Investments in housing influence migration and landscape construction, making them a key component of human-environment interactions. However, the strategic decision-making that builds residential landscapes is an underdeveloped area of research in evolutionary approaches to human behaviour. Our contribution to this literature is a theoretical model and an empirical test of this model using data from Ulaanbaatar, Mongolia. We develop a model of strategic housing decisions using stochastic dynamic programming (SDP) to explore the trade-offs between building, moving and saving over time, finding different trade-offs depending on optimization scenarios and housing costs. Household strategies are then estimated using data on 825 households that settled in the Ger districts of Ulaanbaatar between 1942 and 2020. The Ger districts are areas of self-built housing that feature both mobile dwellings (gers) and immobile houses (bashins). Using approximate Bayesian computation (ABC), we find the parameters of our dynamic programming model that best fit the empirical data. The model is able to capture the time horizon of housing changes and their bi-directionality, showing that moving from a fixed to mobile dwelling can also be an optimal strategy. However, the model underpredicts household persistence in dwelling types. We discuss deviations from model predictions and identify a more detailed exploration of risk and population mixes of strategies as key steps for future research.