A fundamental question for Everettians is whether they can formulate a many-worlds interpretation of quantum theory which explains why, amongst all possible types of intelligent creature with all possible types of evolutionary and experimental history, we find ourselves among those whose histories apparently confirm Copenhagen quantum mechanics. Since the theory clearly allows that we could have found ourselves otherwise, the answer has to be probabilistic. Everettians then need to supply some account of how probability is or can be attached to an apparently deterministic theory. I argue that it cannot arise through any of the various notions of subjective uncertainty advocated by Saunders, Wallace, Vaidman and Greaves, among others, since none of these notions are valid. Nor could an adequate notion of probability be inferred from any account of the caring weights that we, as hypothetical rational Everettian agents, should use when considering the welfare of our Everettian successors even if a unique rational strategy were to exist, which I argue is not the case. A proposition of the desired form could simply be postulated, but at the price of reducing the entire interpretation probability postulate, preferred basis, and interpretation of basis states --to unsupported and maybe untestable hypotheses about consciousness. On the brighter side, I describe a new proposal for solving the measurement problem by proposing a definite mathematical structure for possible branching worlds, which appears to have the advantages claimed for Everettian ideas (in particular, respect of Lorentz invariance and of conservation laws), without the interpretational and scientific difficulties. I also note one subtle distinction between Everettian and standard accounts of evolution, which implies that (in principle, albeit not necessarily in practice) it could be possible to distinguish between the theories.