We present a serendipitous multiwavelength campaign of optical photometry simultaneous with Integral X-ray monitoring of the 2015 outburst of the black hole V404 Cyg. Large-amplitude optical variability is generally correlated with X-rays, with lags of order a minute or less compatible with binary light travel time-scales or jet ejections. Rapid optical flaring on time-scales of seconds or less is incompatible with binary light-travel time-scales and has instead been associated with synchrotron emission from a jet. Both this rapid jet response and the lagged and smeared one can be present simultaneously. The optical brightness is not uniquely determined by the X-ray brightness, but the X-ray/optical relationship is bounded by a lower envelope such that at any given optical brightness there is a maximum X-ray brightness seen. This lower envelope traces out a F_opt ∝ F_X^{0.54} relation that can be approximately extrapolated back to quiescence. Rapid optical variability is only seen near this envelope, and these periods correspond to the hardest hard X-ray colours. This correlation between hard X-ray colour and optical variability (and anticorrelation with optical brightness) is a novel finding of this campaign, and apparently a facet of the outburst behaviour in V404 Cyg. It is likely that these correlations are driven by changes in the central accretion rate and geometry.