Dreicer generation is one of the main mechanisms of runaway electron generation in weakly ionized plasmas. It is often described as a diffusive flow from the Maxwellian core into high energies under the effect of the electric field. In this Letter we demonstrate a critical role of the binary nature of inelastic collisions in weakly ionized plasma during tokamak startup, where some electrons experience virtually no collisions during acceleration to the critical energy. We show that using the Fokker-Planck collisional operator can underestimate the Dreicer generation rate by several orders of magnitude.