Recent studies suggest that only three of the 12 brightest satellites of the Milky Way (MW) inhabit dark matter haloes with maximum circular velocity, Vmax, exceeding ∼30 km s−1. This is in apparent contradiction with the Λ cold dark matter (CDM) simulations of the Aquarius Project, which suggest that MW-sized haloes should have at least eight subhaloes with Vmax > 30 km s−1. The absence of luminous satellites in such massive subhaloes is thus puzzling and may present a challenge to the ΛCDM paradigm. We note, however, that the number of massive subhaloes depends sensitively on the (poorly known) virial mass of the MW, and that their scarcity makes estimates of their abundance from a small simulation set like Aquarius uncertain. We use the Millennium Simulation series and the invariance of the scaled subhalo velocity function (i.e. the number of subhaloes as a function of ν, the ratio of the subhalo Vmax to the host halo virial velocity, V200) to secure improved estimates of the abundance of rare massive subsystems. In the range 0.1 < ν < 0.5, Nsub(>ν) is approximately Poisson distributed about an average given by 〈Nsub〉 = 10.2 (ν/0.15)−3.11. This is slightly lower than that in Aquarius haloes, but consistent with recent results from the Phoenix Project. The probability that a ΛCDM halo has three or fewer subhaloes with Vmax above some threshold value, Vth, is then straightforward to compute. It decreases steeply both with decreasing Vth and with increasing halo mass. For Vth = 30 km s−1, ∼40 per cent of Mhalo = 1012 M⊙ haloes pass the test; fewer than ∼5 per cent do so for Mhalo ≳ 2 × 1012 M⊙ and the probability effectively vanishes for Mhalo ≳ 3 × 1012 M⊙. Rather than a failure of ΛCDM, the absence of massive subhaloes might simply indicate that the MW is less massive than is commonly thought.