Upon further reflection, multiple worst-case streaks in the same fight are important thing to count. My reason for dropping them had been that you're already dead, so why count subsequent streaks? Strictly speaking, that isn't true though, so we can't remove them from the calculation. If I put them back into my calculation, it is likely that I will arrive at numbers similar to yours.

I would still argue that 10 is the correct number of hits to consider unless we start getting into expected shield chance, etc.

Your simulated numbers are certainly within the ballpark for what you predicted originally. Given the inherent imprecision in IEEE double, it seems like the difference could almost be accounted for by accumulated rounding error.

With that said, I would *really* like to know what is wrong with the derivation I made. It seems to be supported by the laws of probability, and yet it doesn't match what our simulations are telling us.

Yeah if we assumed that you died after 10 unmitigated hits that would be a correct assumption. Given that its across 20 seconds my calculations were more geared to showing how often it occurs without killing you.

Likewise, I'd like to know what we're doing wrong with the calculations. I just don't get why its giving us <0.1% probability per fight, yet showing up approximately/at least once every 3 weeks (30 fights). My brain hurts at this stage so I'm gonna take a break and look at it again in the morning.