We explore structure formation in the dark ages ($zsim 30-6$) using two well-known methods for initializing cosmological $N$-body simulations. Overall, both the Zeldovich approximation (za) and second order Lagrangian perturbation theory (lpt) are known to produce accurate present-day dark matter halo mass functions. However, since the lpt method drives more rapid evolution of dense regions, it increases the occurrence of rare massive objects -- an effect that is most pronounced at high redshift. We find that lpt produces more halos that could harbor Population III stars and their black hole remnants, and they produce them earlier. Although the differences between the lpt and za mass functions are nearly erased by $z=6$, this small boost to the number and mass of black holes more than doubles the reionized volume of the early Universe. We discuss the implications for reionization and massive black hole growth.
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