Identifying the optimal set of individuals to first receive information (“seeds”) in a social network to maximize expected diffusion is a widely studied question in many settings. Several studies propose network-centrality-based heuristics to select seeds likely to increase diffusion. Here, we show that, for the classic independent cascade model of diffusion, either seeding a few more individuals at random can prompt a larger diffusion than optimal seeding or optimal seeding itself results in limited spread. These findings hold across a broad range of random networks and are supported by simulations on real-world networks.