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I am a statistician and I buy lottery tickets

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Re: I am a statistician and I buy lottery tickets

#61

Post by gvb »

dimitar wrote: post #51

An honest question: Why don't hedge funds buy lottery tickets?

Hedge funds are hedging against (sort of) specific bad things happening. To do this, they buy into an investment that (hopefully ;-) has a [edit] positive correlation to the "bad thing" they are hedging against so that, if the bad thing messes up your primary investment, the hedge investment gains compensate (some of) your losses.

Example: http://money.stackexchange.com/questions/6473/where-should-i...

Since winning the lottery is not correlated at all with something bad happening to an investment firm's investments, it is a very poor hedge against their investments failing to come through.

Re: I am a statistician and I buy lottery tickets

#65

Post by yummyfajitas »

paulsutter wrote: post #16

Insurance has an interesting comparison to lottery tickets. In a lottery ticket, the expected return is usually about 50%. Which is exactly the same as insurance (the premium is about double the expected payout). Yet people regard insurance as prudent, and lottery tickets as foolish. Me included (as long as its a risk you cant easily cover). But our explanation, that "Lottery tickets are foolish because they have a n…

Insurance is about trading money for utility. The assumption is that your utility curve in the lossy region is sublinear, i.e. U(-$1e6) In that case, if you pay a guaranteed -$1, your expected utility loss is U(-$1). If you have a 1e-6 chance of losing $1e6, your expected utility loss is 1e-6 U(-$1e6) Thus, it makes sense to pay $1 to avoid the risk of losing $1e6.

Insurance which pays for high probability, low cost events (e.g., gas for your car, birth control pills) is indeed foolish.

Re: I am a statistician and I buy lottery tickets

#66

Post by powrtoch »

yummyfajitas wrote: post #65
paulsutter wrote: post #16

Insurance has an interesting comparison to lottery tickets. In a lottery ticket, the expected return is usually about 50%. Which is exactly the same as insurance (the premium is about double the expected payout). Yet people regard insurance as prudent, and lottery tickets as foolish. Me included (as long as its a risk you cant easily cover). But our explanation, that "Lottery tickets are foolish because they have a n…

Insurance is about trading money for utility. The assumption is that your utility curve in the lossy region is sublinear, i.e. U(-$1e6) In that case, if you pay a guaranteed -$1, your expected utility loss is U(-$1). If you have a 1e-6 chance of losing $1e6, your expected utility loss is 1e-6 U(-$1e6) Thus, it makes sense to pay $1 to avoid the risk of losing $1e6. Insurance which pays for high probability, low cost…

> The assumption is that your utility curve in the lossy region is sublinear

Which makes lottery tickets all the more a bad idea. Not only is the expected return in dollars less than your investment, but thanks to the diminishing marginal utility of money your ten millionth dollar will be worth less than your ten thousandth. Lottery tickets are actually worse than their already crappy EV.

Re: I am a statistician and I buy lottery tickets

#67

Post by megablast »

rvkennedy wrote: post #49

The main thing to be learned from this post is that the “Super 7’s Oz Lotto” is clearly a badly run lottery. If the expected return for a ticket is greater than the price, this lottery is losing money for the organizers. Perhaps this explains the glum-looking face on their logo: https://media.tatts.com/images/lotto/tattersalls/site-logo-t...

The money is so big because it has rolled over, it has not been won for a while.

Re: I am a statistician and I buy lottery tickets

#68

Post by yummyfajitas »

powrtoch wrote: post #66
yummyfajitas wrote: post #65

Earlier quoted context omitted.

Insurance is about trading money for utility. The assumption is that your utility curve in the lossy region is sublinear, i.e. U(-$1e6) In that case, if you pay a guaranteed -$1, your expected utility loss is U(-$1). If you have a 1e-6 chance of losing $1e6, your expected utility loss is 1e-6 U(-$1e6) Thus, it makes sense to pay $1 to avoid the risk of losing $1e6. Insurance which pays for high probability, low cost…

> The assumption is that your utility curve in the lossy region is sublinear Which makes lottery tickets all the more a bad idea. Not only is the expected return in dollars less than your investment, but thanks to the diminishing marginal utility of money your ten millionth dollar will be worth less than your ten thousandth. Lottery tickets are actually worse than their already crappy EV.

Well, some people hypothesize that your utility can be superlinear in the positive region. Utility = (gain or loss)^3, for example.

Of course, the stats prof says he buys lottery tickets because they are fun. I do something similar - even though the expected gain from video games is precisely $0, I still play them.

Re: I am a statistician and I buy lottery tickets

#69

Post by koningrobot »

kryptiskt wrote: post #15
hdivider wrote: post #2

Nice calculation, but it doesn't contradict the 'rational' argument at all. Slightly disappointing: looking at the title and first paragraph I expected some weird statistical wizardry on why the calculation of expected values is fundamentally flawed somehow. (Which would be surprising, given that it's an important mathematical tool in quantum mechanics (even though the formalism there is different).) Also, why pay fo…

The expected value isn't flawed, but it's often not an useful guide to what action you should take. Imagine a lottery with an accumulated jackpot of $11 million, and there's one million $10 tickets (this isn't all that rare). Should you take all your savings and buy 1000 tickets? You have a positive expectation value, and 99.9% chance of ending up penniless. Is one that buys the tickets really a much more rational pe…

This is because you're not after money but after welfare (whatever that is).

Re: I am a statistician and I buy lottery tickets

#70

Post by graeme »

paulsutter wrote: post #22
afhof wrote: post #18

Earlier quoted context omitted.

Unless you can sustain a $100,000-$300,000 loss before you have have paid into the insurance pool more than that amount, it makes sense. If you had gobs of money, then it wouldn't make sense for you to have insurance. (preconditioned on insurance being a profitable business, etc.)

By analogy - if a person thinks "spending $5 has no impact on my life, but winning $10M will", is that really any different from our justification of insurance? (I agree with you - thats the same way I view insurance. Yet I view lottery tickets as silly, but I can't clearly articulate why).

The cumulative impact of a lifetime of spending $5 per week is much less than winning a lottery. Most people can sustain a $5 per week hit, especially if they get the mental benefits described by the parent article.

There are better things to spend $5 on, but it's not a huge deal either way - as long as you stay out of the addictive/compulsive zone.

The losses covered by insurance are very impactful. Most people can't sustain the massive financial hit that comes from, say, their house burning down. It can make sense to lessen their day-to-day quality of life by spending money on insurance, to guard against that massive downside risk.

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