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Lottery - February 12, 2010
Rating: 4.4/5 (48 votes cast)
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Spiked Math Comic - Lottery

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And here I thought that gambling was a tax on the mathematically inept...

Does a ticket cost more than $1.41 or less?

Probably more--lotteries usually have (or did anyway) about 45% payout, so a ticked would be in the area of $3.00.

I might buy one ticket on the chance of getting lucky--but more than that would be a waste of money.

Nope, Powerball's a buck.

Lotteries sometimes have decent expected value, because if nobody wins the jackpot in a previous round the winnings continue to increase. Although after taxes I'm not sure that it's worth it...

Which is why one Mafia don once pointed out that his numbers racket was much more "honest" than the official lotteries:

The payout rate was much higher, and you didn't have to pay income tax on the "winnings"...

The ticket costs $1, so when the jackpot gets that high (and it sometimes does), it WOULD be mathematically worth playing, except for three problems:

1.) The jackpot is actually the future value of a 30-year annuity. If you take your payment in the form of a single lump-sum payment you get just about half of the advertised jackpot value.

2.) You have to pay taxes on your winnings, so in conjunction with #1, that $275 million is actually only about $70 million in your pocket, so not enough to cover the odds.

3.) Even if the jackpot DID ever get so high that it was +ev after accounting for the first two points, there's also the problem that if multiple people win in the same drawing, they have to split the jackpot, and if the jackpot were that high there would probably be close to a billion tickets sold and so your odds of splitting the prize would still leave you in a -ev situation.

Don't forget to take into account, though, all the non-jackpot winnings. There's bound to be a lot of $5 and $10 winning tickets, and that stuff adds up.

I haven't actually run the math in a while, and forget the exact numbers, but I think all the non-jackpot prizes combined added up to an EV of something like 18 cents on the $1 ticket, so those other prizes don't really do too much to help.

Which is why the Don said his game was more honest and a better deal--no taxes, no delayed payout or reduced payment for getting a lump sum.

Have you heard of the West Dakota Sweepstakes? The jackpot is $1 per year for the next one million years...

Most Canadian lotteries pay out in one lump sum and if you are
a Canadian citizen residing in Canada they are tax free. (If
you live somewhere like the U.S. your government will still
want a tax bite even if you made the money from outside your
country. ^_-)

"Knowing when to play the lottery is relatively clear. You play when the expected value of a ticket is more than the cost. The Kelly criterion tells you how much to play by calculating what fraction of your bankroll you should bet when the odds are in your favour. ..." -- Do Not Play the Lottery Unless You Are a Millionaire

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Hello my fellow math geeks. My name is Mike and I am the creator of Spiked Math Comics, a math comic dedicated to humor, educate and entertain the geek in you. Beware though, there might be some math involved :D

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