The Equalization Probability of the Pólya Urn
Timothy C. Wallstrom · American Mathematical Monthly · 2012
We consider a Pólya urn, started with b black and w white balls, where b > w. We compute the probability that there are ever the same number of black and white balls in the urn, and show that it is twice the probability of getting no more than w − 1 heads in b + w − 1 tosses of a fair coin.