Lottery offers more chances to lose
The N.C. Lottery may introduce a game that allows the worst chance yet of winning.
For $20, you could buy a ticket for a chance to win one of four $1 million prizes, five $100,000 prizes or 500 $1,000 prizes, director Tom Shaheen told The News & Observer.
Twenty bucks to win a million doesn't sound bad -- or at least that's what lottery officials hope the public believes.
But the odds aren't too good when you consider that 500,000 tickets will be available.
That's a total of 509 winners out of 500,000 tickets. If you buy one ticket, you'll have a one in 982 chance of winning something.
For Powerball, your chance of winning a prize is one in 36.6.
Of course, you could buy all 500,000 tickets and win all $5 million.
It would only cost you $10 million to do it.
Comments (14)
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Thank you for the important, very important, math lesson, Doug. As I've said before, there's a horrible irony in tagging this the "education lottery".
Posted on February 12, 2007 2:20 PM
At least fewer North Carolinians than anticipated are buying into it.
Posted on February 12, 2007 4:21 PM
At least fewer North Carolinians than anticipated are buying into it.*Doug
So you are really against public schools after all eh Doug? What's next? No more bets on the Panthers and Colleges Sports in North Carolina with on-line Indian Casios in Western North Carolina? I bet you thought those little old ladies were playing bingo there with the Church Choir collection money.
Posted on February 12, 2007 5:49 PM
Doug:
While this is a bad bet, you haven't described the expected pay-off correctly. The expected payoff is $10 (= (4x$1000000 + 5x$100000 + 500x$1000)/500000). Unlike Powerball, there are no $2 or $3 prizes.
Anyway, the pay-off is comparable to other state lotteries--again, bad.
Posted on February 12, 2007 8:27 PM
Apparently, more North Carolinians are less mathematically challenged than what we originally thought.
I've heard that more states are seeing a falloff in lottery sales.
Posted on February 12, 2007 8:31 PM
A quick calculation of this week's Powerball lottery (max. cash pay-off is $22 million) indicates that the expected pay-off from a $1 bet is approximately 35 cents.
Posted on February 13, 2007 7:58 AM
Dave,
The overall payoff for this raffle would be $5 million for $10 million in ticket sales, or 50 cents on the dollar. But with 509 winners out of 500,000 tickets, I'm sticking with my odds of one in 982 that the one ticket you buy will win you some money (most likely $1,000).
Posted on February 13, 2007 8:29 AM
Doug,
The title of this article is "Lottery offers more chances to lose".
For a minute there I was taken back to 2004 and thought you were writing about the Southwest kids and the Choice Plan lottery.
Posted on February 13, 2007 9:19 AM
Sorry to frighten you.
Posted on February 13, 2007 9:25 AM
Doug,
I'm disappointed in you for dissin' the lottery. So what if playing the lottery is a loss leader, it's for the children, you know.
Posted on February 13, 2007 10:08 AM
Doug:
A rational calculation of whether to play the lottery should be based on the expected pay-off rather than the probability of any pay-off. Consider a simpler, made-up example. You would most likely prefer a $1 lottery that gave a 1-in-1000 chance of winning $500 to a $1 lottery that gave a 1-in-100 chance of winning just $10 dollars. There is a lower probability of winning something in the first lottery, but a higher expected pay-off (50 cents versus 10 cents). The state of course would like both of these lotteries because the expected pay-offs are lower than the cost of a lottery ticket; however, it would prefer the second lottery in which players lose more money on average.
There are ways to compare the expected values and the variability of pay-offs. But someone would have to have an extremely high aversion to risk to prefer the Powerball's 30 cent on the dollar average (this week's expected pay-off is a little high) to the other lottery's 50 cent on the dollar average. However, that seems unlikely as anyone who would play one of these lotteries (that is, someone who goes in accepting an expected loss of 50 to 70 cents on his/her dollar) must by definition be someone who prefers rather than avoids risks. The safe bet (no risk, higher expected rate of return) would be not to play at all.
Posted on February 13, 2007 11:26 AM
Dave,
I have to yield to your analysis, particularly since I have just looked up your academic credentials.
(Whenever I write anything about numbers or money, I should first run it by my son, Kenny, who has a BS in analytical finance and an MS in accountancy. Not that I'm bragging on him, but he's a smart kid.)
I guess it boils down to a personal perspective. If I were to play the lottery, which I'm not, I'd want to know my odds of coming out ahead rather than coming out way, way ahead. From that standpoint, I would prefer to play the basic scratch-off with a modest top prize but a decent chance of winning back my dollar or maybe making an extra buck.
Anyway, thanks for your explanations, which I hope will persuade readers to spend their own money in better ways.
Posted on February 13, 2007 11:42 AM
Doug:
You have every right to brag :) Congratulations.
Posted on February 13, 2007 12:28 PM
Ah, therein lies the rub (pardon the pun): what is a "decent chance of winning back" one's dollar?
Everyone defines "decency" differently, whether it be fashion or finances.
Posted on February 14, 2007 12:35 AM