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. Roughly, youre looking at a 3-state object. The potential to bounce makes a huge difference. 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.īut 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. If you flip your coin onto sticky pitch, it has a much better chance of landing on edge than if you flip it onto a smooth granite surface.
COIN FLIP ODDS PDF
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. 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.
COIN FLIP ODDS PROFESSIONAL
But if tails comes up more often, you owe him $20.įair bet? Not if Persi Diaconis is right.ĭiaconis is a professor of mathematics and statistics at Stanford University and, formerly, a professional magician. If you flip a coin 1000 times, its most likely that youll get heads somewhere between 47 and 53 percent of the times. Twenty-five spins and if it comes up heads more often than tails, he’ll give you $20 again.
In fact, he’ll even let you provide the penny, just to guarantee there is no funny business. Now, imagine the same offer, except that instead of flipping the coin, the other patron tells you he’s going to spin it. It’s a fair bet - safe to take, if you’re looking for a 50/50 chance. If it comes up tails more than heads, you pay him the same. That means that if you bet 1 on a particular outcome (heads or tails), you win 1 if you’re right and lose 1 if you’re wrong.
A fair coin will have a 50 chance of coming up heads and 50 chance of coming up tails. If it comes up heads more often than tails, he’ll pay you $20. The simplest game of chance I can imagine is flipping a coin. penny like the ones seen above - a dozen or so times. He’s going to flip a coin - a standard U.S. Imagine you’re at a bar and another patron offers you the following wager. There is a Unistable polyhedron which will always eventually roll to the same face each time it it tossed.Posted from Dan Lewis' fantastic Now I Know newsletter. Many objects have unstable sides, and will topple away from them. Results closely followed the Energy State model of my thesis on dice. Cylinders of various size were mechanically rolled thousands of times on a variety of surfaces.
COIN FLIP ODDS SERIES
The amount of energy necessary to topple from one state to another will let you build a transition matrix, and then multiply a series of these together to get expected behavior on a given surface. Each time it lands, it will lose some energy, and the chance that it will change to a different state varies with the energy. Roughly, you're looking at a 3-state object. If you flip your coin onto sticky pitch, it has a much better chance of landing on edge than if you flip it onto a smooth granite surface. I covered this question at my Fair Dice column.
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