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Flipping a coin isn"t as fair together it seems. Courtesy of flickr user MagnuMicah

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You are watching: Probability of a coin landing on its edge

Imagine you’re in ~ a bar and also another patron supplies you the complying with wager. He’s going to flip a coin — a typical U.S. Penny favor the ones seen over — a dozen or therefore times. If it come up heads more often 보다 tails, hell pay girlfriend $20. If it come up tails an ext than heads, you pay him the same. There room no surprise tricks. It’s a fair bet — safe to take, if you’re searching for a 50/50 chance.

Now, imagine the same offer, other than that rather of flipping the coin, the other patron tells you he is going come spin it. In fact, he’ll even let you provide the penny, simply to guarantee there is no funny business. Twenty-five spins and if it comes up heads an ext often than tails, he’ll offer you $20 again. But if tails come up more often, you fan him $20.

Fair bet? not if Persi Diaconis is right.

Diaconis is a professor that mathematics and statistics in ~ Stanford university and, formerly, a experienced magician. When his claim to fame is determining how many times a deck that cards should be shuffled in stimulate to offer a mathematically random an outcome (it’s either 5 or seven, depending upon your criteria), he’s likewise dabbled in the world of coin games. What he and his fellow researchers discovered (here’s a PDF of your paper) is the most games of chance including coins no as even as you’d think. Because that example, even the 50/50 coin toss really isn’t 50/50 — the closer come 51/49, biased toward whatever side was up as soon as the coin was thrown right into the air.

But an ext incredibly, together reported by science News, spinning a penny, in this instance one v the Lincoln Memorial ~ above the back, gives even much more pronounced odds — the penny will land tails side up roughly 80 percent the the time. The reason: the side with Lincoln’s head on the is a little heavier 보다 the flip side, causing the coin’s center of mass come lie slightly towards heads. The turn coin has tendency to autumn toward the more heavier side much more often, leading to a pronounced variety of extra “tails” results as soon as it finally concerns rest.

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Because the coins commonly pick up dirt and also oils end time, trying the experiment at home may no yield together a large percentage the “tails” end “heads” — but a relatively brand-new coin need to still give you noticeable results.