# The Coin-Toss Theory. The 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.

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The Coin-Toss Theory

The 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 Holmes, and Richard Montgomery tried to prove these thoughts wrong. 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” 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 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. So if it started heads up, it landed heads up. They were able to get this result 100% of the time. They were able to get this result 100% of the time.

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

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

Examples

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

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

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

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