So Powerball Jackpot has reached $1.3 billion. There is 1 in 292,201,338 chance to win the Jackpot. That's 4.45 dollars average pay out per $2 ticket. Why aren't you buying yet?
That payout assumes that there's only one winner. But with a jackpot this big, there's going to be a lot of people buying tickets so there's a good chance of the jackpot split, reducing payout
Didn't something similar to this happen? A bunch of people formed this crime ring and bought thousands of tickets from some small national lottery and they were something like 70% of the past winners.
The discrete mathematics class on MIT opencourse has a lecture where the prof talks about this very thing actually. In one of the later ones about probability. Apparently some Australian bank did this and made bank? The prof in the video references this happening but I've never found any news articles pertaining to this.
You have a 1 in 55 chance of having a matching number for every given number. If you multiply that be 6 (1/55)^6 you wind up with an exceptionally low chance. Then multiply it by 1.3 billion, it winds up being a .0470 return to everyone buying tickets. Pretty terrible odds if you ask me.
>you wind up with an exceptionally low chance
If you are doing it right and correctly factor the difference with the powerball, you should end up with the specific exceptionally low chance of 1 in 292,201,338.
If you multiply 1/292,201,338 by 1300000000 you get about 4.45.
Between taxation and multiple winners, it would still be a negative expected return.
There is also the fact that the utility of money is highly non-linear. $100,000,000 is much, much, much less than 100,000,000 times as useful as $1.
>Several years ago, while doing research for a school project, a group of MIT students realized that, for a few days every three months or so, the most reliably lucrative lottery game in the country was Massachusetts’ Cash WinFall, because of a quirk in the way a jackpot was broken down into smaller prizes if there was no big winner. The math whizzes quickly discovered that buying about $100,000 in Cash WinFall tickets on those days would virtually guarantee success. Buying $600,000 worth of tickets would bring a 15%–20% return on investment, according to the New York Daily News.
>When the jackpot rose to $2 million, the students bought in, dividing the prize money among group members. But they didn’t stop there; they were so successful in their caper that they were eventually able to quit their day jobs and bring in investors to front the money they needed to purchase the requisite number of lottery tickets. Several other syndicates sprang up to capitalize on the Cash WinFall loopholes, but the MIT group remained one of the most successful and innovative. By 2005, the group had earned almost $8 million with its system, according to an investigation by the Boston Globe.
>How MIT Students Scammed
>The inspector general’s report claims that lottery officials actually bent rules to allow the group to buy hundreds of thousands of the $2 tickets, because doing so increased revenues and made the lottery even more successful. While the students’ actions are not illegal, state treasurer Steven Grossman, who oversees the lottery, finally stopped the game this year.
Nice "journalism" there, Time.
>mfw americans get like
MFW people hate 'murrica so much they make up whatever nonsense they like, then hate us mostly because of their own made-up bullshit.
Max federal tax bracket is 39.6%, so the winner moves to Florida, Texas, Delaware etc on paper, keeps just over 785 million.
Far more than any Yuropoor socialist scum would be allowed to keep.
went full autismo and as an exercise generated 700m random numbers and sorted them by most common. they're no more likely to win but here're the top numbers not including the sixth powerball number
8 30 38 47 50
6 9 19 21 54
2 25 59 62 65
13 36 43 55 60
2 11 22 31 48
6 23 26 47 55
17 25 46 50 53
11 32 38 43 64
17 46 63 64 69
Your odds of winning the Texas Lotto grand prize is approximately 1 in 25,000,000. So for $1 you can have a 1 in 25,000,000 chance of winning a large prize.
Your chance of winning Powrball is approximately 1 in 300,000,000 and the ticket costs $2. Twelve tickets would increase your odds to approximately 1 in 25,000,000.
So for $24 you can buy Powerball tickets that give you approximately the same odds as one Texas Lotto ticket for $1.
If you're going to play the lottery, it's a no-brainer.
That said, buy a Powerball ticket just for the hell of it if you want.
since I cannot play, here is my numbers
34,64,61,17,56 - 13
/sci/, help me out real quick.
I'm trying to estimate the probability that more than one person will win the pot.
I'm running off of the assumptiion that the number of tickets purchased will be roughly 1.5B, the odds are 1/292M, and the number of winning tickets will be greater than 1.
What function should I use for this?
Actually, the number of tickets purchased are very unlikely to be anywhere near 1.5 billion.
First, the price of a ticket is $2, not $1.
Second, much of the prize is due to previous drawing with no winners, especially to the last drawing. I think thatt the number of tickets sold since Saturday to be more like 350,000,000 to 450,000,000.
>That's 4.45 dollars average pay out per $2 ticket
Because I can use my $2 more effectively in buying something like toilet tissue, than a lottery ticket with a near-infinitesimal chance of winning anything.
