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Dice throw: much less random than you think!

By Jon Wilner and Mark Emmons

Mercury News
Posted: 10/16/2009 06:28:06 PM PDT

Everyone knows the flip of a coin is a 50-50 proposition.

Only it's not.

You can beat the odds.

So says a three-person team of Stanford and UC-Santa Cruz researchers. They produced a provocative study that turns conventional wisdom, well, on its head for anyone who has ever settled a minor dispute with a simple coin toss.

It also could have profound implications in America's favorite sport — pro football — because the coin flip plays an integral role in deciding games that go into overtime.

But first, here's what the researchers concluded: Using a high-speed camera that photographed people flipping coins, the three researchers determined that a coin is more likely to land facing the same side on which it started. If tails is facing up when the coin is perched on your thumb, it is more likely to land tails up.

How much more likely? At least 51 percent of the time, the researchers claim, and possibly as much as 55 percent to 60 percent — depending on the flipping motion of the individual.

In other words, more than random luck is at work.

The humble coin toss has been the subject of considerable study by researchers exploring concepts such as probability and statistics. There even was an unscientific look by a prisoner who once flipped a coin 10,000 times inside his cell.

"But they've all been wrong because people write down whether it comes up heads or tails, but they don't know how it
started," said Susan Holmes, a Stanford University statistics professor who co-authored the study, which was published in 2007. "You have to know how it starts.''

And if you know that, the researchers believe, then you have a better chance of knowing how it will land.

The power of a coin flip

Tossing a coin long has been a choice for deciding trivial matters — like a dinner-table spat over the last piece of pizza. But coin flips also have played much more prominent roles. The Oregon city of Portland got its name after a best two-out-of-three penny toss by two settlers. (Boston was the losing name.)

There was a fateful coin flip on Feb. 3, 1959, that allowed early rock 'n' roll star Ritchie Valens to get a seat on a small plane that was supposed to carry him, Buddy Holly and two others to their next concert site. The plane crashed shortly after takeoff, killing all four.

The coin flip even is found in literature and cinema. Javier Bardem won an Oscar for his role in the 2007 film version of Cormac McCarthy's "No Country for Old Men" in which the villain tosses a coin to decide whether he should kill someone or let them live.

But nowhere in modern society does the coin flip loom larger than in sports — specifically the NFL.

A coin toss determines which team gets the football first in overtime if the score is tied after regulation play. And heading into this season, the team winning the overtime toss had won 63.3 percent of the games — and won the game 43.3 percent of the time on its first possession, preventing the other team from even touching the ball.

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Comment by Dominic Pouzin on October 22, 2009 at 12:11pm
Interestingly, Von Neumann came up with a simple method to generate a fair coin toss from a biased coin.

Flip the coin twice. If it comes up heads followed by tails, then call the outcome head. If it comes up tails followed by heads, then call the outcome tail. Otherwise repeat the process. Assuming that flips are independent, the procedure simulates an unbiased coin, no matter what the coin's bias is. This is easy to verify using probability p for heads, and 1-p for tails: p * (1-p) = (1-p) * p.

By requiring that the starting position for all coin tosses be the same (ex: always heads), we should still be able to get fair NFL toss coins :)
Comment by Arun on October 21, 2009 at 3:36am
That's some cool stuff!! I can't believe it.. They're saying the which ever side you toss the coin, it has the bias created there itself! It does feel a little logical, since if we were to toss the coin from "Neither Heads Nor Tails" position, then maybe we could argue that the Expected Probablility could be 50:50.
Atleast this is how I see it, since we're giving an initial bias i.e. here the position for the side tossed from, it is logical to say that that side might more probability of landing.

But, even so, I'd still say, it's hardly a problem since the probability goes to about 55:45? That's not too significant to affect the outcome, and it can be safely considered random still right?? Only if the value can be predicted beforehand with a certain level of accuracy does the problem of affecting Randomness arise!

Is there someone who feels otherwise??

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