## If Lottery Tickets Told the Truth

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### 11 Responses:

1. cjensen says:

Lotteries can make mathematical sense once you realize that some dollars are worth more than others.

Plus we have to make the poor pay their taxes somehow...

• jng27 says:

People would still buy those if they were real.

• hukuma says:

Only if you have some weird sense of marginal utility, where your first dollar is worth a lot less than your millionth.

• cjensen says:

Actually, it's a pretty common situation. A single dollar is worth exactly nothing to many people. A large lottery win can be life changing and allow a person to subsidize a nightclub. Assuming nightclubs and supporting the arts without appreciation are worth a very lot to you, then the value of a lottery ticket can be worth more than the value of a single dollar.

Or for the more self-interested, retirement *right now* is worth so much more than working that the value of a lottery ticket with its chance of a retirement can be worth more than a single dollar spent exactly once.

Of course, econ theory agrees that if you are poor and are buying a lottery ticket every freaking week, then you are certifiably insane.

• fnivramd says:

But in practice most lotteries are structured eerily like the St Petersburg lottery thought experiment. The relatively high expected value consists almost entirely of a microscopic chance of a huge win. An evaluation function that takes this microscopic chance seriously needs to consider other equally unlikely things too. Derren Brown's "how I predicted the lottery" show drops in the idea that on average a middle-aged man who buys a [UK lotto] ticket an hour before the draw is more likely to die before the draw happens than win the jackpot.

Also, this is about scratchcards, not a weekly draw. The scratchcard prizes tend to be smaller, maximum prize could be as little as \$100 000. Suppose you're the kind of person for whom a dollar's marginal utility really is low. You're earning \$50 000 and you buy a scratchcard with your morning coffee (\$250 per year). But in the rare chance that you win, the "jackpot" is only two years salary. Is that really "life changing" ? Marginal utility comes back to haunt you.

• hukuma says:

I don't believe that a) your dollar is worth exactly nothing, and b) that winning the lottery is so valuable that even on expectation, it's good to play. For point a), consider a Starbucks that charged you \$1 to put chocolate sprinkles on your mocha. Would you pay? Probably not. (If you don't like mochas or sprinkles, I'm sure there's another example you could come up with.)

For point b), the marginal value of the millionth dollar is even less than the (small) marginal value of your \$1 now. (If you had a million bucks, you might spring for the sprinkles, e.g.) And the marginal value of all the dollars leading up to it are no larger than your \$1 right now, so on expectation, you lose.

Think about it another way. If it's rational for you to spend \$1 on a lottery ticket today, it's rational for you to do the same thing tomorrow. After all, you'll be in a similar situation: you have a \$1 that's worth almost nothing, and you still dream of subsidizing that nightclub. In fact, if you manage your money responsibly and spend less than you earn, your net worth is probably slightly larger tomorrow, so the dollar is not worth any more to you today. But this implies that it's rational to play the lottery every day.

2. telecart says:

This looks like something out of MAD magazine.

3. elena says:

I'd play the first ticket. :B

4. don_negro says:

I smell a snarky libertarian in this. The federal government doesn't sell lottery tickets.

• volkris says:

I suspect most libertarians, being down with the concepts of federalism, would be aware that the federal government neither sells lottery tickets nor earmarks lottery revenues toward education.

5. kencf0618 says:

It's great entertainment value for my dollar, and I only play Powerball when the gross hits three figures, which is when the corporate pot gets passed around at work.