Random search can be an effective strategy due to bounded rationality. As pointed elsewhere on this thread, the expected utility of a mixed strategy is not greater than the maximum utility of the pure strategies in its support. But determining the utility of the pure strategies may not be possible. For example, an ant cannot carry the neural machinery necessary to remember everything it has seen, or to use such information to determine with accuracy the most likely direction to food -- but it can carry sufficient neural machinery to perform a random walk.