When is it ever rational to enter a sweepstakes where you may have a 1/10,000 chance of winning?

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.

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 is it ever rational to enter a sweepstakes where you may have a 1/10,000 chance of winning?

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.

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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.