Mega Millions
I'm not sure of the implications for you as a Canadian, but for someone from the U.S., that's really a very good plan, just in case you hit the jackpot. My understanding is that California explicitly excludes their lottery payout from state income taxes. If you hit the big one, just change your tax residence to California or to a state without income tax prior to redeeming your prize. That could save you a million or two bucks per year in taxes, depending on where you pay your taxes now.Quote: boymimboI'm in SoCal this week so will have to pick up my lotto tickets here.
BTW, I am neither an accountant nor a tax lawyer.
For this week's draw, you would have won $31,979,069 from all of the non-winning prizes. The total number of tickets sold would have been 363,815,583.
You would hold a winning ticket for $363,000,000.
Your expected return then is as follows:
31,979,069 + 363,000,000 * .342827584 + 181,500,000 * . 36700064 + 121,000,000 * .196445238 + 90,750,000 * .070100015 + 72,600,000 * .018761 + 60,500,000 * .004016834 + 51,857,143 * .000716689 .....
=254,816,465 - 175,711,536 = $79,104,929.
The thing is that if there are more than 2 other winners (odds .290165979) you're down!
With 188,104,000 tickets the break even jackpot is $234,000,000.
On the last draw, there was approximately 114,844,000 tickets sold for a jackpot of $290,000,000. The break even point for the jackpot to be profitable is $195,800,000.
The previous draw, there was approximately 80,763,000 tickets sold for a jackpot of $241,000,000. Breakeven = 179,300,000.
So, there are plenty of opportunities when a jackpot is at a certain amount to buy a certain number of tickets and come out ahead. And of course when you buy every ticket the jackpot also increases, so if you bought say all of the tickets, the jackpot might go up by $50 - $60 million?
I'm a non-resident alien, so they would take out 30% of taxes as a withholding tax, which you would declare on a 1040NR. Because gambling winnings are not considered income in Canada, there would be no additional tax hit in Canada.
I understand what BoyMimbo is trying to say about it not being a good bet. I kinda agree (although I will be throwing $10 at it).
Sure, it's now at a positive EV, but it's still very much a long shot for being able to cash in on that +EV. It's not a very good expectation.
Let's say a casino was doing some sort of silly promotion, where Roulette was paying 40 to 1 for a straight up bet. That's a +EV situation too. But while this is also a long shot, it's not nearly so outrageously long as the MegaMillions bet. Therefore, this +EV Roulette bet is not only a positive expectation, but a reasonable expectation.
Based upon that criteria, MegaMillions is not a good bet, whereas the hypothetical 40:1 promotion would be.
"California's nine second-tier winners will each get $308,573 under that state's pari-mutuel system."
In California all prizes are pari-mutuel, meaning payouts are based on sales and the number of winners.
There were forty-seven second place winners last night...
Probably the worst you can feel after winning $250,000...
Quote: Hollywood12I completly disagree with it being a good bet. Just because the amount you win is a ridiculous sum doesnt disqualify the fact its still a 1 in 175 million odd. Who gives a sh** that the math says hey! 220% return. Sure the math says that, but I say bullsh** to that. Just because its a 220% doesnt mean anything for the odds. 20 millioin or 359 million your odds are always the same. Im not getting all up in the posters face, but sometimes math needs to be taken with a very big grain of salt. Even if the mega millions was 1 billion dollars which im guessing be like 700% return doesnt mean your odds change to like 1 in a million to win that 1 billion. Odds stay the same. The thought process lets buy one we got a positive expected return makes about as much sense to me as playing a side bet in a casino for a dollar that has an odd of 1 in 175 million. But wait you'll get 400 million if you hit it. IF IF IF you hit it. Not saying I'm not playing I am. But not because the math says its a good bet which to me its still a bad bet no matter how much you can win because the odds are so horrible. I look at math when gambling, but also common sense and sometimes math and common sense dont add up to 1.
It is also a bad bet because of the diminishing marginal value of money. The first few million you win have a dramatic effect on your life. However, once you have, say, $150 million, the difference between $157 million and $159 million is negligable by comparision. Therefore, IMO with when the prize gets this big, the combined loss of all the people who buy $10 worth of tickets instead of using the money to have a beer with a friend or go out to lunch is greater than the amount of utility that the winners and the state gain.
Just for fun, I'm curious where you draw the line. If the odds were "only" 5,000 to 1 against you, and you could win $10,000 would that be a good bet? What about 10,000 to 1 against, to win $50,000? What number is so high that it doesn't make a difference to you what the return is ?
After $35 million after taxes, the value of money goes away. I would probably sock the rest away and setup a charitable foundation. Those extra millions of dollars would make a heck of alot a difference to other people. Heck, I'd even pay HB's hospital bills.
Quote: EdCollinsI completly disagree with it being a good bet. Just because the amount you win is a ridiculous sum doesnt disqualify the fact its still a 1 in 175 million odd...
