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Studies of crime and place have long sought to estimate the role of randomness in crime concentration at place. Traditionally, simulations assume that crime incidents occur randomly across microgeographic units, such as block groups, street segments, and parcels, treating crime as a random selection of geographic units with replacement. This paper takes a different approach, modeling crime as a random selection of potential targets with replacement. Under this assumption, the resulting simulated patterns become pure reflections of the spatial distribution of potential targets. Using burglary data from Bexar County, TX, from 2017 to 2019, this study estimates the effects of randomness and target availability on crime concentration at place. By refining how randomness is conceptualized, this research contributes to a more precise understanding of the role of randomness in crime concentration and the influence of target availability on observed patterns. The results indicate that randomness and target availability account for more than half of the observed crime concentration at place. The findings have implications for crime prevention policies and suggest new directions for future research on crime and place.