Is it possible to measure the dispersion of ex-ante chances (i.e. chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex-ante chances in various areas with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk to become ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk like the overwhelming majority of the population but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.