A geological statistician
Mr. Srivastava living in Toronto, was working in his office in June 2003, waiting for
some files to download onto his computer, when he discovered a couple of
old lottery tickets buried under some paper on his desk. The tickets
were cheap scratchers—a gag gift from his squash partner—and Srivastava
found himself wondering if any of them were winners. He fished a coin
out of a drawer and began scratching off the latex coating. “The first
was a loser, and I felt pretty smug,” Srivastava says. “I thought, ‘This
is exactly why I never play these dumb games.'”
The second ticket was a
tic-tac-toe game.
Its design was straightforward: On the right were eight tic-tac-toe
boards, dense with different numbers. On the left was a box headlined
“Your Numbers,” covered with a scratchable latex coating. The goal was
to scrape off the latex and compare the numbers under it to the digits
on the boards. If three of “Your Numbers” appeared on a board in a
straight line, you’d won. Srivastava matched up each of his numbers with
the digits on the boards, and much to his surprise, the ticket had a
tic-tac-toe. Srivastava had won $3. “This is the smallest amount you can
win, but I can’t tell you how excited it made me,” he says. “I felt
like the king of the world.”
Delighted, he decided to take a lunchtime walk to the gas station to
cash in his ticket. “On my way, I start looking at the tic-tac-toe game,
and I begin to wonder how they make these things,” Srivastava says.
“The tickets are clearly mass-produced, which means there must be some
computer program that lays down the numbers. Of course, it would be
really nice if the computer could just spit out random digits. But
that’s not possible, since the lottery corporation needs to control the
number of winning tickets. The game can’t be truly random. Instead, it
has to generate the illusion of randomness while actually being
carefully determined.”
As a trained statistician with degrees from MIT and Stanford University,
Srivastava was intrigued by the technical problem posed by the lottery
ticket. In fact, it reminded him a lot of his day job, which involves
consulting for mining and oil companies. A typical assignment for
Srivastava goes like this: A mining company has multiple samples from a
potential gold mine. Each sample gives a different estimate of the
amount of mineral underground. “My job is to make sense of those
results,” he says. “The numbers might seem random, as if the gold has
just been scattered, but they’re actually not random at all. There are
fundamental geologic forces that created those numbers. If I know the
forces, I can decipher the samples. I can figure out how much gold is
underground.”
The North American lottery system is a
$70 billion-a-year business,
an industry bigger than movie tickets, music, and porn combined. These
tickets have a grand history: Lotteries were used to fund the American
colonies and helped bankroll the young nation. In the 18th and 19th
centuries, lotteries funded the expansion of Harvard and Yale and
allowed the construction of railroads across the continent. Since 1964,
when New Hampshire introduced the first modern state lottery,
governments have come to rely on gaming revenue. (Forty-three states and
every Canadian province currently run lotteries.)
In some states, the lottery accounts for more than 5 percent of education funding.
While approximately half of Americans buy at least one lottery ticket
at some point, the vast majority of tickets are purchased by about 20
percent of the population. These high-frequency players tend to be poor
and uneducated, which is why critics refer to lotteries as a regressive
tax. (In a 2006 survey, 30 percent of people without a high school
degree said that playing the lottery was a wealth-building strategy.) On
average, households that make less than $12,400 a year spend 5 percent
of their income on lotteries—a source of hope for just a few bucks a
throw.
The tic-tac-toe lottery is seriously flawed. It took Srivastava a few hours of
studying his tickets and some statistical sleuthing, but he discovered a
defect in the game: The visible numbers turned out to reveal essential
information about the digits hidden under the latex coating. Nothing
needed to be scratched off—the ticket could be cracked if you knew the
secret code.
The trick itself is ridiculously simple. (Srivastava would later teach
it to his 8-year-old daughter.) Each ticket contained eight tic-tac-toe
boards, and each space on those boards—72 in all—contained an exposed
number from 1 to 39.
As a result, some of these numbers were repeated
multiple times. Perhaps the number 17 was repeated three times, and the
number 38 was repeated twice. And a few numbers appeared only once on
the entire card. Srivastava’s startling insight was that he could
separate the winning tickets from the losing tickets by looking at the
number of times each of the digits occurred on the tic-tac-toe boards.
In other words, he didn’t look at the ticket as a sequence of 72 random
digits.
Instead, he categorized each number according to its frequency,
counting how many times a given number showed up on a given ticket. “The
numbers themselves couldn’t have been more meaningless,” he says. “But
whether or not they were repeated told me nearly everything I needed to
know.” Srivastava was looking for singletons, numbers that appear only a
single time on the visible tic-tac-toe boards. He realized that the
singletons were almost always repeated under the latex coating. If three
singletons appeared in a row on one of the eight boards, that ticket
was probably a winner.
The next day, on his way into work, he stopped at the gas station and
bought a few more tickets. Sure enough, all of these tickets contained
the telltale pattern. The day after that he picked up even more tickets
from different stores. These were also breakable. After analyzing his
results, Srivastava realized that the singleton trick worked about 90
percent of the time, allowing him to pick the winning tickets before
they were scratched.
His next thought was utterly predictable: “I remember thinking, I’m
gonna be rich! I’m gonna plunder the lottery!” he says. However, these
grandiose dreams soon gave way to more practical concerns. “Once I
worked out how much money I could make if this was my full-time job, I
got a lot less excited,” Srivastava says. “I’d have to travel from store
to store and spend 45 seconds cracking each card. I estimated that I
could expect to make about $600 a day. That’s not bad. But to be honest,
I make
more as a consultant, and I find consulting to be a lot more interesting than scratch lottery tickets.”
What’s most disturbing, perhaps, is that even though Srivastava first
brought these flaws to the attention of the authorities in 2003, they
continue to appear. A few months ago, Srivastava bought some scratch
tickets at convenience stores in Toronto.
\He started out with a Bingo
ticket, which featured an elaborate hook. After a day of statistical
analysis, Srivastava was able to double his chances of choosing a
winning ticket. (Normally, 30 percent of the tickets feature a payout—he
was able to select winners approximately 60 percent of the time.) “That
might not sound very impressive, since I’m still going to buy plenty of
losers,” Srivastava says. “But it’s a high enough percentage that one
could launder money effectively.”
In one of his most recent trials,
conducted at the request of
Wired, Srivastava identified
six unscratched tickets as probable winners out of a set of 20 cards. If
the tickets were uncrackable, approximately two of them should have
been winners. Instead, Srivastava ended up with four. The odds of this
happening by chance are approximately one in 50. And yet he’s done it
multiple times with a variety of Bingo and Super Bingo games.
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