Seance-room and other large-scale psychokinetic phenomena have fascinated humankind for decades. Experimental research has reduced these phenomena to attempts to influence (a) the fall of dice and, later, (b) the output of random number generators (RNGs). The meta-analysis combined 380 studies that assessed whether RNG output correlated with human intention and found a significant but very small overall effect size. The study effect sizes were strongly and inversely related to sample size and were extremely heterogeneous. A Monte Carlo simulation revealed that the small effect size, the relation between sample size and effect size, and the extreme effect size heterogeneity found could in principle be a result of publication bias.