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Alternate game play ratchets up winnings: It's the law

Sandra Blakeslee

02-Feb-2000 Wednesday

A Spanish physicist has discovered what appears to be a new law of nature
that may help explain, among other things, how life arose out of a
primordial soup, why President Clinton's popularity rose after he was
caught in a sex scandal, and why investing in losing stocks can sometimes
lead to greater capital gains.

Called Parrando's paradox, the law states that two games guaranteed to make
a player lose all of his money will generate a winning streak if played

Named after its discoverer, Juan Parrando, who teaches physics at the
Complutense University in Madrid, the newly discovered paradox is inspired
by the mechanical properties of ratchets -- the familiar saw-tooth tools
used to lift automobiles and run self-winding wristwatches.

By translating the properties of a ratchet into game theory -- a relatively
new scientific discipline that seeks to extract rules of nature from the
gains and losses observed in games -- Parrando discovered that two losing
games could combine to increase one's wealth.

"The importance of the paradox in real life remains to be seen," said
Charles Doering, a mathematician at the University of Michigan, who is
familiar with the research. "It gives us a new and unexpected view of a
variety of phenomena," he said, "and who knows? Sometimes finding that one
piece of the puzzle makes the whole picture suddenly clear."

Derek Abbott, director of the Center for Biomedical Engineering at the
University of Adelaide in Australia, said that many scientists were
intrigued by the paradox and had begun applying it to engineering,
population dynamics, financial risk and other disciplines.

Abbott and a colleague at his center, Gregory Harmer, recently carried out
experiments to verify and explain how Parrando's paradox works. Their
research is described in the Dec. 23 issue of Nature.

The paradox is illustrated by two games played with coins weighted on one
side so that they will not fall evenly by chance to heads or tails.

In game A, a player tosses a single loaded coin and bets on each throw. The
probability of winning is less than half.

In game B, a player tosses one of two loaded coins with a simple rule
added. He plays Coin 1 if his money is a multiple of a particular whole
number, like three. If his money cannot be divided by the number three, he
plays Coin 2.

In this setup, the second will be played more often than the first. Both
are loaded, one to lose badly and one to win slightly, with the upshot
being that anyone playing this game will eventually lose all of his money.

"Sure enough," Abbott said, when a person plays either game 100 times, all
money taken to the gambling table is lost. But when the games are
alternated -- playing A twice and B twice for 100 times -- money is not
lost. It accumulates into big winnings. Even more surprising, he said, when
game A and B are played randomly, with no order in the alternating
sequence, winnings also go up and up.

This is Parrando's paradox. Switching between the two games creates a
ratchetlike effect. With its saw-tooth shape, a ratchet allows movement in
one direction and blocks it in the other.

"You see ratchets everywhere in life," Abbott said. "Any child knows that
when you shake a bag of mixed nuts, the Brazil nuts rise to the top. This
is because smaller nuts block downward movement of larger nuts." This
trapping of heavier objects -- moving them upward when one would expect
them to fall down -- is the essence of a ratchet.

The same is true for particles that tend to move randomly within cells but
can be captured, or ratcheted, into performing useful work. This is how
many proteins and enzymes are designed, Abbott said.

Slippery slope

Sharing an interest in microscopic ratchets, Abbott and Parrando met in a
coffee shop in Madrid in 1997 to discuss the phenomenon. They started to
wonder what might happen with a so-called flashing ratchet. First, they
imagined two tilted slopes that could be laid on top of each other or held
apart. One is smooth and straight, the other saw-toothed. Particles placed
at the top of either slope would fall down to the bottom under the pull of
gravity. Particles placed at the bottom of either slope would go nowhere.
But if the two slopes were superimposed and alternated or "flashed" back
and forth, particles resting at the bottom could be made to move uphill.

Parrando then translated a flashing ratchet into the language of game
theory. Then, he devised the two coin games that Abbott confirmed in recent
experiments. Game A is like the smooth slope. The single loaded coin
produces steady losses, just like particles sliding straight downhill. Game
B is like the saw-tooth slope that can catch objects. Each tooth on a
ratchet has two sides, one that goes up and one that goes down.

The two coins, one good and one bad, are like two sides of a single
saw-tooth. In a computer, the games are played 100 times, mimicking a
ratchet with many teeth.

Each winning round carries the player's money uphill, Abbott said. Capital
starts accumulating, just like particles moving up the slope of the
flashing ratchet. Switching the game traps the money before new rounds of
the game cause the money to be lost.

Unfortunately, Parrando's paradox will not work for the kinds of games
played in casinos, Abbott said. Games A and B must be set up to copy a
ratchet, which means they must have some direct interaction. In the
experiments carried out by Abbott, game B depends on the amount of capital
being played and game A affects those amounts. They are subtly connected,
he said.

Parrando's paradox may help scientists find new ways to separate molecules,
design tiny motors and understand games of survival being played at the
level of individual genes. Life itself may have been bootstrapped by
ratchets, Abbott said. When simple amino acids were formed by chance,
environmental forces would tend to destroy incipient order. Ratchets could
help move life along its evolutionary pathways toward greater complexity.

In life

Economists are studying Parrando's paradox to help find the best strategies
for managing investments. Sergei Maslov, a physicist at Brookhaven National
Laboratory in Upton, N.Y., recently showed that if an investor
simultaneously shared capital between two losing stock portfolios, capital
would increase rather than decrease.

"It's mind-boggling," Maslov said. "You can turn two minuses into a plus."
But so far, he said, it is too early to apply his model to the real stock
market because of its complexity.

The paradox may shed light on social interactions and voting behaviors,
Abbott said. For example, Clinton, who at first denied having a sexual
affair with Monica Lewinsky (game A) saw his popularity rise when he
admitted that he had lied (game B.) The added scandal created more good for

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