The presence of asymmetric information makes the behavior of insurance markets very difficult to predict. But I argue that the increasing use of Big Data by insurers will not result in forecasts of loss that are so accurate that they eliminate uncertainty, and with it, the possibility of insurance. Big Data techniques might lead to a “flip” in informational asymmetry, resulting in a situation in which insurers know more about their customers than the latter know about themselves. But the effects of such a development could actually be benign. Finally, the article considers the potential for Big (or at least, More) Data to create new markets for spreading risks that are currently uninsurable.