Mega Millions
Given that 3 prizes were actually won, the EV of the ticket was actually .9153 (after taxes). And the states got $256,356,258 in taxes from all of the tickets sold.
Given this number of tickets, the probability was 0.2082 that 3 winners would be sold and it is still the most likely outcome. The expected value of a single ticket based on the grand prize only, not accounting for taxes or the cash option, and not accounting for lesser prizes, is 34 cents.Quote: boymimbo652,306,000
Quote: boymimbo3 winners. Total of 16,352,618 prizes. Works out to to 652,306,000 tickets sold. (16,352,618 * 39.89).
As an alternative estimate you could look at the numbers of winners of the $2 prize (which is to match a Megaball only ). Although the Megaball is drawn from 46 numbers you have to exclude the combinations that win higher prizes. Multiply the number of $2 winner by 74.8 to get your estimate of number of tickets sold. It should agree with the 39.89% technique within a margin of error.
8,727,236 * 74.8 = 652,797,253 (number of tickets drawn)
244,148 * 74.8 = 18,262,270 (27 January 2012 which is the seed drawing after last jackpot win)
So in a seed drawing if they sell 18 million tickets, the secondary prizes add up to roughly $4 million. If someone hits the jackpot on the seed, and takes the non-annuity prize of $8 million, then the States only win $6 million (less expenses).
Quote: teliotGiven this number of tickets, the probability was 0.2082 that 3 winners would be sold and it is still the most likely outcome. The expected value of a single ticket based on the grand prize only, not accounting for taxes or the cash option, and not accounting for lesser prizes, is 34 cents.
Why is this significant? What about all of the other options, with 1 winner, 2 winners, 4 winners, and so on. Why are you multiplying by .2082? Isn't the expected value the sum of all number of jackpots won x the jackpot x the probability of the jackpot.
Yes. The following calculation only covers through 10 concurrent winners. Take the sumproduct of the rows to get an expected prize of $222,980,000 (before taxes, cash option). So, the expected value per ticket purchased is $222,980,000/652,306,000 = 34.2 cents. If taxes and the "cash distribution" eat 50% or so of that, then the main prize is worth about 17 cents per ticket.Quote: boymimboIsn't the expected value the sum of all number of jackpots won x the jackpot x the probability of the jackpot.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 2.4% | 9.227% | 16.827% | 20.823% | 19.326% | 14.349% | 8.878% | 4.708% | 2.185% | 0.901% | 0.335% |
| $0 | $640,000,000 | $320,000,000 | $213,333,333 | $160,000,000 | $128,000,000 | $106,666,667 | $91,428,571 | $80,000,000 | $71,111,111 | $64,000,000 |
651,915,940 tickets from last nights drawing.
1,491,082,270 total tickets sold since last jackpot winner.
Quote: mipletjust posted the final sales figures:
That would have been a convenient website to find earlier. Median sales are usually 20 million a drawing, and there have been only 10 previous drawings over 100 million. So they really shattered the record.
Quote: teliotYes. The following calculation only covers through 10 concurrent winners. Take the sumproduct of the rows to get an expected prize of $222,980,000 (before taxes, cash option). So, the expected value per ticket purchased is $222,980,000/652,306,000 = 34.2 cents. If taxes and the "cash distribution" eat 50% or so of that, then the main prize is worth about 17 cents per ticket.
0 1 2 3 4 5 6 7 8 9 10 2.4% 9.227% 16.827% 20.823% 19.326% 14.349% 8.878% 4.708% 2.185% 0.901% 0.335% $0 $640,000,000 $320,000,000 $213,333,333 $160,000,000 $128,000,000 $106,666,667 $91,428,571 $80,000,000 $71,111,111 $64,000,000
Right, but there were 3 winners so you multiply by 3 since there were 3 winners?
Quote: pacomartinThat would have been a convenient website to find earlier. Median sales are usually 20 million a drawing, and there have been only 10 previous drawings over 100 million. So they really shattered the record.
