...recent research into coin flips has discovered that the laws of mechanics determine the outcome of coin tosses: The startling finding is they aren't random. Instead, for natural flips, the chance of a coin coming up on the same side as it started is about 51 percent. Heads facing up predicts heads; tails facing up predicts tails.The full story is here.
Three academics—Persi Diaconis, Susan Holmes, and Richard Montgomery—through vigorous analysis made an interesting discovery at Stanford University. As they note in their published results, "Dynamical Bias in the Coin Toss," laws of mechanics govern coin flips, meaning, "their flight is determined by their initial conditions."
The physics—and math—behind this discovery are very complex. But some of the basic ideas are simple: If the force of the flip is the same, the outcome is the same. To understand more about flips, the academics built a coin-tossing machine and filmed it using a slow-motion camera. This confirmed that the outcome of flips isn't random. The machine could make the toss come out heads every time.
When people, rather than a machine, flipped the coin, results were less predictable, but there was still a slight physical bias favoring the position the coin started in. If the coin started heads up, then it would land heads up 51 percent of the time. Part of the reason real flips are less certain isn't just that the force of the flip can vary; it's that coins flipped by humans tend to rotate around several axes at once. Flipped coins tumble over and over, but they also spin around and around, like pizza dough being twirled.
Monday, August 3, 2009
Getting the Edge in Coin Tosses
Stanford researchers figure out the angle:
at 8:59:00 AM