Exact moments and probabilities for Wei's urn randomization model

We provide closed-form expressions for the probabilities in Wei's [1997. A class of designs for requential clinical trials. J. Amer. Statist. Assoc. 72, 382–386] urn randomization model, and develop a non recursive, exact variance expression, with extensions for K colors, and M:N randomization. Accuracy of the exact variance expression exceeds that of a previously published asymptotic expression.