  Randomized controlled trials are susceptible to imbalance on covariates
predictive of the outcome. Rerandomization and deterministic treatment
assignment are two proposed solutions. This paper explores the relationship
between rerandomization and deterministic assignment, showing how deterministic
assignment is an extreme case of rerandomization. The paper argues that in
small experiments, both fully randomized and fully deterministic assignment
have limitations. Instead, the researcher should consider setting the
rerandomization acceptance probability based on an analysis of covariates and
assumptions about the data structure to achieve an optimal alignment between
randomness and balance. This allows for the calculation of minimum p-values
along with valid permutation tests and fiducial intervals. The paper also
introduces tools, including a new, open-source R package named fastrerandomize,
to implement rerandomization and explore options for optimal rerandomization
acceptance thresholds.
