We examine welfare outcomes for non-market allocation mechanisms of public housing. We make use of a quasi-natural experiment in Amsterdam where public houses are allocated through lotteries to households already on waiting lists. We demonstrate that a lottery reduces waiting time by 8.5 years and offers benefits to lottery winners. Households in public housing value these benefits at about €875 per year. We demonstrate that the lottery experiment resulted in different – and less efficient – household and public housing matches than those based on waiting time. Using a structural approach, the annual welfare loss associated with lottery due to an inefficient match is estimated to be €275 for each public house. JEL: C78 D82 R21 R31.