This chapter introduces one novel feature of the game Zombies and Survivors, that randomness is embedded within its definition. In the game of Zombies and Survivors, as zombies have limited intelligence, in each round, a given zombie moves toward the survivor along a shortest path connecting them. If there is more than one neighbor of a given zombie that is closer to the survivor than the zombie is, then they move to one of these vertices chosen uniformly at random. Results in the chapter focus on the analysis of the zombie number for several graph classes, such as cycles, hypercubes and toroidal grids. The chapter considers the zombie number of grids formed by products of cycles. Since the zombies' trajectories may depend on the survivor's trajectory and vice versa, it is convenient to formulate the strategy of each player a priori in a way that does not depend on the other player's choices.