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The coin flip conundrum - Po-Shen Loh

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When you flip a coin to make a decision, there's an equal chance of getting heads and tails. What if you flipped two coins repeatedly, so that one option would win as soon as two heads showed up in a row on that coin, and one option would win as soon as heads was immediately followed by tails on the other? Would each option still have an equal chance? Po-Shen Loh describes the counterintuitive math behind this question.

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Suppose that you were playing an abstract board game similar to the heads/tails game, except that it had four positions in this order: Start, B, C, and End. Suppose that on each turn, from any position except for End, there is a 50% chance of staying at that position and a 50% chance of moving to the next position. What is the average number of turns to move from Start to End?

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Meet The Creators

  • Educator Po-Shen Loh
  • Director Mimi Chiu
  • Script Editor Eleanor Nelsen
  • Producer Aaron Augenblick
  • Animator Mimi Chiu
  • Collaborator Andrea Janov , Zach Nelkin, Mark Paulson
  • Associate Producer Elizabeth Cox, Jessica Ruby
  • Content Producer Gerta Xhelo
  • Editorial Producer Alex Rosenthal
  • Narrator Addison Anderson
  • Fact-Checker Brian Gutierrez

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