Wednesday, April 24, 2019

I'LL FLIP YOU FOR THAT

Who gets the last slice of pizza? Flip a coin. On second thought ... maybe not. The coin toss is a time-honored solution to indecision, but, weirdly, it's not a truly fair method. Better to just split that slice.
Imagine all the qualms in history ever settled by the flip of a coin. I’ll bet few of those involved knew the odds weren't quite even. It turns out that a spinning penny will land tails-up a staggering 80% of the time, according to Persi Diaconis from Stanford University's Department of Statistics, who performed a mathematical analysis on the matter in 2004.  That's because a penny is slightly heavier on the heads side, skewing the center of mass and making the coin more likely to turn up tails. Coins with unserrated edges (like a nickel) tend to be slightly more biased too. (Insider info: Magicians will often shave the tails side down so the weight discrepancy even greater, making it even more likely to land tails-up.)
Flipping a coin could get you a similar bias, too. If you flip a coin into the air and let it fall onto a hard surface to reveal the result, the coin often ends up spinning before settling, anyway. And, as we learned earlier, a spinning coin is, way more often than not, a tails-up coin. Note that older pennies may not give you quite as pronounced a bias as newer ones. It's gross, but you have to account for all the dirt, grime, and other junk that can build up on coins over time and throw off the center of mass.

Catch or Drop?
Forget heads or tails, let's ask a better question: Catch or drop? It may seem silly, but according to Diaconis, it is fairer to catch a coin that was flipped into the air than to let the coin bounce and spin on the ground until it lies flat. Your hand isn't a hard, flat surface like the ground, so it'll land wherever you stick your hand in its descending path. But--you guessed it-- even that is not truly random.
Diaconis holds that any flipped coin will still be slightly biased toward landing tails-up, at about 51-49 odds to be precise. In 1986, mathematician Joseph Keller proved that one fair way to toss a coin is to throw it so that it spins perfectly around a horizontal axis through the coin's center. Doing that would require superhuman ability, so don't count on it. For us mere mortals, just stick to calling it tails. You'll probably be right.

1. How lucky that I do always call tails.
Love the cartoons. And missing your cheery presence out and about in the blogosphere.

2. Ok, now I am convinced. Tails it is. I use to pull "heads I win, tails you lose," on my younger sisters. Bad Patti.

3. I can't remember if I ever took part in a coin toss. Love the last cartoon.

4. On the Stock Exchange disputes between brokers were usually settled with a coin flip.

It is easy to toss a coin with a waggle so it looks like it is flipping but in reality it never actually flips over at all. For that reason I think it is best to let the coin fall if you don't completely trust the flipper.

5. I think we used to toss a coin to settle disputes when I was a kid, but that was long ago.

Love,
Janie

6. Very interesting factoid. I shall try to remember to call tails.
Loved the last cartoon the best--hehe! ;)

7. Flip the coin over the dirt, i think it won't land edgewise and spin on dirt. Or switch to rock/paper/scissors.

8. It never occurred to me that coins are unevenly weighted. This explains why Val from unbagging the cats blog so often finds coins that are face down.

9. Catch or drop -- I vote catch! That way, I don't have to go chasing after it.

Cherdo
Cherdo on the Flipside
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