> But it would still halt. Infinity is weird like that
What are you tring to say?
> The probability of having a 2:1 ratio of heads/tails - at some point - in an infinite sequence of fair flips is 1, is it not?
Yes, but "probability = 1" absolutely does not mean "will happen eventually" in pure mathematics. Infinity is weird like that.
The probability is less than 1, and in fact it exponentially goes to 0, since the halting condition can be modeled as a biased random walk [0].
[0] https://wiki.bbchallenge.org/wiki/Antihydra#Trajectory