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From: usenet on 7 Jul 2010 06:04
Lady Wins Fourth Lottery: What Are the Odds?

By William M. Briggs
Wednesday, July 7, 2010

I'm in the wild blue yonder today; so here is a distraction. Thanks
to reader Jade for suggesting the topic.

Nobody can scratch better than Las Vegas resident Joan Ginther,
http://buzz.yahoo.com/buzzlog/93820?fp=1
who has just scrapped that little gray fuzz off of her fourth winning
lottery ticket. Her fourth win!

The two questions on everybody's mind are: How do I hit Ginther up
for a loan? and How do I work her magic? I don't have a sure answer
for the first, other than to say that, she being female, flattery
rarely fails; but I can tell you all about the chances of duplicating
her performance.

First, her achievements, according to the (as it is sometimes
miscalled) Corpus Crispi Caller
http://www.caller.com/news/2010/jul/02/bishop-native-wins-millions-for-4th-time/?print=1
and Yahoo Buzz:

o 1993: $5.4 million (paid in yearly installments). Odds: 1 in 15.8
million,

o 2006: $2 million (lump-sum payoff). Odds: 1 in 1,028,338,

o 2008: $3 million (lump-sum payoff). Odds: 1 in 909,000,

o 2010: $10 million (lump-sum payoff). Odds: 1 in 1,200,000.

It's not clear if these are the pre-government confiscation amounts,
or the actual dollars she pocketed; probably the former. Still, even
considering the (approximate) 40% federal tax bracket, if the lovely
Ginther has been living clean, then she likely has at least has
several million in the bank.

But since she's been camped out in Vegas, and she has quite
positively evinced a love of gambling, she might not have much left
after all. For to win that many lotteries requires her to buy many,
many tickets.

Let's simplify a bit, just to make it easier on ourselves. The
probability of winning her lotteries are approximately 1 in 15
million, and three 1 in a millions. I'll assume the 1 in 15 million
was a "bouncing ball" lottery, and that the others are all scratch-
off tickets: the kind of gamble doesn't matter in calculating the
odds of winning, but naming it makes it easier to describe. We don't
know, but it's a good guess that she likely bought more than one
ticket per game.

Take her 2006 win. If she bought just one ticket for that gamble,
then she had a 1 in a million chance of winning. If she bought two
tickets, then she roughly doubles her chance of winning. If she was
like a lot of folks I see lining up at the bodega windows, she might
have laid down as much as a 100 bets in a few months' time. Buying
that many tickets pushes the chance of winning to 1 in a 100
thousand, a substantial jump.

There are about 13 years (we don't know the exact dates of her wins)
between her jackpot payout of 1993 and her next winning ticket in
2006. Assuming she bought 100 tickets a year -- a not uncommon
figurel; probably on the low side -- then she might have racked up
1300 tickets. That gave her a just over a 1 in a 1000 chance of
winning. Pretty good odds! If she bought 200 tickets a year, her odds
of winning rise to almost 3 in a 1000.

Anyway, she did win in 2006, then she won again in 2008, which, of
course, is only two years later. How many tickets did our Joan buy in
those two years? We can only guess: but she had a pocketful of money,
so, at least as a first approximation, we can imagine she bought
another 1300 tickets. That gave the odds of winning (in 2008) 1 in a
1000 again.

And the same thing, or something like it, is true for her last win in
2010. That is, she likely had a 1 in 1000 chance of winning the last
payout.

The lottery has no memory, by which I mean that winning before does
not affect the probability of winning again. Given that and the rule
that chances multiply, we can calculate that Ginther had a 1 in a
billion (which is 1 in 1000 multiplied by itself three times) chance
of winning her last three payouts. If she bought twice as many
tickets as we guessed, then she had about a 2 in 100 million chance
of winning thrice.

But what about her first win? It's the same process. We have to make
a guess about how many tickets she bought. It's not impossible to
imagine, this being her first win, that she dropped a substantial
bundle before seeing her numbers come up. Say she blew six grand:
that gave her the odds of 4 in 10,000 of taking home the jackpot.

Altogether, this makes the chances anywhere from 7 in a trillion to 9
in 10 trillion of winning four times, depending on the number of
tickets purchased. Even if we assume she bought twice as many tickets
as we guessed, this still works out to about 1 in 10 billion.

But that's just the odds that she, Joan Ginther, wins four times. The
odds that somebody wins that many times is much, much higher. As much
as 2 in a 1000, if there were 20 million inveterate gamblers like
Joan out there. And if there were 100 million -- a distinct
possibility: remember, we're talking about many decades of lotteries
from which to find four winners -- then the chance of at least one
Joan Ginther is about 1 in a 100.

Which suddenly doesn't seem so small.

More at:
http://wmbriggs.com/blog/?p=2597

Jai Maharaj, Jyotishi
Om Shanti

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