So . . . if you've been reading this blog for a little while you are undoubtedly familiar with my constant (obsessive?) interest in outcomes and chance. Almost a year ago now I wrote this post, which used as an example the idea of entering a lottery and making the best decision (the decision that makes the most sense prior to a deciding event like a lottery drawing) and the right decision (the decision that ultimately proves most beneficial after the event). Well, two weeks ago there was a lottery drawing that is (almost) right in line with my reasoning, and it proves to be a very difficult test case for me to defend. But I'll try anyway.
Poor Michael Kosko. He buys into the office lottery pool every week, and then one week he decides that it's not worth borrowing $2 to participate, and declines (twice!). Of course, as luck would have it, that's the week the pool hits it big, winning the MegaMillions $319 million jackpot. After the split (amongst seven participants), the buyout reduction (U.S. lotteries often offer a choice of the total amount paid out over many years or a reduced lump-sum amount), and taxes, that's $19 million that he missed out on because he wouldn't borrow two bucks from a co-worker who offered. In the wake of the story of the massive jackpot, Kosko's story got a lot of coverage (example here), and even though he doesn't feel sorry for himself, I can't help but pity him.
It's clear he did not make the right decision, but did he make the best decision? Nope. The odds of winning the lottery were about 176 million to one, and one ticket is $1. Which means that each ticket promised a return of almost $2 when you consider the odds (not even taking into account the non-jackpot prizes). So probabalistically speaking, he should have bought in once the jackpot passed the $176 million mark (and some consortia have actually taken advantage of such arbitrage opportunities in lotteries, like in this example).
That's all well and good, but come on, the odds are ridiculous! To put it in perspective, you would have to buy a ticket every week for each of over 42,000 80-year lifetimes before you were likely to win. So the odds of winning are essentially zero. It's like one of my old statistics profs used to say: he can understand buying one lottery ticket for the thrill; what he can't understand is buying two. From a basic math perspective, sure, two tickets double your odds. But if your odds are essentially zero, doubling those odds don't help (and they're pretty close to zero at 0.000000057%. If each of Kosko's winning co-workers kicked in $2, that's 14 tickets, which brings their odds to a whopping 0.0000008% . Still zero.
Who knows why Kosko said no (and by the way, Kosko wasn't the only one who declined; apparently four others did too, but they aren't talking to the media). All I know is that in essential 100% of situations such as this, we never hear about it because those tickets don't win. Maybe he was worried that if he borrowed the money, it would spoil the relationship between him and the co-worker, and one night at the bar things would get heated and there would be a brawl and an innocent bystander would get killed by a flying beer mug. Seems unlikely, doesn't it? Well, to me it's no more unlikely that something that is 176,000,000 against.
So I defend Kosko as well as pity him. Now, if he always makes sure to buy tickets from here on, that I can't defend. Just like I can't defend my irrational expectation that the $50 million Lotto Max drawing tonight will go my way.
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