I think it is important to clarify the meaning of "chance", as you refer to it.
If I say that the behavior of a flipped coin is almost certainly deterministic, the remaining uncertainty is not part of the system, it is caused by my inability to predict the outcome. This is not the kind of "chance" that you are referring to.
The type of "chance" related to quantum immortality is the probability attached to non-zero quantum wave-function amplitudes.
It is not enough for there to be a conceptual "chance" that quantum wave-functions could influence the outcome of a coin toss. There must be actual reachable sequences of quantum state sets, all with non-zero wave-function amplitudes, that result in alternate outcomes.
It may also not be enough to utilize a hypothetical model of the quantum wave-functions. It may be possible that real low probability wave-functions don't result in universe splits. For example, those world-lines might merge with higher probability world lines, or there might be resolution limits set by the holographic universe, or by quantum foam noise.
With these restriction and granting (just for this argument) that the MWI is the right way to think about the universe, I'll agree with your statment:
"even the most infinitesimal chances are guaranteed to come up somewhere."
I understand this, but thanks for the clarification regardless.
I had an incredibly frustrating conversation this morning trying to explain the idea of quantum immortality to someone whose understanding of MWI begins and ends at pop sci fi movies. I think I've identified the main issue that I wasn't covering in enough depth (continuity of identity between near-identical realities) but I was wondering whether anyone has ever faced this problem before, and whether anyone has (or knows where to find) a canned 5 minute explanation of it.