I linked to it on page 6. Its also mentioned on page 19 and 20. It was also mentioned back in August 2010 link
Quote: mipletI linked to it on page 6. Its also mentioned on page 19 and 20. It was also mentioned back in August 2010
Sorry, didn't look through all the posts.
It didn't really matter, as ticket sales varied from 37.93% to 52.28% of the increase in the jackpot just since the last win on 24 January. So it would have narrowed down the number of tickets sold to something between 530 and 730 million based on a $277 million increase in the jackpot.
Just enough to get them in serious trouble. Odds are
one of them will be bankrupt in 5-8 years.
Quote: EvenBob3 winners, each will get 120M if they take the cash.
Just enough to get them in serious trouble. Odds are
one of them will be bankrupt in 5-8 years.
Your overly negative assumption also suggests that none of the tickets were part of an office or friendly pool.
Quote: cclub79Your overly negative assumption also suggests that none of the tickets were part of an office or friendly pool.
I'm just going with what the news is saying.
3 winners splitting a cash payout of 360M.
Why is that negative?
Quote: EvenBobI'm just going with what the news is saying.
3 winners splitting a cash payout of 360M.
Why is that negative?
Well negative because you say it's just enough for them to be bankrupt, but it's also very possible that 1, 2 or all 3 will not win $120M, but be sharing it with multiple people on the same ticket, meaning they won't have "just enough" to have problems.
edit-
I also have a theory that when it's these "larger than life" payouts, it's more likely that casual players win, and they are LESS likely to blow all the winnings. The addicted people that play $25 every week on their food stamps and win are more likely to not be able to handle it. Perhaps the reason there are so many bankruptcies with lottery winners is because so many of the people that play the lottery compulsively enough to win have gambling and money problems to begin with...
Quote: cclub79Well negative because you say it's just enough for them to be bankrupt, but it's also very possible that 1, 2 or all 3 will not win $120M, but be sharing it with multiple people on the same ticket, meaning they won't have "just enough" to have problems.
Sure they will. Big lotto winners are notorious for
blowing all the money and ruining their lives. Whole
books have been written on it. We even had a local
big winner who barricaded himself in his house and
took pot shots at police rather than let the sheriff
take it. He went to prison.
Quote: EvenBob3 winners, each will get 120M if they take the cash.
Just enough to get them in serious trouble. Odds are
one of them will be bankrupt in 5-8 years.
The cash option was $462 M total, so divided by 3 that gives each one $154 M before taxes, not $120 M.
Quote: EvenBobSure they will. Big lotto winners are notorious for
blowing all the money and ruining their lives. Whole
books have been written on it. We even had a local
big winner who barricaded himself in his house and
took pot shots at police rather than let the sheriff
take it. He went to prison.
Again, as said above, I think it speaks more to the people that are winning and their motivations and behaviors. The little old lady who wins $100M is not going to go bankrupt. The guy that is stealing from his kids' college fund to buy more tickets is.
Its astounding how fast some people can go thru any
amount of money if you let them. They weren't rich before
they won for a reason.
Quote: Toes14The cash option was $462 M total, so divided by 3 that gives each one $154 M before taxes, not $120 M.
I quoted the after taxes total, the only one that counts. Its actually closer
to 115M.
This is a big BS
Quote: edwardI do not understand why to have to pay taxes for the winnings??
This is a big BS
Federal income tax. State income tax. Some cities tax
your earnings.
Quote: edwardI do not understand why to have to pay taxes for the winnings?? This is a big BS
The repeated taxation of already-taxed money is one of the hidden costs of gambling in the U.S.
More civilized countries, such as Australia, Canada and the UK, do not tax gambling winnings.
Quote: EvenBobFederal income tax. State income tax. Some cities tax
your earnings.
What state taxes lottery winnings on a lottery that is run in that state?
As for countries that don't tax winnings, how many of those countries don't run lotteries at the national government level?
Quote: ThatDonGuyWhat state taxes lottery winnings on a lottery that is run in that state?
this site has a breakdown of taxes on lottery winnings by state
Quote: Ibeatyouraces3 winning tickets now. Maryland, Illinois and Kansas.
Baltimore County winner bought one ticket and a slurpee. Why the hell didn't I buy a slurpee, might have won also?
