Abstract: Recent discrepancies between theoretical predictions and experimental data in multi-lepton plus b-jets analyses for the tt¯W± process, as reported by the ATLAS collaboration, have indicated that more accurate theoretical predictions and high precision observables are needed to constrain numerous new physics scenarios in this channel. To this end we employ NLO QCD computations with full off-shell top quark effects included to provide theoretical predictions for the R=σtt¯W+/σtt¯W- cross section ratio at the LHC with s=13 TeV. Depending on the transverse momentum cut on the b-jet we obtain 2–3% theoretical precision on R, which should help to shed some light on new physics effects that can reveal themselves only once sufficiently precise Standard Model theoretical predictions are available. Furthermore, triggered by these discrepancies we reexamine the charge asymmetry of the top quark and its decay products in the tt¯W± production process. In the case of charge asymmetries, that are uniquely sensitive to the chiral nature of possible new physics in this channel, theoretical uncertainties below 15% are obtained. Additionally, the impact of the top quark decay modelling is scrutinised by explicit comparison with predictions in the narrow-width approximation.