This Is NOT 50/50

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: ~sdunbar1/ProbabilityTheory/BackgroundPapers/Penney ante/ “Humble-Nishiyama Randomness Game - A New Variation on Penney’s Coin Game,” by Steve Humble and Yutaka Nishiyama: “Probability of a tossed coin landing on edge,” by Daniel B. Murray and Scott W. Teare: “Antibiotic-mediated antagonism leads to a bacterial game of rock–paper–scissors in vivo,” by Benjamin C. Kirkup & Margaret A. Riley: *** LINKS *** Vsauce2 Links Twitter: Facebook: Hosted and Produced by Kevin Lieber Instagram: Twitter: Podcast: Research And Writing by Matthew Tabor Editing by AspectScience Huge Thanks To Paula Lieber Get Vsauce’s favorite science and math toys delivered to your door! Select Music By Jake Chudnow: #education #vsauce2