# Spinning a penny is not a 50/50 chance event (but flipping it still is...)

• I
Look at this email I received from a company called ;Wisegeek' they send out interesting news items each day ..

"If you spin a clean, new Lincoln penny, it will fall tails-side up about
eight times out of 10.

Forget what you know about statistical probability. If Persi Diaconis and
researchers at Stanford University are right, spinning a standard-issue
penny (the one with the Lincoln Memorial, clean and shiny) will come up
tails side up roughly 80 percent of the time -- not 50-50, give or take a
percent either way, as we’ve all come to expect. The reason: The side
with Lincoln’s head is a tad heavier than the other side, causing the
coin’s center of mass to be slightly skewed. And so, the spinning coin
tends to fall toward the heavier side more often, leading to significantly
more “tails.” "

This, I am certain, is rubbish ....Thoughts?

## Answers and Replies

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Look at this email I received from a company called ;Wisegeek' they send out interesting news items each day ..

"If you spin a clean, new Lincoln penny, it will fall tails-side up about
eight times out of 10.

Forget what you know about statistical probability. If Persi Diaconis and
researchers at Stanford University are right, spinning a standard-issue
penny (the one with the Lincoln Memorial, clean and shiny) will come up
tails side up roughly 80 percent of the time -- not 50-50, give or take a
percent either way, as we’ve all come to expect. The reason: The side
with Lincoln’s head is a tad heavier than the other side, causing the
coin’s center of mass to be slightly skewed. And so, the spinning coin
tends to fall toward the heavier side more often, leading to significantly
more “tails.” "

This, I am certain, is rubbish ....Thoughts?
No, this is very true and easy to do yourself. The thing to realize is that they are not flipping the coin. They are spinning it on its edge on a table. Due to the high relief image of Lincoln when you stand it on edge the center of mass is not centered over the edge of the penny. Naturally it tends to fall over toward the heavier side. I think the image of Lincoln used to be executed in higher relief than it is now, so I think the effect used to be more pronounced.

No, this is very true and easy to do yourself. The thing to realize is that they are not flipping the coin. They are spinning it on its edge on a table. .....
That's all you need to say !!!

Idiots !! have they got nothing better to do ... this is a deceptive article... will mislead many , who spins a coin ??

berkeman
Mentor
I edited the thread title.

That's all you need to say !!!

Idiots !! have they got nothing better to do ... this is a deceptive article... will mislead many , who spins a coin ??
Yes, but most people do not realize there is any difference. You can bias the odds in your favor for all kinds of coin flipping occasions. Just spin a penny instead of flipping it. Most people won't think twice about it.

berkeman
Mentor
Just spin a penny instead of flipping it. Most people won't think twice about it.
I will now! Learn something new at the PF every day...

sophiecentaur
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2019 Award
We should all remember to determine if something is true before trying to figure out why something is true.

I found the shiniest penny in the bank (get it?) and spun it 25 times. (Coin flipped, picked up from the table and spun each trial). I got 15 heads and 10 tails. If this coin were 50-50, the odds of getting a result at least that large is 1 in 5. For an 80-20 coin, it's 1 in 73,700.

One can always say, "But your penny isn't good enough!". By requiring a Lincoln Memorial reverse, one guarantees that the coin is at least eight years old. Those tend not to be very shiny.

We should all remember to determine if something is true before trying to figure out why something is true.

I found the shiniest penny in the bank (get it?) and spun it 25 times. (Coin flipped, picked up from the table and spun each trial). I got 15 heads and 10 tails. If this coin were 50-50, the odds of getting a result at least that large is 1 in 5. For an 80-20 coin, it's 1 in 73,700.

One can always say, "But your penny isn't good enough!". By requiring a Lincoln Memorial reverse, one guarantees that the coin is at least eight years old. Those tend not to be very shiny.
I remember seeing this tested with a very large number of coins on some science show, but I can't seem to find that on the web. I found several little experiments and conversations about it but not many large enough statistically significant tests. The best I found was this article from the "Chance News" a news letter curated by Math professors from Dartmouth, the University of Minnesota, and a few others promoting statistical literacy.

https://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.02.html

They show some of their own experiments with Euros, but then they show their experiments with spin bias of a US penny. They further show the data they gathered from some colleagues who had been performing this experiment in undergraduate classes for years and had built up large statistics. What they found:

1) A quality testing environment is important: smooth table and some initial practice getting "ball like" spins.
2) The bias in 1960s pennies is around 60-65%
3) The bias in more recent pennies is around 55%

The only place I ever saw 80% referenced a theoretical calculation of Perci Diaconis.

I also saw some interesting comments that suggested the bias was less to do with the center of mass and more to do with the edge being slightly beveled to allow (or perhaps caused by) removal from the die. They indicated you could prove the existence of this bevel by lining up coins on a table against a straight edge and measuring the length of the line. If the coins are all heads up he says the line will be longer than if they are every other one heads up due to the bevel. I haven't tried it though. (I haven't had cash in years!)

Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2019 Award
I see. You need a shiny, fifty-year old penny to make this work, and even then, it's not 80%.