Pólya’s Urn Model

Back in 2015, when I wrote a Mathematical Enchantments piece about the Pólya urn model, I made two videos about the model, showing how one can simulate the model quasirandomly. Quasirandom (or “average case”) simulation makes it clearer why the distribution at each level is uniform (unlike the bell-shaped distribution that one gets from tossing a fair coin repeatedly and keeping track of the number of heads). Both videos are based on Engel’s “abacus” approach to discrete probability. The first video shows what happens when we feed lots of chips into the Engel machine at the start; the second video shows what happens when feed chips into the Engel machine one at a time. One of the great features of Engel-machine computation is the confluence property, which guarantees that both styles of quasirandom simulation give the same end result.

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