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Context: Thirteen years after the discovery of the first afterglows, the nature of dark gamma-ray bursts (GRB) still eludes explanation: while each ng-duration GRB typically has an X-ray afterglow, optical/NIR emission is only seen for 40-60% of them. Aim: Here we use the afterglow detection statistics of the systematic follow-up observations performed with GROND since mid-2007 in order to derive the fraction of "dark bursts" according to different methods, and to distinguish between various scenarios for "dark bursts". Method: Observations were performed with the 7-channel "Gamma-Ray Optical and Near-infrared Detector" (GROND) at the 2.2m MPI/ESO telescope. We used the afterglow detection rate in dependence on the delay time between GRB and the first GROND exposure. Results: For long-duration Swift bursts with a detected X-ray afterglow, we achieve a 90% (35/39) detection rate of optical/NIR afterglows whenever our observations started within less than 240\,min after the burst. Complementing our GROND data with Swift/XRT spectra we construct broad-band spectral energy distributions and derive rest-frame extinctions. e detect 25-40% "dark bursts", depending on the definition used. The faint optical afterglow emission of "dark bursts" is mainly due to a combination of two contributing factors: (i) moderate intrinsic extinction at moderate redshifts, and (ii) about 22% of "dark" bursts at redshift $>$5.