Now logically, the difficulty in picking all 6 numbers correctly never changes week after week. For most of us, even winning $12 million dollar prize ($9 million lump sum), would change our lives dramatically. As everyone observed, when the prize gets really big, it will probably be split.
They interviewed one accountant who was buying 55 tickets. He said know that 55 tickets is 55 times better odds than one ticket, but the reality is that even 55 tickets is still an insignificant probability. "I realize that I am just wasting money", he said, but he didn't want the feeling to end after looking at a few tickets.
Suddenly the Mega Millions goes from selling 20.58 million tickets for a biweekly drawing, to a billion tickets over a two week period. It goes from a minor topic in public's imagination to a national obsession.
Quote: pacomartinIt goes from a minor topic in public's imagination to a national obsession.
I had dinner with an older friend tonight. He recounted how he
went to sleep every night this week spending the money he
would win. He was basically going to be the savior of his entire
family. Pay off everyone's debts, buy them all new homes, and
set his grandchildren up for life. It was one of the saddest and
depressing conversations I've had in a long time.
Formula 1: Conditions are x = 2 and y ≥ x
x y – x
p = ————
x y
For example, if you randomly pick 5 different bits, the probability that you will NOT pick 00000 or 11111 is:
25 – 2
p = ——— = 0.9375
25
Formula 2: Conditions are x ≥ 2 and y = x
x!
p = ——
x y
For example, if you tell 10 people to randomly pick a number from 1 to 10, the probability that every person will pick a different number is:
10!
p = ——— = 0.00036288 ≈ 1 in 2755.73
1010
Unfortunately these aren't terribly useful, but I think they might be a good start to finding a better formula that can solve all cases where y ≥ x ≥ 2.
Quote: ewjones080How come nobody's mentioned how crazy it is that there were TWO tickets sold per EVERY American over the course of just three days.
In Pennsylvania the expenditures on lottery tickets over 3 days are $2.08 per EVERY Pennsylvania citizen (including children). Normally Megamillions are 3.36% of total sales, while instant games are 59.92% of sales. Possibly the Megamillions sales were partly a transfer of money that would otherwise be spent on different kinds of lottery tickets.
Some people think the idea of lotteries are stupid. Why would you play a game that keeps half the money? But I am sure a lot of those people bought a ticket just for the novelty, and to be part of the obsession.
Quote: pacomartinLooking at the Mega Millions sales figures, I am struck by what seems to be the way things explode in the public imagination. The median sale is 20.58 million tickets, and the minimum is 13.26 million tickets.
It shows how advertising works, and if you can get every news outlet to make something a major story, people will buy...
Quote: EvenBobI had dinner with an older friend tonight. He recounted how he
went to sleep every night this week spending the money he
would win. He was basically going to be the savior of his entire
family. Pay off everyone's debts, buy them all new homes, and
set his grandchildren up for life. It was one of the saddest and
depressing conversations I've had in a long time.
For a reasonable size family, he could probably do that with $9 million. Maybe not set all his grandchildren up for life. So he could play the game any day of the week, and face the same odds of winning.
I don't get the crazy long lines though. I mean, when I was in California, I just got some gas for my rental car, went in and bought my tickets -- there was no line.
I'm $10 poorer, which is fine, because instead of ordering Pizza and Wings on Friday night, I made my own, saving $18.
Quote: EvenBobFederal income tax. State income tax. Some cities tax
your earnings.
You should also note that all the media lists "after tax amounts" that only reflect the tax withheld. I believe in CA (with no state tax on Lottery Winnings), they withhold 25% for federal tax purposes. Your actual federal liability is going to be in the 35% range.....hope those winners save 10% of the cash prize and earmark it for federal taxes. A mere $15 million or so.....that is going to be a fun check to write!
Quote: pacomartinFor a reasonable size family, he could probably do that with $9 million. Maybe not set all his grandchildren up for life. So he could play the game any day of the week, and face the same odds of winning.
Nuh Uh. Everybody knows its easier to win the
big jackpots than it is the small ones... LOL!
