Being able to count worlds in the manner you describe is apparently not easy to justify. If I recall correctly, this is actually a pretty thorny epistemological problem with the theory. IIRC the current response among Many Worlds people is that either (1) it doesn't really matter because there is no reason to believe that probabilities are "real" in the first place, or (2) attempting to show that if you did insist on finding a metric that looked like probability, it would provably have to be the Born probability (see https://arxiv.org/abs/1405.7577). All this stuff is way over my head so I have no way of evaluating whether it's persuasive or not, but it does at least seem to be contentious among physicists.

Or an infinity of worlds, with two thirds of them with heads, and one third with tails.