  Tables of sizes of random complete arcs in the plane $PG(2,q)$ are given. The
sizes are close to the smallest known sizes of complete arcs in $PG(2,q)$, in
particular, to ones constructed by Algorithm FOP (fixed order of points). The
random arcs are obtained in the region $\{3\leq q\leq 46337,~q \mbox{prime}\}$.
