Optimal Stopping Time on a Minority Color in a 2-Color Urn Scheme

An urn contains \(2n + 1\) balls in two colors. The number of balls of a particular color is a random variable having binomial distribution with \( p = \frac{1}{2} \). We sample the urn removing balls one by one without replacement. Our aim is to stop the process maximizing the probability that the color of the last selected ball is the minority color. We give an algorithm for an optimal stopping time, evaluate the probability of success and its asymptotic behavior.