Polya's Urn model

Polya's Urn model is a probability process where an urn contains balls of different colors. Each step involves randomly drawing a ball, then returning it to the urn, along with additional balls of the same color. This reinforcement means that colors drawn early become more likely to be drawn again later, leading to "rich-get-richer" dynamics. The process illustrates how initial randomness can influence long-term outcomes, making it useful for studying phenomena like learning, diffusion, or popularity growth, where the likelihood of an event increases with its prior occurrence.