Urn models provide some approaches for adaptive randomization. Here is an exercise that will help to explain this type of scheme. Suppose that there is one "A" ball and one "B" ball in an urn and the objective of the trial is the equal allocation between treatments A and B. Suppose that an "A" ball is blindly selected so that the first patient is assigned treatment A. Then the original "A" ball and another "B" ball are placed in the urn so that the second patient has a 1/3 chance of receiving treatment A and a 2/3 chance of receiving treatment B. At any point in time with $$n_A$$"A" balls and $$n_B$$"B" balls in the urn, the probability of being assigned treatment A is $$\dfrac{n_A}{(n_A+ n_B)}$$. The scheme changes based on what treatments have already been assigned to patients.
This type of urn model for adaptive randomization yields tight control of balance in the early phase of a trial. As $$n_A$$ and $$n_B$$ get larger, the scheme tends to approach simple randomization, so the advantage of such an approach occurs when the trial has a small target sample size.