>I think thatt the number of tickets sold since Saturday to be more like 350,000,000 to 450,000,000.
Actually, the 900M drawing from last Saturday netted 450,000,000.
Based on that, I'm willing to guess that there will be an exponential increase in the number of tickets sold. I'd be willing to go as high as 1B.
That said, I've been doing some calculations regarding the estimated ticket values, the potential numbers of winners and their respective payoffs per person.
Around 900,000,000 tickets, the estimated jackpot value drops to about 40%, which is roughly the inverse of the current estimated ticket value.
There's a 60% chance that the pot will be split between 2-4 players.
Anyone want to do some fancy math? I'm specifically talking about the question at the end of my post I copypasted from /biz/
Let's assume the estimated jackpot is correct at 1.5 billion. Divide that by 30 (number of payments) and you get 50 million per payment. Now I'll do some more math and actually add it all up for you, with a COLA of 5%. The total amount of money that you get for choosing the annuity (before taxes, but we'll assume that taxes will just chop it in half) in ten years, meaning 11 payments (you get the first one immediately) is $710,339,358.12, almost as much as you'd get for taking the lump sum, but that still isn't as much as you will be getting, and it's also assuming that you aren't spending or investing any of your payments. At twenty years and 21 payments, the total amount of money given to you you is $1,785,962,590.40 which is more than the total of the jackpot with only slightly under one third of the payments still left unpaid. The grand total amount of money given to the jackpot winner (assuming that there is only one, and that the winner does not spend any of their winnings or make any further investments on the issued winnings is $3,321,942,375.16 which is over three times the cash jackpot.
Feel free to check my math, I might have made a mistake somewhere, so please correct me if I'm wrong. As stated above, this is only gross winnings issued by the lottery and does not take into account spending, further investment on the part of the winner, or the monetary cost of waiting 29 years for 3.3 billion dollars. If there are other math gurus about, who I'm sure are better at it than me, it'd be great if they could make a cost-benefit analysis on who would have more money over 29 years (discounting taxes, as they vary state by state), the person who chooses the annuity, or the person who chooses the cash option, assuming no spending, and a 7% rate of return for personal investments for both.
Your math doesn't matter because of your invalid assumptions.
There's no COLA involved. If you win $1.5 billion and take it in annual payments of $50 million, each annual payment is $50 million.
Take a look at calculating the net present value of money. To a degree, the cash value is the net present value of all the annual payments.
Once all 30 payments are made, then you will have been paid $1.5 billion.
My understanding is that when you take the annual payments, they get bids from private companies to pay you that money in annual payments and then take the cheapest. If that private company disappears, don't expect to get the rest of your money.
Buying a $2 ticket is financially sound and has a net-positive marginal benefit, because it's raising your chances to a number above 0
Buying any more than one isn't sound because it doesn't raise your chances by any significant margin.
"With the annuity, you get an annual payment that is increased by 5% each year to keep up with the cost of living." straight from the powerball website, so blow me. As for the chance of you possibly not getting paid every year for all 29 years, "FROM MR: On the FAQ page, it say an annuity is guaranteed. In this economy, how is it guaranteed?
The word "guarantee" is certainly overused from time to time, but if it can have any meaning in the English language, then it can be used with the Powerball jackpot. You can imagine some instances where even a Powerball jackpot will not continue:
(1) A meteor strikes North America, wiping out all life.
(2) The U.S. government is overrun by [insert name of feared enemy here].
Short of these events, the Powerball annuity prize will be paid on schedule. What we actually use for our investments is not important; the Powerball prize -- which pays a graduated annuity, rising at 5% per year to keep up with inflation -- is a contract between each of the lottery members (the states) and you. As long as the U.S.A is in business, you will be paid. If the U.S.A. fails, then you will have other things to worry about. " also from the Powerball website.
It's absolutely true though
The marginal utility of 0 > 1 is theoretically infinite, but the marginal utility of 1 > 80 or 1 > 100 isn't very high, because your chance of winning doesn't increase very much.
Why not just go to a casino and bet your money on one number at the roullete table? There's a 1 in 38 chAnce of winning which is around the same odds of getting one number correctly in the powerball except with a much bigger payout
I was talking about grand prize winners.
If you bought one of every ticket in the lottery, it would have cost you something less than $600,000,000.
Compare that to the cash value of something like $920,000,000. If you were the only grand prize winner, you would come out ahead. But in fact, there were other grand prize winners splitting up the grand prize.
You would have lost hundreds of millions if you had done that.
I read once that someone had tried to convince the state of Texas to sell them one of every number for a lottery in a single transaction. To their credit, the state refused and told them they were free to go buy all the lottery tickets they wanted at a lottery seller.