Wednesday, January 13 was the drawing for the largest lottery ever in the US, possibly in the world. At stake was a jackpot for 1.5 billion dollars. Yes billion with a B.
I normally do not gamble. So I surprised myself when I got 10 tickets for the Powerball on Wednesday afternoon, spending $20. The probability of getting the numbers in the jackpot was 1 in 292 million. The probability of getting all of it, was less than 1 in 900 million.
So with odds so low, why would so many people including me, waste or invest, depending on your point of view in the Powerball. Like almost every interesting question, an Economics school has published a paper on it.
The School of Economics and Management at the Technical University in Lisbon, published "Why do People Buy Lottery Products ?" The paper examines the lottery sales of 99 countries in order to explain gambling consumption around the world. You can download and read the paper at:
https://ideas.repec.org/p/ise/isegwp/wp12009.html
Americans spend more on lottery tickets than they spend on America. John Oliver explains in his inimitable style why Americans buy lotteries and who benefits
Several people makes several assumptions about the Powerball. I have a simple solution. Don't assume. Check out the most authentic source on the Powerball. The organization that organizes the Powerball. In addition to a well designed site, the webmaster has a brilliant sense of humor. The FAQ's in addition to being informative are funny.
http://www.powerball.com/
That still doesn't answer the question, Why did I buy the Powerball. This brilliant article from Business Insider, a part of which I'm giving below explains why. Well almost.
"
...
Powerball and similar lotteries are a wonderful example of this kind of random process. As of October in Powerball, five white balls are drawn from a drum with 69 balls, and one red ball is drawn from a drum with 26 balls. As an aside, that rule change is why prizes can get as big as the current record jackpot: The probability of winning the jackpot is much lower than it used to be.
Prizes are then given out based on how many of a player's chosen numbers match the numbers written on the balls. Match all five white balls and the red Powerball, and you win the jackpot. In addition, several smaller prizes are won for matching some subset of the drawn numbers. Powerball's 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 $2 Powerball 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:
At first glance, we seem to have a positive expected value at $3.45. The situation, however, is more complicated.
Annuity vs. lump sum
Our first problem is that the headline $1.5 billion grand prize is paid out as an annuity. Rather than getting the whole amount all at once, you get the $1.5 billion spread out in smaller — but still multimillion-dollar — annual payments over 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 $930 million. Looking at the lump sum, our expected value drops dramatically to just $1.50.
"
http://www.businessinsider.com/powerball-lottery-expected-value-jan-13-draw-2016-1
As you can see, the expected value of a $2 ticket is 1.50 or about as close to $2, as we are likely to get. And the fun value of dreaming, priceless. And so on this rare occasion, I succumbed to purchasing a few tickets.
And for all of you skeptics, I won the Powerball.
Well okay, not the 1.5 billion jackpot, but a modest $4 for getting the Poweball number correct.
I normally do not gamble. So I surprised myself when I got 10 tickets for the Powerball on Wednesday afternoon, spending $20. The probability of getting the numbers in the jackpot was 1 in 292 million. The probability of getting all of it, was less than 1 in 900 million.
So with odds so low, why would so many people including me, waste or invest, depending on your point of view in the Powerball. Like almost every interesting question, an Economics school has published a paper on it.
The School of Economics and Management at the Technical University in Lisbon, published "Why do People Buy Lottery Products ?" The paper examines the lottery sales of 99 countries in order to explain gambling consumption around the world. You can download and read the paper at:
https://ideas.repec.org/p/ise/isegwp/wp12009.html
Americans spend more on lottery tickets than they spend on America. John Oliver explains in his inimitable style why Americans buy lotteries and who benefits
Several people makes several assumptions about the Powerball. I have a simple solution. Don't assume. Check out the most authentic source on the Powerball. The organization that organizes the Powerball. In addition to a well designed site, the webmaster has a brilliant sense of humor. The FAQ's in addition to being informative are funny.
http://www.powerball.com/
That still doesn't answer the question, Why did I buy the Powerball. This brilliant article from Business Insider, a part of which I'm giving below explains why. Well almost.
"
...
Powerball and similar lotteries are a wonderful example of this kind of random process. As of October in Powerball, five white balls are drawn from a drum with 69 balls, and one red ball is drawn from a drum with 26 balls. As an aside, that rule change is why prizes can get as big as the current record jackpot: The probability of winning the jackpot is much lower than it used to be.
Prizes are then given out based on how many of a player's chosen numbers match the numbers written on the balls. Match all five white balls and the red Powerball, and you win the jackpot. In addition, several smaller prizes are won for matching some subset of the drawn numbers. Powerball's 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 $2 Powerball 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:
At first glance, we seem to have a positive expected value at $3.45. The situation, however, is more complicated.
Annuity vs. lump sum
Our first problem is that the headline $1.5 billion grand prize is paid out as an annuity. Rather than getting the whole amount all at once, you get the $1.5 billion spread out in smaller — but still multimillion-dollar — annual payments over 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 $930 million. Looking at the lump sum, our expected value drops dramatically to just $1.50.
http://www.businessinsider.com/powerball-lottery-expected-value-jan-13-draw-2016-1
As you can see, the expected value of a $2 ticket is 1.50 or about as close to $2, as we are likely to get. And the fun value of dreaming, priceless. And so on this rare occasion, I succumbed to purchasing a few tickets.
And for all of you skeptics, I won the Powerball.
Well okay, not the 1.5 billion jackpot, but a modest $4 for getting the Poweball number correct.
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