We report on a multiepoch campaign of rapid optical/X-ray timing observations of the superbright 2018 outburst of MAXI J1820+070, a black hole low-mass X-ray binary system. The observations spanned 80 d in the initial hard state and were taken with NTT/ULTRACAM and GTC/HiPERCAM in the optical (u_sg_sr_si_sz_s filters at time resolutions of 8-300 Hz) and with ISS/NICER in X-rays. We find (i) a growing anticorrelation between the optical and X-ray light curves, (ii) a steady, positive correlation at an optical lag of ~0.2 s (with a longer lag at longer wavelengths) present in all epochs, and (iii) a curious positive correlation at negative optical lags in the last, X-ray softest epoch, with longer wavelengths showing a greater correlation and a more negative lag. To explain these, we postulate the possible existence of two synchrotron-emitting components - a compact jet and a hot flow. In our model, the significance of the jet decreases over the outburst, while the hot flow remains static (thus, relatively, increasing in significance). We also discuss a previously discovered quasi-periodic oscillation and note how it creates coherent optical time lags, stronger at longer wavelengths, during at least two epochs.