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Journal of No. 118

August 26th, 2009

The math of losing money @ 10:56 am

So the Mega Millions jackpot will be up to about $325 million for Friday's drawing. California is one of the several states that takes part in MM. The odds of winning are 1:175 million, so the expected value of a ticket is greater than $1. Even if you take the lump-sum payout of $205 million, each ticket is 'worth' more than the $1 you pay for it. Of course, unless you're a fucking badass like Voltaire, it's hard to really use this fact to your benefit.
[With taxes, no doubt the ticket is worth less than $1, but I don't understand the math of taxes.]

One interesting wrinkle is that for California players of Mega Millions, the prizes are pari mutuel, while for most (all?) other states, the lesser prizes (for matching fewer numbers) are fixed amounts.

In parimutuel betting, the total pool of bets (less the betting company's take or 'vig,' as it's known in the trade) is divided proportionately among those who placed winning bets. It seems quite simple, and it guarantees profit for the house, but a strange consequence is that the bettors don't know the odds until after all the bets are taken.

Parimutuel betting had its origins in the 19th century, but really took off with the invention of the totalizator: a mechanical (later electrical, and later still digital) device for totalling all the bets and rapidly calculating the payout. Check that link for a picture of the first mechanical totalizator - miles of wire (not for electricity! the thing was run by falling weights!) and bicycle chain.

As mechanical/electrical computation got more sophisticated, the totalizator could show automatically generated odds that changed in real-time on the Automatic Odds Barometer Indicators, or more generally the totalizator board, or more informally, the tote board.

Which is all to say that...

... though the straight odds of matching three numbers offers a $7 payout in most states, and one would think that the huge amount of the total prize of yesterday's drawing should ensure a good payout in parimutuel California, there must have been a shitload of three-number winners (56,575 to be exact), because I only get $6.
[it looks like these other prizes are not cumulative in the way that the jackpot is, so the prize appears to only fluctuate from $6 to $8, based on the take from that specific drawing and the number of winners]

Usually, I decry the lottery (as Voltaire did) as a tax on the poor, but as Laslo Hollyfeld remarks, "Lately I've come to realize I have certain material needs." And the lottery would suffice, despite the unlikeliness of winning. I can try to rationalize it with mumbo-jumbo about expected value, but mostly I'm just throwing money away on a dream. But if you also throw money away, and lightning strikes, please remember me for my kind service of introducing you to new ways to lose money.
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Date:August 26th, 2009 06:55 pm (UTC)
May family always calls the occasional lotto purchase as "an investment in our fantasy lives" cos we can spend the next 3 days imagining what we'll spend the money on if we win. ;)
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Date:August 26th, 2009 07:03 pm (UTC)
I've found that thinking along those lines provides a strange psychological lift.
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Date:August 26th, 2009 07:11 pm (UTC)
I made the mistake of telling LB that Phil had bought a ticket when it was at $138M. He had ALL KINDS of ideas about what to do with it. Sadly, we didn't win. There's always next time right?
Date:August 26th, 2009 11:28 pm (UTC)
Oso sez: I've been paying the Bad-At-Statistics Tax since Friday (when the jackpot was $207 million). As observed, I view it as an inexpensive payment for a temporary fantasy.
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Date:August 27th, 2009 01:35 am (UTC)
Exactly. The no-fun smarty-pantsy statistical argument ignores two pretty much inarguable truths about the lottery:

1) $1.00 is not so high a price to pay for an hour's worth of fuel for daydreaming about what you might do with a "Fuck You Money" jackpot. The average crappy movie might cost ten times as much for a less pleasurable experience -- but do we find fault with the desperately poor seeing crappy movies? If it's your retirement strategy, yes, that's a problem; as harmless entertainment it's fine.

2) The only person with lower odds of winning the lottery than a person who buys a ticket is the person who buys zero tickets. Despite the struck-by-lightning-on-a-unicycle-halfway-up-Mount-Everest odds, someone always does win, eventually...

--- Ajax.
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Date:August 27th, 2009 05:26 am (UTC)
I may be mistaken, but when people decry the lottery as a tax on the poor, isn't it more about the person buying 50 tickets or a ticket twice a week, rather than the person who buys one occasionally as a means of entertainment?
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Date:August 28th, 2009 12:24 am (UTC)
Certainly people who are gambling addicts are a serious problem, but that's different from the lottery being a 'tax on the poor'.

Overall, the lottery keeps half the money it takes in, so on average, the government takes money from the players. In that sense it is a tax.
If we compared a poor person and a rich person who each played the lottery the same amount, the amount spent/lost makes up a larger fraction of the poor person's income. So the lottery is a regressive tax, like sales tax or the gas tax, that affects the poor more severely.
Compounding that fact is the fact that poor people tend to play the lottery a lot more than rich people. It's difficult to find data supporting a sweeping blanket statement like that, but a study of the Connecticut lottery showed that, per capita, the poorest 10 ZIP codes won 6 times as many prizes as the 10 richest ZIP codes. Unless the powerballs are taking pity on the poor people, this suggests that poor people are spending 6 times as much money on the lottery. So not only does each dollar hurt poor people more, but they're spending more dollars. On average.

Of course, by the same token, the 1 in 175 million winner of the jackpot is more likely to be poor than rich. But the fraction of poor people 'promoted' to rich people is pretty tiny.

If the entertainment value is worth the money they're spending, that's fine. But as a means of funding the government, the burden of the lottery falls more heavily on the poor.
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Date:August 27th, 2009 05:06 pm (UTC)
I usually hear the lottery decried as a tax on the stupid, not the poor. But yes, the poor are more likely to buy a ticket, and each ticket they buy represents a larger fraction of their income. And they tend to buy more tickets.
The largest jackpot winner ever was worth $18M... before he won the lottery. :-(

And I would like to claim that I've been encouraging people to buy lottery tickets long before Mike. He also left out some reasons
1) Taxes on lotto money go to education!
2) You are participating in a massively distrubted dream-granting machine.
3) If you spent $5k on tickets throughout your lifetime (one ticket per drawing for the rest of your life), it would not significantly impact your lifestyle. $100M, on the other hand, would. So in the sense of utility theory, the downside is almost non-existent, and the potential upside is enormous.

And the reason so many people hit the 3-number combo is because the bigger the drawing, the more people play. I'm willing to bet the number of 3-hits increases this week.

Journal of No. 118