We introduce random evolving lotteries to study preference for non‐instrumental information. Each period, the agent enjoys a flow payoff from holding a lottery that will resolve at the terminal date. We provide a representation theorem for non‐separable risk consumption preferences and use it to characterize agents' attitude to non‐instrumental information. To address applications, we characterize peak‐trough utilities that aggregate trajectories of flow utilities linearly but, in addition, put weight on the best (peak) and worst (trough) lotteries along each path. We show that the model is consistent with recent experimental evidence on attitudes to information, including a preference for gradual arrival of good news and the ostrich effect, that is, decision makers' tendency to prefer information after good news to information after bad news.