This paper introduces the concept of a numeraire e-variable, a special e-variable that satisfies a key property under any e-variable. The numeraire e-variable is strictly positive and satisfies $ E_Q[X/X^*] \leq 1 $ for every e-variable X. It is log-optimal in the sense that $ E_Q[\log(X/X^*)] \leq 0 $. The numeraire identifies a sub-probability measure $ P^* $ via the density $ dP^*/dQ = 1/X^* $. This measure $ P^* $ is shown to coincide with the reverse information projection (RIPr) when additional assumptions are made. The paper establishes that $ P^* $ is a natural definition of the RIPr in the absence of any assumptions on P or Q. The paper also provides tools for finding the numeraire and RIPr in concrete cases, and discusses several nonparametric examples where the numeraire and RIPr can be identified despite not having a reference measure. The results have interpretations outside of testing, yielding the optimal Kelly bet against P if we believe reality follows Q. The paper also presents a more general optimality theory that goes beyond the ubiquitous logarithmic utility, focusing on certain power utilities leading to reverse Rényi projections in place of the RIPr. The paper concludes with a more general optimality theory that goes beyond the ubiquitous logarithmic utility, and shows that the method of universal inference is inadmissible.This paper introduces the concept of a numeraire e-variable, a special e-variable that satisfies a key property under any e-variable. The numeraire e-variable is strictly positive and satisfies $ E_Q[X/X^*] \leq 1 $ for every e-variable X. It is log-optimal in the sense that $ E_Q[\log(X/X^*)] \leq 0 $. The numeraire identifies a sub-probability measure $ P^* $ via the density $ dP^*/dQ = 1/X^* $. This measure $ P^* $ is shown to coincide with the reverse information projection (RIPr) when additional assumptions are made. The paper establishes that $ P^* $ is a natural definition of the RIPr in the absence of any assumptions on P or Q. The paper also provides tools for finding the numeraire and RIPr in concrete cases, and discusses several nonparametric examples where the numeraire and RIPr can be identified despite not having a reference measure. The results have interpretations outside of testing, yielding the optimal Kelly bet against P if we believe reality follows Q. The paper also presents a more general optimality theory that goes beyond the ubiquitous logarithmic utility, focusing on certain power utilities leading to reverse Rényi projections in place of the RIPr. The paper concludes with a more general optimality theory that goes beyond the ubiquitous logarithmic utility, and shows that the method of universal inference is inadmissible.