The outflow efficiency (η) from black hole (BH) accretion disc systems is known to depend upon both the BH spin (a) and the amount of large-scale magnetic flux threading the BH and disc. Semi-analytical flux-trapping models suggest retrograde BHs should trap much more large-scale magnetic flux near the BH leading to much higher η than for prograde BHs. We self-consistently determine the amount of large-scale magnetic flux trapped by rapidly spinning (a=−0.9 and 0.9) BHs using global 3D time-dependent non-radiative general relativistic magnetohydrodynamic simulations of thick (h/r≈ 0.3–0.6) discs. We find that BH-trapped flux builds up until it is strong enough to disrupt the inner accretion disc. Contrary to prior flux-trapping models, which do not include the back-reaction of magnetic flux on the disc, our simulations show prograde BHs trap more magnetic flux, leading to about three times higher η than retrograde BHs for |a|= 0.9. Both spin orientations can produce highly efficient jets, η∼ 100 per cent, with increasing η for increasing disc thickness. The similarity of η for prograde and retrograde BHs makes it challenging to infer the sign of a based on jet energetics alone.