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The Coin-Toss Theory

The Coin-Toss Theory. The Coin-Toss. Has been known to be random. Has been known to be 50-50. But a study by Persi Diaconis, Susan Holmes, and Richard Montgomery tried to prove these thoughts wrong. “The Coin Flipper”. First they designed a machine called the “Coin Flipper”

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The Coin-Toss Theory

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  1. The Coin-Toss Theory

  2. The Coin-Toss • Has been known to be random. • Has been known to be 50-50. • But a study by Persi Diaconis, Susan Holmes, and Richard Montgomery tried to prove these thoughts wrong.

  3. “The Coin Flipper” • First they designed a machine called the “Coin Flipper” • It was created to flip a coin into a cup making it land in the state it was flipped • So if it started heads up, it landed heads up. • They were able to get this result 100% of the time.

  4. “The Coin Flipper” • With these results, they concluded that coin-tossing is physics, not random.

  5. The Research • They used a lot of physics, math, a motion capture camera, and a bunch of random experimentation. • They came up with a 31 page paper to try to prove their theory. • Dynamical Bias in the Coin Toss

  6. Examples

  7. Findings in their Experiments • If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was flipped. (If it starts out as heads, there's a 51% chance it will end as heads). • If the coin is spun, instead than tossed, it can have a much larger than 50% chance of ending with the heavier side down. Spun coins can have a "huge bias" (some spun coins ended up falling tails-up 80% of the time). • If the coin is tossed and allowed to bounce on the floor, this probably adds randomness.

  8. Findings in their Experiments • If the coin is tossed and allowed to bounce on the floor and it starts to spin, which happened in some experiments, the spinning bias probably comes into play. • A coin will land on its edge around 1 in 6000 throws. • The same initial coin-flipping conditions produce the same coin flip result, which can give you certain amount of determinism to the coin flip.

  9. References • http://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfair-proposition • http://www-stat.stanford.edu/~susan/papers/headswithJ.pdf

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