September 12, 1988
"Someone Else has Your Lucky Number"
San Jose Mercury News
By Timothy Taylor
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I'M sure that Robert Barnett of Riverside and Christene Lentz of Capistrano
Beach are deserving people. Very deserving. But despite how very deserving I'm
sure they are, the news that the two of them will split a $39.1 million jackpot
in the state lottery must raise a fundamental question in the mind of every public-spirited
How can I improve my chances of getting that money?
The odds of winning the lotto jackpot by picking the correct six numbers between
1 and 49 are just terrible. The odds of matching the six numbers are about one-fortieth
as good as the chance of dying this year by accidental electrocution.
However, there is a perfectly serious system to beat the lottery over time,
and I am going to tell it to you right here. I am not joking or making fun. This
method is as certain as mathematics.
First of all, you must understand that unless someone has inserted a carefully
placed monkey wrench in the machinery, no one can choose the six winning numbers
The combination 1, 2, 3, 4, 5, 6 is just as likely to come up as any other
combination of six numbers between 1 and 49.
Anyone who tries to tell you that they can predict the winning numbers is just
blowing smoke. If they know, after all, why aren't they rich already?
Remember, Barnett and Lentz let a machine choose their ticket numbers at random.
Letting the machine choose is just as accurate a way of choosing the winning six
numbers as betting, say, the age of your cousins or the humidity during the past
week or the predictions of your neighborhood psychic.
So if I'm not going to tell you what the winning numbers will be, how can I
tell you a way to beat the lottery?
Here's the answer. The numbers that come up as winners are chosen at random,
but the numbers that people bet on are not chosen at random.
For example, studies done by William T. Ziemba, a professor of management science
at the University of British Columbia, show that the numbers from 1 to 31 are
generally bet more often than numbers from 32 to 49, because so many people bet
their birth dates.
Research (later confirmed by Ziemba's work) done by Herman Chernoff, a professor
of mathematics at the Massachusetts Institute of Technology, showed that people
also tend not to choose numbers ending in 0, 9 or 8. The same numbers seem to
stay unpopular year after year.
For all you greedballs still following this explanation, here's the payoff:
If you bet the same popular numbers as everyone else, then if you win the lottery
it is relatively likely that you will have to share the prize with someone else
who bet on the same numbers. But if you bet on the unpopular numbers, then if
you win it is fairly likely the prize will be yours and yours alone.
This advantage can be quite substantial. Normally, for every dollar bet in
the lottery, 50 cents is paid out in prizes. On average, you should expect to
lose 50 cents in the lottery every time you bet a dollar.
If you bet the popular numbers you should expect to lose even more, because
you're likely to have to share the prize when you win.
But by choosing the unpopular numbers, you can improve your expected winnings
dramatically. The fact that you are unlikely to have to share the prize means
that your expected return will climb as high as $2 for every dollar bet. Instead
of expecting to lose 50 cents on average, you expect to win a dollar on average
for every dollar bet.
I emphasize again that there are no tricks here. Betting the unpopular numbers
is, on average, a winning bet. But before you hock the house and the spouse to
play the lottery, two words of warning.
First of all, even with the odds in your favor, you will probably have to lose
a lot of money for a long time before you collect your winnings.
Richard Thaler, an economics professor at Cornell University, uses this metaphor
to explain the problem in a recent article: "Consider a hypothetical carnival
game with 1 million spokes. You pay $1 for a number between one and 1 million,
and you get $2 million if your choice comes up. While you have an edge, the chance
of winning is so small that you will probably go bankrupt before you win the jackpot."
The second problem is that if everyone bets on the unpopular numbers, then
they won't be unpopular any more, and this whole system won't work.
So don't mention this article to anyone.
But just for your information, the 19 most unpopular numbers, in order, are
40, 39, 20, 30, 41, 38, 42, 46, 29, 49, 48, 32, 10, 47, 1, 37, 28, 34 and 45.
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