Friday, March 30, 2012

Buying a Lottery Ticket Is a Rational Investment - For Tomorrow Only

For once, it's actually a rational investment to buy a lottery ticket.

Public service announcement - for tomorrow only, buying a lottery ticket is a rational investment.

I noticed that one of my news feeds said that the MegaMillions lottery jackpot has reached an all-time high - an estimated $540 million for the drawing tomorrow, Friday, March 30. The MegaMillions site currently lists the cash-out option at $389 million, which could leave the winner with as much as a $250 million lump-sum payday after taxes.

Most of the time, lotteries are taxes on people who don't understand probability and statistics. But in a situation such as this, that's no longer the case.

With the value of the jackpot so high, the expected value of a lottery ticket is now greater than what it costs to buy a ticket. It costs $1 to buy a ticket, and the expected value of the ticket is $250 million times the odds of winning (1 in 175,711,536) = $1.42.

So, even though my chances of winning are practically zero, the probability theorist in me is compelling me to go out and play the lottery for the first time in my life, since the expected value of a lottery ticket is greater than the cost of the ticket. If you want to please the probability theorist in you, then go play the MegaMillions lottery tomorrow as well, and keep playing until someone hits the jackpot - and if you win, I expect a cut, if my observations on the expected value of a lottery ticket compelled you to buy a ticket ;)

4 comments:

  1. Someone once told me the lottery is a stupidity tax. So every time I do something stupid and get away with it, I buy a lottery ticket.

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  2. Since more than 400 million tickets have already been sold, isn't it likely there will be more than one winner to split the proceeds? If two share it, then the post-tax payout is only $125 million, so the purchase is irrational.

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  3. Joe: That's pretty funny - way to maintain the karmic balance ;)

    Mike: Touche. Just eyeballing the list of jackpot winners, it looks like somewhere between one-third and one-fourth of the "big" jackpots were split among 2+ winners. So, I think that leaves us still above $1, but below $1.42. If my odds of winning were higher, I'd work out the exact amount above $1 taking all that into account, but that would be too much work for an off-the-cuff blog post like this one.

    -The Angry Bureaucrat

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