Gamblers Take Note: The Odds in a Coin Flip Aren't Quite 50/50
And the odds of spinning a penny are even more skewed in one direction, but which way?
- By Dan Lewis
- Smithsonian.com, November 30, 2012, Subscribe
Posted from Dan Lewis' fantastic Now I Know newsletter. Subscribe here or follow him on Twitter.
Imagine you’re at a bar and another patron offers you the following wager. He’s going to flip a coin — a standard U.S. penny like the ones seen above — a dozen or so times. If it comes up heads more often than tails, he’ll pay you $20. If it comes up tails more than heads, you pay him the same. There are no hidden tricks. It’s a fair bet — safe to take, if you’re looking for a 50/50 chance.
Now, imagine the same offer, except that instead of flipping the coin, the other patron tells you he’s going to spin it. In fact, he’ll even let you provide the penny, just to guarantee there is no funny business. Twenty-five spins and if it comes up heads more often than tails, he’ll give you $20 again. But if tails comes up more often, you owe him $20.
Fair bet? Not if Persi Diaconis is right.
Diaconis is a professor of mathematics and statistics at Stanford University and, formerly, a professional magician. While his claim to fame is determining how many times a deck of cards must be shuffled in order to give a mathematically random result (it’s either five or seven, depending on your criteria), he’s also dabbled in the world of coin games. What he and his fellow researchers discovered (here’s a PDF of their paper) is that most games of chance involving coins aren’t as even as you’d think. For example, even the 50/50 coin toss really isn’t 50/50 — it’s closer to 51/49, biased toward whatever side was up when the coin was thrown into the air.
But more incredibly, as reported by Science News, spinning a penny, in this case one with the Lincoln Memorial on the back, gives even more pronounced odds — the penny will land tails side up roughly 80 percent of the time. The reason: the side with Lincoln’s head on it is a bit heavier than the flip side, causing the coin’s center of mass to lie slightly toward heads. The spinning coin tends to fall toward the heavier side more often, leading to a pronounced number of extra “tails” results when it finally comes to rest.
Because the coins typically pick up dirt and oils over time, trying the experiment at home may not yield such a large percentage of “tails” over “heads” — but a relatively new coin should still give you noticeable results.
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Comments (9)
my statistics teacher in high school did a similar demonstration. We balanced pennies on their edge and hit the table and counted how many time the coin landed heads or tails. It wasn't even, and based on this i guess it came up tails more than heads. His explanation was that the cross-section of the coin was trapezoidal as opposed to rectangular. This allows the coins to easily exit their dies after being struck. Seems like this, if true, could be behind the imbalance observed in coin spinning.
Posted by wheelinshirt on December 21,2012 | 09:10 PM
Like Al, I have seen a coin land on its edge. It was about ten years ago and it was in a Tim Horton's restaurant. I dropped a penny accidentally and it came to rest on the counter on its edge. It was a Canadian penny so the Abraham Lincoln factor was not in play.
Posted by Shaun S on December 5,2012 | 10:51 AM
> For example, even the 50/50 coin toss really isn’t 50/50 — it’s closer to 51/49, biased toward whatever side was up when the coin was thrown into the air. "Flipped off" must have skipped that part.
Posted by CloseReader on December 3,2012 | 02:22 PM
even the 50/50 coin toss really isn’t 50/50 — it’s closer to 51/49, biased toward whatever side was up when the coin was thrown into the air.
Posted by to: flipped off on December 3,2012 | 08:46 AM
A coin can be balanced on its rim, which is then a possible resting side. Does this affect the dual expectation always associated with coin tossing?
Posted by Ray Musumba on December 3,2012 | 08:09 AM
There is also a possibility also that a coin flip can land and the end up on its edge. Unlikely as that is, I once had it happen 60+ years ago.
Posted by Al Chukitus on December 2,2012 | 10:44 PM
Please unsubscribe mefrom your newsletters.
Posted by Elsie Millar on December 2,2012 | 12:45 PM
Heads I win, tails you lose!
Posted by Deirdre on November 30,2012 | 03:08 PM
flipping a coin and spinning a coin are not the same thing, so the headline of a flip not being 50/50 is innacurate. sorry, just irked me.
Posted by flipped off on November 30,2012 | 12:29 PM