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There will be a universe where you never ever die
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This is not strictly true. It would only be the case in a universe where the only causes of death were quantum machine gun events like the one you describe above. That one relies on you having a finite chance of survival in every event. There are certain events for which everybody's chance of dying is exactly 1.
To give an example of what I mean, take a modified version of your experiment. Lets assume that your original experiment says that if the nuclear coin toss flips heads, you get shot in the head and if it flips tails, you don't. Now lets change it to heads you get shot in the head, tails you get your head chopped off. Now all subsequent universes result in you dying.
"On a long enough timeline, the survival rate for everyone drops to zero." - Fight Club