The Coin-Toss TheoryThe Coin-Toss Theory

The Coin-TossThe Coin-Toss

Has been known to be random.Has been known to be random. Has been known to be 50-50.Has been known to be 50-50. But a study by Persi Diaconis, Susan But a study by Persi Diaconis, Susan

Holmes, and Richard Montgomery Holmes, and Richard Montgomery tried to prove these thoughts wrong.tried to prove these thoughts wrong.

““The Coin Flipper”The Coin Flipper”

First they designed a machine called the First they designed a machine called the “Coin Flipper”“Coin Flipper”

It was created to flip a coin into a cup It was created to flip a coin into a cup making it land in the state it was flippedmaking it land in the state it was flipped

So if it started heads up, it landed heads So if it started heads up, it landed heads up.up.

They were able to get this result 100% of They were able to get this result 100% of the time.the time.

““The Coin Flipper”The Coin Flipper” With these results, they concluded that With these results, they concluded that

coin-tossing is physics, not random.coin-tossing is physics, not random.

The ResearchThe Research

They used a lot of physics, math, a They used a lot of physics, math, a motion capture camera, and a bunch motion capture camera, and a bunch of random experimentation.of random experimentation.

They came up with a 31 page paper They came up with a 31 page paper to try to prove their theory. to try to prove their theory.

Dynamical Bias in the Coin TossDynamical Bias in the Coin Toss

ExamplesExamples

Findings in their Findings in their ExperimentsExperiments

If the coin is tossed and caught, it has about a If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was 51% chance of landing on the same face it was flipped. (If it starts out as heads, there's a 51% flipped. (If it starts out as heads, there's a 51% chance it will end as heads). chance it will end as heads).

If the coin is spun, instead than tossed, it can If the coin is spun, instead than tossed, it can have a much larger than 50% chance of ending have a much larger than 50% chance of ending with the heavier side down. Spun coins can have with the heavier side down. Spun coins can have a "huge bias" (some spun coins ended up falling a "huge bias" (some spun coins ended up falling tails-up 80% of the time). tails-up 80% of the time).

If the coin is tossed and allowed to bounce on If the coin is tossed and allowed to bounce on the floor, this probably adds randomness. the floor, this probably adds randomness.

Findings in their Findings in their ExperimentsExperiments

If the coin is tossed and allowed to bounce on If the coin is tossed and allowed to bounce on the floor and it starts to spin, which happened in the floor and it starts to spin, which happened in some experiments, the spinning bias probably some experiments, the spinning bias probably comes into play. comes into play.

A coin will land on its edge around 1 in 6000 A coin will land on its edge around 1 in 6000 throws.throws.

The same initial coin-flipping conditions produce The same initial coin-flipping conditions produce the same coin flip result, which can give you the same coin flip result, which can give you certain amount of determinism to the coin flip.certain amount of determinism to the coin flip.

ReferencesReferences

http://www.codingthewheel.com/archhttp://www.codingthewheel.com/archives/the-coin-flip-a-fundamentally-unfives/the-coin-flip-a-fundamentally-unfair-propositionair-proposition

http://www-stat.stanford.edu/~susan/http://www-stat.stanford.edu/~susan/papers/headswithJ.pdfpapers/headswithJ.pdf