full HP you're looking at ~0.0000003% chance of instantly dying of massive damage, at 1HP you're looking at ~13.4%, if I'm reading my first anydice program correctly. It's non-linear between those two endpoints, and in your favor. Check out the graph if you want to see.}

^{**- The probability of surviving death saves unassisted is ~60%.}

Answer 2

Yes: Your barbarian has virtually no chance of dying

I was intrigued by your claim of "his chance of death is about 0% as long as he was conscious and raging before he hit the ground," and assuming he is at Max HP = 55.

In the PMF of 20d6 below, you can see that there is very little possibility of rolling >110HP on 20d6 (in fact, that possibility is about 0.00001).