Basically by virtue of the "world record" draw sales tripled. It is interesting to note that some states, like Georgia, sales grew dramatically while others, like California saw more modest growth.
Quote: calwatchBasically by virtue of the "world record" draw sales tripled. It is interesting to note that some states, like Georgia, sales grew dramatically while others, like California saw more modest growth.
Interesting table. The reason for your observation is that some states buy a disproportionate share of Mega Millions tickets before the jackpot got huge. For instance New Jersey on 13 March bought 6.8% of the tickets, while only having 3.2% of the population in those states.
The following five states bought the most number of Mega Million lottery tickets relative to their population
before the jackpot exploded on 13 March,
New Jersey
New York
California
Maryland
Michigan
The following five states bought the least number of Mega Million lottery tickets relative to their population
before the jackpot exploded on 13 March,
Maine (lowest)
Montana
South Dakota
Kansas
Minnesota
If you already are buying a large percentage of the tickets, then you can't increase sales by as much. You pointed out that most of the extreme hysteria was concentrated in rural or suburban America. For instance Maine increased their normal buying by 30 times.
I assume urban people buy more lottery tickets in general, but it also may be the demographics. Lots of Latinos come from countries where lotteries are very significant. Perhaps people from Maine are more likely to buy an instant ticket if they buy a lottery ticket at all.
Quote: pacomartin
I assume urban people buy more lottery tickets in general, but it also may be the demographics. Lots of Latinos come from countries where lotteries are very significant. Perhaps people from Maine are more likely to buy an instant ticket if they buy a lottery ticket at all.
I also wonder how much of that was from states that added Mega Millions a couple years ago (former Powerball only states). Since most states have both now, it doesn't make much of a difference. But my mom is in Nebraska, and she didn't even know it got up that high when it was 370 million (she usually buys 5 tickets when it gets over 100 million). When we were talking about it, she didn't know how Mega Millions worked, but can tell you exactly how Powerball works (pretty much the same).
Quote: TiltpoulI also wonder how much of that was from states that added Mega Millions a couple years ago (former Powerball only states). Since most states have both now, it doesn't make much of a difference.
I think Floridians will pressure the state to let them play Mega Millions.
The federal government seems to be clearing the way to permit the states to sell tickets online, instead of through stores. I think the remaining states will be persuaded to let people bet online. Even Utah can probably be persuaded not to interfere with what people do in the privacy of their own homes.
Quote: WongBo
Its no surprise, the more religiously repressed you are,
the more you want to look at porn.
Quote: WongBo
Very interesting. So the only two states that don't permit any gambling at all (not even for charity) are also number #1 and #2 on the online porn list
Utah 1.69
Hawaii 1.37
Talk about casual statistics, but I can't help but wonder if there is a connection.
I was reading that India was trying to introduce family planning to cut their fertility rate. Do you know what was one of the highest priorities on the list?
You guessed it. More television.
Md. woman won't share $105M lotto jackpot with McD's co-workers
Quote: WongBoa good reason not to be part of a betting pool...
Md. woman won't share $105M lotto jackpot with McD's co-workers
It's good reason to know the people you're getting into a pool with, and to set up ground rules.
A rule we had when I managed a pool was "no one EVER buys ANY lotto tickets by themselves." If someone wanted to play outside the pool, that was fine, but he or shee would not be welcome to keep playing in the pool. Otherwise you allow disputes like on that link.
Of cruse, it helped we were all family in that pool...
if she doesn't have documentation, i think she would have a hard time defending a lawsuit.
Quote: JBPlaying devil's advocate here, I can't help but wonder how many of these "we were in a pool" claims are really just jealous coworkers ganging up on the winner and getting away with it simply because they outnumber the winner. Even if the winner was truly innocent and had bought the winning ticket on her own, I doubt she would win the inevitable trial that would follow.
The PA lottery has a game where the odds are 1 in 4.5 million. The Jackpot has reached as high as $6.9 million.
I would think that $10 spent on my own tickets, instead of in a pool for a game with odds of 1 in 176 million would make slightly more sense.
But I thought that casino progressive jackpots were a much better value than lottery tickets.
