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, 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 and Yahoo Buzz:
- 1993: $5.4 million (paid in yearly installments). Odds: 1 in 15.8 million,
- 2006: $2 million (lump-sum payoff). Odds: 1 in 1,028,338,
- 2008: $3 million (lump-sum payoff). Odds: 1 in 909,000,
- 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.