Histogram of the initial inclination of cusp binaries: the upper panel shows results for γ = 0.5 and the lower panel shows results for γ = 1.5. Approximately 0.25%–1% of the systems are likely to merge while on the main sequence. Similar to the case of stellar-disk binaries, all "mergers" occur for high mutual inclinations and already on the first Kozai–Lidov cycle. The number of evaporated systems is higher in the steep density profile model case, as expected on the basis of Equation (1). Vertical axes are normalized to the total number of simulated binaries.