In theories with universal extra dimensions (UED), the γ1 particle, first excited state of the hypercharge gauge boson, provides an excellent dark matter (DM) candidate. Here, we use a modified version of the SuperBayeS code to perform a Bayesian analysis of the minimal UED scenario, in order to assess its detectability at accelerators and with DM experiments. We derive, in particular, the most probable range of mass and scattering cross sections off nucleons, keeping into account cosmological and electroweak precision constraints. The consequences for the detectability of the γ1 with direct and indirect experiments are dramatic. The spin-independent cross section probability distribution peaks at ˜10-11pb, i.e. below the sensitivity of ton-scale experiments. The spin-dependent cross section drives the predicted neutrino flux from the center of the Sun below the reach of present and upcoming experiments. The only strategy that remains open appears to be direct detection with ton-scale experiments sensitive to spin-dependent cross sections. On the other hand, the LHC with 1fb-1 of data should be able to probe the current best-fit UED parameters.