Cracked had an article on this a while ago. Quantum Immortality
<the towel>
I like this! 
The webcomic “Wayward Sons” just introduced a character whose power is affecting luck like that. His name is K’rma.
(Wayward Sons’ premise is a group of beings from another universe who were tunneled into ours. The power fluxes involved gave them alterations in physical appearance and what passes for superpowers. They were worshipped.)
If these events always fall in his favor, wrongdoers just pop before he needs to hear about it.
Reminds of the sci-fi Terry Prachett book The Dark Side of the Sun, in which the main dude always has luck in his favor because probability math and anti-death food
quantum man causes a vacuum metastability event because long words which closes this unvierse and creates another in which the CCTV was blanked by cosmic rays
So he’ll always get the eigenstate that will benefit him the most?
Never mind crime fighting; have him create a working theory of quantum gravity, invent advanced molecular nanotechnology, solve all of the Millennium Prize mathematics problems, cure all forms of cancer, cure aging, cure diseases in general, somehow luck his way to world peace, and make humanity into a space-faring race.
The OP was not clear, but I have been very clear since then. It doesn’t mean he has perfect luck or godlike powers.
He has single quantum events happen and those single events must be the same for all particles involved. So having a block of particles tunnel through something, or all not emit a beta particle for the next n seconds is fine.
Affecting the course of trillions of particles in trillions of different ways, not ok.
And no it’s not that he gets to manually choose eigenstates, or for some bizarre reason has precognition so knows what eigenstate will lead to what future.