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# MegaMillions At \$640M Is Still A Losing Bet

"May the odds be ever in your favor!" - This sinister line from the blockbuster movie The Hunger Games could easily be the ironic tag line of every lottery system in America. A lot of ink has been spilled about how bad of an investment a lottery ticket is. I would argue that it is a regressive tax on the numerically challenged and the statistically disabled. Megamillions helpfully points how unlikely you are of winning.

However, I have an old friend that always bought the big PowerBall or MegaMillions tickets whenever the payout got above the odds of winning. MegaMillions is in the news this week with a current estimated Jackpot of \$640 million. Given the odds of winning the jackpot are *only* 1 in 175 million - he must be buying tickets by the fistful. Plus, even if he doesn't win the jackpot he can still win \$250k, \$10k, or even \$2! I must admit a jackpot of half a billion is exciting any way you slice it. I decided to go digging to see if I should buy some tickets. So… are the odds really in your favor?

Nope. According to an awesome post written by Jeremy Elson of Microsoft Research, you must factor in taxes, the present value of the award AND the likelihood of other potential winners. His key insight is that when jackpot sizes rise beyond a couple hundred million, the pace of ticket buying goes super-linear - meaning it accelerates. To quote Jeremy:

"This means there is a point of diminishing return where the negative expectation due to ties outweighs the positive expectation due to having a larger jackpot. Taking this into account, it is unlikely that buying a lottery ticket is ever profitable in expectation, no matter how big the jackpot gets."

In fact, Jeremy posits that the peak expected value of \$0.693 per \$1 ticket, including the value of non-jackpot prizes, happens when the jackpot reaches \$420 million. The expected value then begins to decline again because you will most likely split the winnings with one or more winners.

Ok, so if it never makes sense to buy a MegaMillions ticket - who wins? At the end of Durango Bill's insightfulMegaMillions analysis, he lists the winners:

"1) Federal Government (Lottery winnings are taxable)
2) State Governments (Again lottery winnings are taxable)
3) State Governments (Direct share of lottery ticket sales)
4) Merchants that sell tickets (Paid by the lottery organizers)
5) Lottery companies (Hint: They are not doing all this for free)
6) Advertisers and promoters (Paid by the lottery companies)"

There is a footnote provided by Jeremy however… if you happen to have gambling winnings, the purchase of the lottery tickets are tax deductible against those winnings! So, don't be surprised if you see Doyle Brunsonor Phil Hellmuth at your local convenience store stocking up on lottery tickets.

When you buy a coffee today, don't buy the lottery ticket - it ain't worth it. Hmmm, it is less than your coffee - buy one ticket. You gotta be in it to win it, right?

Disclosure: I bought some tickets… Heck, why not?