I don't want the player to feel competent and fearless, I want them to mess up badly and recover from the worst situation. I believe they will enjoy beating the odds stack against them and I also believe the characters should have abilities that reflect their desire to overcome

It makes me think a bit about the tension I feel playing a VLT. In the background is some random number generator that is going to decide whether I win or loose. I don't see the "dice roll", just the outcome of either having won or (more likely) lost my money. But I think part of what makes the tension rewarding is that I feel as though I have some kind of control when I'm pushing my luck. I can take my time deciding whether to push the button to start the next round or increase or decrease my bet. So, I believe, that you'll want to provide the player that sense of control in some way.

Aside from that, I'd recommend that you do some kind of prototype or graphing of the formula you're planning on using so you can see just how often the player will survive. Then you'll know whether you're on the right path or not.

Remove randomness and make clear, understandable rules.

I'm currently making a platformer engine and I first had complex rules that determined if the player get adherence or not depending on its speed and angle, but it gave the impression it was semi random to the player (the rules were too complex to be easily understandable), thus was frustrating. A good game is an equilibrium between expected behaviors and surprises, and i think gameplay mechanics should be mostly made of expected behaviors, while the surprises are build into the level design, art, enemies...

Even for RPG i think randomness in damages should be removed, or taking effect for only 5% of the total damages. Random critical strike/dodges are one of the worst thing...

The difference between you and me xxFuttBucker444 is that my idea doesn't potentially get people killed with strange platforming physics. My concept is a reward and random rewards are good and addicting according to https://www.google.com/?gws_rd=ssl#q=pigeon+addicted+to+gambling+experiment. Sure this article is about gambling but random rewards are addicting so random surviving will be addicting too.

Matter of fact one of my favorite game called mutant alien assault was a highly praised game based completely around random weapon pick ups. You didn't know which weapon you would get but all of them are way better than the pistol and my game follow a similar design. Surviving a death blow is better than death and restarting over. It was only when super mutant alien assault came around where the randomness starting working against it because explosive weapons including the my much loved grenade launcher could hurt you and reviewers made it clear they did not like it.

I originally said "a random chance of death" but now I take that back. I'm claiming "a random second wind". Randomness or not I still need to do testing but these are my justifications.