Who knew?
Most people believe that a tossed coin has a 50-50 chance of landing heads or tails.
Not true.
Long story short: Its 51-49, with the more likely outcome being the side facing up when it was flipped.
Heres David E. Adlers story from todays Washington Post with the science behind this surprising finding.
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A Reliable Randomizer, Turned on Its Head
In the Physics of a Coin Toss, It Turns Out, Theres No Such Thing as 50-50 Odds
Coin tosses are a classic metaphor in economics for randomness. For
instance, in his book about market efficiency, 'A Random Walk Down Wall
Street,' economist Burton Malkiel compares the price movements of the
stock market to the random outcome of a flipped coin: '[S]ometimes one
gets positive price changes for several days in a row; but sometimes
when you are flipping a coin you also get a long string of heads in a
row.' According to Malkiel, mathematicians term for a sequence of
numbers produced by a random process is a random walk. To him, this is
exactly what stock-price movements look like, hence the title of his
book.
Similarly, Nassim Taleb, in 'Fooled by Randomness,' points out that
the seemingly amazing success of money managers at beating the market
is often best explained by pure chance. People misperceive patterns in
what are, in fact, purely random sequences, akin to the outcomes of a
coin flip. And as everyone knows, coin flips produce 'heads and tails
with 50 percent odds each.'
Lately, the idea of randomness in stock prices has come under
attack; prices for individual stocks (but not the market on the whole)
often show small momentum effects: stocks that go up tend to keep going
up, and stocks that are going down tend to keep going down. But the
metaphor of a coin flip for randomness remains unquestioned. We use
coin tosses to settle disputes and decide outcomes because we believe
they are unbiased, with 50-50 odds.
Yet recent research into coin flips has discovered that the laws of
mechanics determine the outcome of coin tosses: The startling finding
is that they arent random. Instead, for natural flips, the chance of a
coin landing in the same position as it started is about 51 percent.
Heads facing up predicts heads; tails predicts tails.
Three academics -- Persi Diaconis, Susan Holmes and Richard
Montgomery -- made an interesting discovery through vigorous analysis
at Stanford. As they note in their published results, 'Dynamical Bias
in the Coin Toss,' the laws of mechanics govern coin flips, meaning
that 'their flight is determined by their initial conditions.'
The physics and math behind this discovery are complex. 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 is not random. The machine could produce heads every
time.
When people flipped the coin, results were less predictable, but
there was still a slight physical bias favoring the coins initial
position 51 percent of the time. The reason real flips are less certain
isnt just that the force can vary, its that coins flipped manually
tend to rotate around several axes at once. They tumble over and over,
but they also spin around and around, like pizza dough being twirled.
The more a coin spins, the more unpredictable the outcome.
I spoke to Holmes, one of the Stanford researchers, about this. She
told me that when most people hear about this weird finding, they think
it has something to do with the density of the coin, but she was able
to disprove that by constructing a coin made out of balsa wood on one
face and metal on the other. It made no difference come flip time. The
dynamics of the coin flip, and its outcome, are determined not by the
lack of balance in the coin but instead by the physics of spinning and
flipping.
I asked Holmes whether coin flips used for, say, football, should be
eliminated because they are biased. The answer is no, as long as the
person calling the flip doesnt know how the coin is going to start
out. In football, the tosser is never the caller; the tosser is
supposed to be a referee. But if you are both the caller and the
tosser, well, that changes things. Knowing about the bias in coin
tosses give you an edge, albeit a tiny one.
Certain people, however, can make a toss come out heads (or tails)
100 percent of the time. Diaconis, Holmess co-author and husband, is
one of the people with this rare talent. Before becoming a
mathematician, he was a professional magician. So how exactly is
Diaconis able to make a coin toss come out a certain way? Holmes wont
tell me: 'It comes from his previous career -- its magic.'
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Adler is the author of 'Snap Judgment.'
More?
OK.
You can read the first chapter here.
Free, the way we like it.
(Via bookofjoe.)
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