We did the math to see if it's worth buying a ticket for the $393 million Mega Millions jackpot

The Mega Millions drawing for Friday evening has an estimated jackpot, as of noon ET Friday, of about $393 million.

While that's a huge amount of money, buying a ticket is still probably a losing proposition.

Consider the expected value

When trying to evaluate the outcome of a risky, probabilistic event like the lottery, one of the first things to look at is "expected value."

The expected value of a randomly decided process is found by taking all of the possible outcomes of the process, multiplying each outcome by its probability, and adding all of these numbers up. This gives us a long-run average value for our random process.

17 Things More Likely to Happen to You Than Winning the Lottery (GOBankingRates.com)
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17 Things More Likely to Happen to You Than Winning the Lottery (GOBankingRates.com)

1. Being Killed by a Meteorite

You're actually more likely to be killed by a meteorite than be hit by one, according to Discover Magazine. That's because you're a small target on Earth while the planet itself isn't too unlikely to be hit by an asteroid. In fact, the odds of an asteroid causing enough havoc on Earth to take you out are about 1 in 700,000, according to astronomer Alan Harris.

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2. Becoming the Next Warren Buffett

Looking to be the next Warren Buffett? Chances are you'll climb your way to the top before you ever win the lottery.

The 2015 World Health Report from Capgemini showed 15.37 million individuals worldwide are worth $1 million or more. Even with a relatively small pool of millionaires and billionaires, Americans (millennials in particular) are hopeful they'll be rich someday.

The television network Fusion polled millennials on whether they expected to become millionaires in their lifetimes. Roughly 28 percent said they planned on it, even though 40 percent of respondents claimed to still receive financial support from their parents.

Get Rich: 7 Things Successful People Don't Waste Their Money On

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3. Dying in a Plane Crash

If you're scared of flying, you might want to read this one. As terrifying it is to think about a hunk of metal sitting at a cruising altitude of 36,000 feet, chances are you won't be falling out of the sky any time soon.

The Economist estimated your odds of dying by plane crash are about 1 in 5.37 million. Slim odds to say the least. Chances you'll be stuck between a crying baby and a guy who won't give you elbow room? Much higher.

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4. Being Killed by Hornets, Wasps or Bees

Painful as a bee or wasp sting, chances are it won't kill you. The National Safety Council estimated the odds of dying by hornet, wasp or bee sting are 1 in 64,706.

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5. Being Canonized

In his book "Life: The Odds," author Gregory Baer pegs your chances of becoming a saint at 1 in 20 million, given that about 100 billion people have lived on this planet and about 5,000 have been canonized.

If you're looking to boost your chances, try becoming the pope.

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6. Getting Audited

Tax season might make you sweat, but your chances of ever being audited aren't too bad — about 1 in 119, reported Kiplinger. And unless you're making millions of dollars or reporting nothing at all on your taxes, chances are your lone W2 won't be getting a lot of attention from the taxman.

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7. Becoming President of the U.S.

If being blamed for all of America's problems are on your shortlist of things to do, you're in luck. The chances of becoming president are about 1 in 10 million, according to Baer. Those odds increase drastically when you're between the ages of 40 and 72, have a law degree, are a military veteran or a man of faith above six feet tall.

If you're America's favorite Republican nominee Donald Trump, your chances are even higher.

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8. Being Wrongfully Convicted of a Crime

Supreme Court Justice Antonin Scalia (RIP) cited the odds of a wrongful conviction at about 0.027 percent, or 1 in 3,703, in a 2006 court opinion. This was based on rough math an Oregon district attorney cobbled together for a New York Times op-ed, but many experts place your odds of being wrongfully convicted much higher.

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9. Becoming a Movie Star

Fame and fortune don't go hand-in-hand. According to the Bureau of Labor Statistics, the median pay for actors was $18.80 in 2015, with over 69,000 jobs available in 2014.

Although few acting jobs will put you on the A-list, landing a role for a big-screen film is far easier than winning the lottery. Long story short: You're better off buying a ticket to Los Angeles than putting in your share of the $73.8 billion lotteries made in 2015.

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10. Having Your Identity Stolen

Over the years, businesses like Target and Sony have been the targets of large scale data breaches, exposing millions of customers to identity theft. If you've received letters in the past that your information was compromised due to a data breach, take caution. A 2013 report by Javelin Strategy & Research found that 1 in 4 data breach letter recipients became victims of identity theft.

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11. Writing a New York Times Bestseller

If you're already a published author, writing the next New York Times bestseller is stupidly easy. Your chances of making the cut are about 1 in 220. According to Baer, you actually have worse odds of catching a foul ball at a baseball game (1 in 563).

