Coin Flips Aren’t 50/50

“What? Are you crazy? There’s two sides to a coin so you have 50/50 chance of it ending on either heads or tails.”

Yeah, yeah, okay cool it. I know we all grew up learning that if you flip a coin then you have an even chance of it landing on either side. So it’s kind of odd to think that isn’t totally true.

What do you mean?

Persi Diaconis, a math and statistics professor at Stanford, decided to put the idea of coin tosses to a test in his paper Dynamical Bias in the Coin Toss. The experiment was done using a mechanical spring that tossed the coins evenly in the air each time. Funny thing is with this machine they were able to make heads come up 100% of the time if the coin started on heads. Source.

Of course, no person can flip a coin perfectly so they came up with some pretty math-y looking theorems. Source.theorem 1 theorem 2 theorem 3 theorem 4

They then put it to the test, they had the mechanism act more like a real flip. It didn’t come out 50/50 but it was close. It 51/49 with the higher probability going to the side of the coin that started up. Source.

That’s it? 51/49? That’s nothing!

I’m not done. There was another part of the test where coins were spun to see if it made a difference. Turns out it did, especially with pennies. If a penny is spun it is an 80% chance that the penny will land tails up. It’s because Lincoln’s head is heavier than the monument on the back. Source.

So what does spinning coins do with flipping coins?

Well the study didn’t look at the 3rd confounding variable.

Yes, if I flip a penny I have 51/49 chance of it ending up either way depending what side I started up. If I spin that same penny I have an 80% chance of it landing tails. What happens if I flip the penny and it spins on the ground before stopping?

I’d do that math but I’m not too great at it.

I hope you enjoyed this post and remember this when making a bet with a coin flip.

5 thoughts on “Coin Flips Aren’t 50/50

  1. Millie Rachel Dweck

    This is so cool! I would have never thought that a coin flip would not have been even! I guess that is why people use a quarter rather than a penny to flip; it is the closest to an even playing field. I find it interesting that the coin is a universally used tool that people rely on to make a decision, thinking it is a 50/50 chance. I guess in todays time, we can use websites like this to digitally flip the coin for a true 50/50 chance! Interesting blog! Great job!

  2. Stephanie Ann Loesch

    I would never even have thought to question this commonly accepted concept as I have completed many probability problems using coin tosses in which I had to assume the probability of the penny landing on heads or tails was 50:50. After you mentioned that the side of the penny with Lincoln’s head is heavier, I really became intrigued. Why do such accepted truths continue on without more of us questioning them? This relates to scientific knowledge as theories and information are accepted for the time in which they are not proven wrong. A team of Stanford and UC- Santa Cruz researchers claim that the side in which the penny starts on before it is flipped is most likely the side the penny will land on. They decided this after analyzing photographs from a high-speed camera. Holmes, a Stanford professor, claims bias is created when a person decides to flip a coin on a certain side. I have decided to be much more open to questioning accepted concepts after looking at this blog and other research.
    http://phys.org/news/2009-10-tails-key-variables.html

  3. Alana Marie D'agnese

    I found this post very interesting. When you flip a coin you usually know which side you want it to land on. I wonder is somehow you sub-consciously flip it in a way to try and make it land on heads or tails. It seems like a stretch but anything’s possible. I think it’s crazy how a penny will land tails up 80% of the time. I wonder what the ratios are for other coins like quarters or nickels. Since change is constantly dropped and passed around, a third variable that could affect these experiments is the amount of dirt on the coin, making it heavier.

  4. David Tyler Bond

    When reading your title, I thought that there is no way this person is right about this. But after reading this blog, its interesting to see that with a lot of math and science, you can make a coin land on a certain side every time. Although, it is nearly impossible for a human to do this, so I would consider that usually, coin flips are 50/50 or extremely close to that. But its interesting to see that someone made a machine that could make the chances 100/0. that’s pretty cool.

  5. Caitlin Emily Whelan

    I thought this post was very interesting because as a kid the solution to every problem was a coin toss. I did a little research on this, and found this video on it. In the video, he explains that if you knew how fast the coin went up and how fast it is turning, you could know whether it would be heads or tails when it came down. Basically, if you use a little bit of science and a lot of math, you could actually calculate what side your coin will end up on. So next time you’re flipping a coin with someone, make sure they are not so good at math!

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