Stochasticity in collisional growth of cloud droplets is studied in a box model using the super-droplet method (SDM). The SDM is compared with direct numerical simulations and the master equation. We use the SDM to study fluctuations in autoconversion time and the sol-gel transition. We determine how many computational droplets are necessary to correctly model expected number and standard deviation of autoconversion time. Also, growth rate of lucky droplets is determined and compared with a theoretical prediction. Size of the coalescence cell is found to strongly affect system behavior. In small cells, correlations in droplet sizes and droplet depletion affect evolution of the system. In large cells, unrealistic collisions between rain drops, caused by the assumption that the cell is well-mixed, become important. Maximal size of a volume that is turbulently well-mixed with respect to coalescence is estimated at Vmix = 1.05 · 10−2 cm3. It is argued that larger cells can be considered approximately well-mixed, but only through comparison with fine-grid simulations. In addition, validity of the Smoluchowski equation is tested. Discrepancy between the SDM and the Smoluchowski equation is observed if droplets are initially relatively small. This implies that cloud models that use the Smoluchowski equation might produce rain too soon.