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Abstract Double detonations of sub-Chandrasekhar-mass white dwarfs (WDs) in unstably mass-transferring double WD binaries have become one of the leading contenders to explain most Type Ia supernovae. However, past theoretical studies of the explosion process have assumed relatively ad hoc initial conditions for the helium shells in which the double detonations begin. In this work, we construct realistic C/O WDs to use as the starting points for multidimensional double detonation simulations. We supplement these with simplified one-dimensional detonation calculations to gain a physical understanding of the conditions under which shell detonations can propagate successfully. We find that C/O WDs ≲1.0M_⊙, which make up the majority of C/O WDs, are born with structures that can support double detonations. More massive C/O WDs require ∼10⁻³M_⊙of accretion before detonations can successfully propagate in their shells, but such accretion may be common in the double WD binaries that host massive WDs. Our findings strongly suggest that if the direct impact accretion stream reaches high enough temperatures and densities during mass transfer from one WD to another, the accreting WD will undergo a double detonation. Furthermore, if the companion is also a C/O WD ≲1.0M_⊙, it will undergo its own double detonation when impacted by the ejecta from the first explosion. Exceptions to this outcome may explain the newly discovered class of hypervelocity supernova survivors.