The easiest fair games depend on equal, binary outcomes like flipping a coin or drawing a playing card that can only be either red or black. If a game depends on both players choosing an equally-probable outcome, how can one player have a massive advantage over the other?

Welcome to the Humble-Nishiyama Randomness Game, a variant of Walter Penney’s classic demonstration of the power of non-transitivity in simple games. In a straightforward transitive situation, A beats B and B beats C -- which means A beats C, too. But if A beats B, B beats C, and C beats A… we’ve gone non-transitive just like Rock, Paper, Scissors. By jumping into the non-transitive game loop at the most advantageous point, Player 2 can become an overwhelming favorite every time. It looks like dumb luck, but it’s really just smart math.

** SOURCES **

“Penney Ante: Counterintuitive Probabilities in Coin Tossing,” by RS Nickerson: http://www.math.unl.edu/~sdunbar1/Pro...

“Humble-Nishiyama Randomness Game - A New Variation on Penney's Coin Game,” by Steve Humble and Yutaka Nishiyama: http://citeseerx.ist.psu.edu/viewdoc/...

"Probability of a tossed coin landing on edge,” by Daniel B. Murray and Scott W. Teare: https://journals.aps.org/pre/abstract...

"Antibiotic-mediated antagonism leads to a bacterial game of rock–paper–scissors in vivo,” by Benjamin C. Kirkup & Margaret A. Riley: https://www.nature.com/articles/natur...

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