Friday, June 7, 2013

Gamblers Take Note: The Odds in a Coin Flip Aren't Quite 50/50

A topic we last looked at in 2009.
From Smithsonian Magazine:

And the odds of spinning a penny are even more skewed in one direction, but which way? 
Spinning penny
Flipping a coin isn't as fair as it seems. (Courtesy of flickr user MagnuMicah)
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....MORE
Think a coin toss has a 50-50 chance? Think again.