Polya urn scheme

The Polya urn scheme is a process that models how the likelihood of future outcomes can change based on past results. Imagine an urn containing balls of different colors. Each time you draw a ball, you note its color, then return it to the urn along with additional balls of the same color. Over time, this increases the chance of drawing that color again, creating a reinforcing cycle. This process captures phenomena where popular choices become even more likely, illustrating concepts like chance, learning, and feedback in probabilistic systems.