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When is it ever rational to enter a sweepstakes where you may have a 1/10,000 chance of winning?
It may be free to enter the sweepstakes, but it costs time to enter the sweepstakes. So the time is the first part of the cost. Then you may also have monitoring costs as well (if you monitor the progress of the sweepstakes, which may also cost valuable time).
But at the same time, there are other sweepstakes where the time it takes to enter is virtually 0. This could result in additional time costs if it results in increased spam, however (which may not come with most sweepstakes, but which may come with some).
And, of course, you have to factor in the expected gain if you entered, say, 1000 sweepstakes in your life. Eventually, you get to the point where you may have a decent probability of winning something big by entering so many of them
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Comments (15)
Relevant reading:
http://en.wikipedia.org/wiki/Expected_value
http://en.wikipedia.org/wiki/Decision_tree
Try to quantify the cost of entering the sweepstakes. Sure, entry is free, but as you point out there are other less tangible costs of time and energy. But let's try. Let's say it takes 1 hour to enter, and another 1 hour in a couple weeks to follow up. Let's say you're a reasonably successful person, and your time is worth $50 per hour. So it will cost you roughly $100 to enter the sweepstakes.
Next we need to determine the expected value of winning the sweepstakes. Let's say the prize is $1 million. If the chance of winning is truly 1 in 10,000, then our expected value is ($1 million) x (1/10,000) = $100.
So... in this contrived little example, we are exactly neutral. It costs us approximately $100 to enter and our expected value is approximately $100. This is equal to the $0 of not messing with the sweepstakes at all.
When would it be rational to enter? We can tweak the variables on either side. For example, if your time is only worth $20 per hour and it only takes 5 minutes to enter and 5 minutes to follow-up, your total cost is $3.33. It costs you $3.33, but the expected value is $100, so the net benefit of entering is $96.67. That is better than the $0 of ignoring the contest, so rationally you should enter.
Or, consider if the sweepstakes prize was worth $1 billion. Now the expected value is ($1 billion) x (1/10,000) = $100,000. Pretty good prize! It is clearly worth your time.
We could generalize this...
For any sweepstakes where you have a 1/10,000 chance of winning, it is rational to enter if the prize is 10,000 times more valuable than the cost of entering.
The problem with generalizing it is that the value of money isn't constant. I would much rather have a million dollars free and clear than a 1/10,000 chance at ten billion dollars.
The technical term that behavior is risk aversion: http://en.wikipedia.org/wiki/Risk_aversion
Furthermore, the behavior you are describing can be modeled with Utility Theory: http://en.wikipedia.org/wiki/Utility
Utility theory explains many human quirks, such as loss aversion: http://en.wikipedia.org/wiki/Loss_aversion
It also explains why we're willing to pay for insurance, when often times insurance is more expensive than they payouts we receive.
*edited to a more neutral tone
Money is not linear in utility. Even granting that risk-neutrality in utility is the only rational approach, risk-neutrality in money does not follow.
Indeed, you are correct.
In my finance education, professors always argued that your money curve should be as close to 1:1 with your utility curve as possible. Granted, that's a dubious setting. Probably correct for money managers, but not for humans in daily life.
I would not call what utility theory explains in this case a quirk. Ten billion dollars are not actually ten thousand times more useful to me than a million dollars, and as a rational person I should presumably care about utility more than dollars.
Two months ago, I read Justified Expectation of Pleasant Surprises and was vaguely reminded of the site Win For Me (link zapped by a spam filter, looks like). For a fee of $71, Win For Me enters you into every free sweepstake it can for a year. I decided to try it out, mainly because if it actually works it'll be a fun birthday present to give others.
Yesterday I won my first sweepstakes. The prize was a copy of the book "The Amish Midwife," by Mindy Stafford. It's available for $7.55 on Amazon, meaning my expected monetary value for the year's subscription to Win For Me can now be estimated at $45.30, plus a ridiculous amount of variance.
Interesting. It reminds me of the something store, which isn't a sweepstakes-type thing in the traditional sense, but fills a similar niche.
That looks brilliant.
A neighbor of mine enters every sweepstakes she can find, sending in dozens of applications per day. She wins at least one prize a month, ranging from kitchen gadgets to trips. The listed likelihood of winning is often an underestimate, she says, since some sweepstakes do not receive the number of expected applications. This is a life-defining hobby for her: it takes a significant amount of her time each day to find and enter these contests; most of her stories center around the prizes she's won. Here is an article about a woman in a similar situation: http://www.post-gazette.com/pg/08335/931083-54.stm
When you are desperate. ie. You owe money to a loan shark and will do anything to reduce the chance of having your kneecaps busted.
Even in other debtor situations where you face a set penalty, like (non-violent) bankruptcy, for falling $X short and $(X-1) dollars short, it can be rational to spend money to enter sweepstakes.
It can in theory, though it is worth remembering that in practice it is vastly more likely that you are better off to forget about long shots, grit your teeth and focus on putting together a realistic proposal for paying off the debt in installments.
It's not just about sweepstakes being a long shot - being in debt is a very tough test of rationality, because you have a terribly strong incentive to say what your creditors want to hear, combined with a death spiral of learned helplessness. It's the one time when you can't afford any emotional distractions.
On the bright side, if you can get enough of a grip on reality to navigate your way out of that situation, tougher tests than that will be few and far between.
Ignoring sweepstakes as such[1], a focused rationalist should regard all bets with odds far from a coin flip with suspicion; there are often better bets, and with more information for calibration.
[1] Perhaps justifiably, as the "may" in the title of this Discussion post implies more uncertainty than you find in a typical sweepstake scenario where the fine print and simple arithmetic are enough calculation in themselves.
Indeed, and this made me wonder if we attach some privileged weight to things explicitly defined as "the lottery" and "sweepstakes." In other words, are they such because they give you a chance at a prize for no money down?
If that's all, then someone who can reliably win at poker or some other set-ruled game could be said to be winning "sweepstakes" all the time were we able to conclude that their skills made it highly improbable that the buy-in would ever be lost (thus equivalent to "no money down", in a sense).