The Eternal Triangle: UNO for Three

Basic Theory

The syncopated dynamics of three-player UNO are more simply defined by the Feigenbaum constants α and δ. Using the simple bifurcation diagrams found below, you can see an example of how game dynamics progress where x = the number of cards in the discard pile and r = the number of turns in the game.

This particular model displays how a player with a hand with 59% yellow cards and 31% red cards would expect the makeup of his hand to change from moves 24 to 40. Grey areas of the diagram indicate predictions beyond the event horizon. A reassement of the bifurcation at a later point (say, at move 36) would provide greater clarity (below). Note the unpredictability of green cards in both models.

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