  Efron [Biometrika 58 (1971) 403--417] developed a restricted randomization
procedure to promote balance between two treatment groups in a sequential
clinical trial. He called this the biased coin design. He also introduced the
concept of accidental bias, and investigated properties of the procedure with
respect to both accidental and selection bias, balance, and randomization-based
inference using the steady-state properties of the induced Markov chain. In
this paper we revisit this procedure, and derive closed-form expressions for
the exact properties of the measures derived asymptotically in Efron's paper.
In particular, we derive the exact distribution of the treatment imbalance and
the variance-covariance matrix of the treatment assignments. These results have
application in the design and analysis of clinical trials, by providing exact
formulas to determine the role of the coin's bias probability in the context of
selection and accidental bias, balancing properties and randomization-based
inference.
