As one of the primary backgrounds to $pp \to t\bar{t}H(H\to b\bar{b})$, the QCD process of $t\bar{t}b\bar{b}$ hadroproduction demands very accurate theoretical predictions and estimates of uncertainties. On top of that, the capacity of properly identifying prompt $b$-jets is beneficial for many analyses. In this contribution we discuss state-of-the-art predictions for $t\bar{t}b\bar{b}$ production with dilepton decays at the LHC, as obtained from full off-shell NLO QCD calculations. We evaluate the dominant uncertainties of the calculation and the impact of the off-shell effects on fiducial cross sections. Furthermore, we explore a kinematic prescription for the categorisation of prompt $b$-jets.