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12. Becoming an Astronaut

Money can't buy a trip to the moon, although it could buy a ticket on Virgin Galactic. If you fantasize about being an astronaut on the ISS or just about any other spacecraft with a view of Earth, your chances of joining NASA's 2017 astronaut class of eight to 14 are around 1 in 2,300, or 1 in 1,300 if you're feeling optimistic.

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13. Being the Victim of a Chainsaw Accident

Mother always told you not to run with scissors. Well, she should have warned you about chainsaws, too. Your odds of getting injured in a chainsaw accident are 1 in 4,464, according to estimates from the University of Nebraska-Lincoln.

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14. Going to the E.R. With a Pogo Stick-Related Injury

To be fair, pogo sticks are terribly difficult to use. Just be aware that if you have the misfortune of spending an afternoon on one, your chances of bouncing your way into the ER are about 1 in 115,300, according to one report.

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15. Winning an Olympic Gold Medal

You have about a 1 in 662,000 chance of taking home Olympic gold in your life — but, of course, you have to get yourself into the games first. The YouTube channel AsapSCIENCE ran the numbers on how to increase your chances of becoming a winter Olympian and found that hailing from Liechtenstein gives you the best odds at the Winter Olympics (1 in 9,000).

Curling is your best bet for a sport, given its high number of participants and the fact that many curling Olympians are in their 40s — and aren't exactly in what many would consider "Olympian" shape.

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16. Dying From Natural Heat

A little fun in the sun never hurt — or so you thought. The National Safety Council reported 1 in 10,784 people die of exposure to excessive heat. So drink your water, wear a pretty sun hat or just stay indoors forever and you'll be fine.

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17. Having Conjoined Twins

Your odds of birthing conjoined twins are about 1 in 200,000, according to the University of Maryland Medical Center. Your odds of giving birth to normal twins? About 3 in 100.

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Expected value is helpful for assessing gambling outcomes. If my expected value for playing the game, based on the cost of playing and the probabilities of winning different prizes, is positive, thenin the long run the game will make me money. If expected value is negative, then this game is a net loser for me.

Mega Millions and similar lotteries are a great example of this kind of probabilistic process. In Mega Millions, for each $1 ticket you buy, you pick 5 numbers between 1 and 75, and then an extra number between 1 and 15. Prizes are then given out based on how many of the player's numbers match the numbers chosen in the drawing.

Match all five of the numbers between 1 and 75, and the extra number between 1 and 15, and you win the jackpot. After that, smaller prizes are given out for matching some subset of those numbers.

The Mega Millions website helpfully provides a list of the odds and prizes for each of the possible outcomes. We can use those probabilities and prize sizes to evaluate the expected value of a $1 ticket. Take each prize, subtract the price of our ticket, multiply the net return by the probability of winning, and add all those values up to get our expected value:

pre tax annuityBusiness Insider/Andy Kiersz, odds and prizes from Mega Millions

Looking at the basic case, we end up with a positive expected value of $0.69, making it look like a Mega Millions ticket might be a good investment.

But there are a few catches.

Annuity vs. lump sum

Looking at just the headline prize is a vast oversimplification.

First, the headline $393 million grand prize is paid out as an annuity: Rather than getting the whole amount all at once, you get the $393 million spread out in smaller — but still multimillion-dollar — annual payments over the course of 30 years. If you choose to take the entire cash prize at one time instead, you get much less money up front: The cash payout value at the time of writing is $246 million.

Looking at the lump sum, we get a pretty big cut into our expected value, falling to just $0.13:

pre tax lump sumBusiness Insider/Andy Kiersz, odds and prizes from Mega Millions

The question of whether to take the annuity or the cash is somewhat nuanced. The Mega Millions website notes that the annuity option gives out payments that increase by 5% each year, presumably keeping up with and somewhat exceeding inflation.

On the other hand, the state is investing the cash somewhat conservatively, in a mix of various US government and agency securities. It's quite possible, although risky, to get a larger return on the cash sum if it's invested wisely.

Further, having more money today is frequently better than taking in money over a long period of time, since a larger investment today will accumulate compound interest more quickly than smaller investments made over time. This is referred to as the "time value of money."

Taxes make things much worse

In addition to comparing the annuity to the lump sum, there's also the big caveat of taxes. While state income taxes vary, it's possible that combined state, federal, and, in some jurisdictions, local taxes could take as much as half of the money.

Factoring this in, if we're only taking home half of our potential prizes, our expected value calculations move into negative territory, making our Mega Millions "investment" a bad idea. Here's what we get from taking the annuity, after factoring in our estimated 50% in taxes. The new expected value is now underwater, at -$0.07:

after tax annuityBusiness Insider/Andy Kiersz, odds and prizes from Mega Millions

The hit to taking the one-time lump sum prize is just as devastating:

after tax lump sumBusiness Insider/Andy Kiersz, odds and prizes from Mega Millions

After factoring in taxes, then, our "investment" in a Mega Millions ticket is not necessarily a great idea.

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