Just for fun, I'm curious where you draw the line. If the odds were "only" 5,000 to 1 against you, and you could win $10,000 would that be a good bet? What about 10,000 to 1 against, to win $50,000? What number is so high that it doesn't make a difference to you what the return is ?
I think conceptually the answer is that its a good bet if you can bet it enough times to either get to or approach 'the long term'.
PS: If you're only interested in 35 million, theoretically, you could find 10 other guys and split the jackpot. You'd each have to shell out roughly 17.5 million to win 50 million, and it should be noted that the 17.5 million would be tax deductible. (Assuming no one else took this initiative)...
I'm going to guess that you don't have 17.5 million laying around.
PS: At 500 million jackpot, the 26 year anuity would payout at 19.2 million/year assuming they did an even distribution. Versus recieving $140 million less up front. If you can get an investment return of 4% (reasonable), after 26 years, the 360 million would be worth ...wait for it... 1 billion dollars (actually 998 million, but close enough)....
$250,000 1 in 3,904,701
$10,000 1 in 689,065
$150 1 in 15,313
$150 1 in 13,781
$10 1 in 844
$7 1 in 306
$3 1 in 141
$2 1 in 74.8
not one of these would meet the criteria of a good bet, going strictly by the odds of winning.
but to the person who wins, i am sure they would tell you it was the best bet they ever made.
Quote: ewjones080Why is the differential between cash and annuity so small, while the annuity is like 3X as much as the cash for a big prize for the Powerball?
Saturday's Powerball has a $50MM annuity, and a $30MM cash option. That's not as close as the Mega Millions, but it's not 3X either.
Quote: WongBojackpot 1 in 175,711,536
$250,000 1 in 3,904,701
$10,000 1 in 689,065
$150 1 in 15,313
$150 1 in 13,781
$10 1 in 844
$7 1 in 306
$3 1 in 141
$2 1 in 74.8
not one of these would meet the criteria of a good bet, going strictly by the odds of winning.
but to the person who wins, i am sure they would tell you it was the best bet they ever made.
Those odds are based off winning that amount solely.
For instance, you odds of winning $2 is 1 in 74...but that doesn't account for winning $3 or $7..or whatever. Overall odds are actually 1 in 40.
With that said, you are correct. The lottery has a pretty good HE. Right now, it's in the players favor.
Does anyone know, so I don't have to dig for it?
Quote: WongBojackpot 1 in 175,711,536
not one of these would meet the criteria of a good bet, going strictly by the odds of winning.
but to the person who wins, i am sure they would tell you it was the best bet they ever made.
The cash option on the jackpot on friday is $360MM. After tax, it'll be about $260MM. How is a 1:175MM chance to win $260MM a bad bet going by the odds of winning?
Yesterday at work, I told a coworker I bought some tickets for the drawing. Another coworker who collects a pool and always wants me in on the action couldn't believe I bought them. If it's a player +EV, why not throw $10 for the chance of a life-changing jackpot? As somebody I know pointed out, "You're buying a dream..." And I will have fun thinking about what I could do with the money if/when I win!
Quote: POTUSThe cash option on the jackpot on friday is $360MM. After tax, it'll be about $260MM. How is a 1:175MM chance to win $260MM a bad bet going by the odds of winning?
Easy. If there is more than 1 winner. And with 190,000,000 tickets sold the odds of there being more than one winner is 29.4%. The actual expected value of a jackpot based on 190,000,000 tickets sold is .749784 of the jackpot itself before of the odds of there being more than one winner. The after tax breakeven point of the jackpot alone is $234,350,000 based on the volume of tickets sold.
I'm going to guess that there will be about 300M tickets sold for Friday's draw, in which case the odds of there being more than one winner is 50.9%. The actual expected value of the jackpot based on 300M tickets sold is .686965 of the jackpot itself. After tax breakeven point of the jackpot alone is $255,779.461 based on the volume of tickets sold. So, if 300M tickets sold, 260M is marginally a good bet.
Quote: boymimboSo, with 4,715,569 total prizes won and odds at 39.89:1, the estimated number of tickets sold was 188,104,000.
With 47 prizes at 250,000, that megabill was surely elusive!
The odds of 0 winners (k) given that 188,104,000 tickets (n) were sold and the odds of winning are 175,711,536:1 (o) can be expressed as:
combin(n,k)*((1/o)^k)*(((o-1)/o)^(n-k))
0 0.342827594
1 0.3670064
2 0.196445238
3 0.070100015
4 0.018761
5 or more: 0.0048598
In fact, the most likely number of winners = (the number of tickets - 1) * (the probability that any particular ticket wins the jackpot), rounded down. In this case, 188,103,999 / 175,711,536 rounded down = 1.
Proof:
Let P = the probability of winning the jackpot
Q = 1 - P
N = the number of tickets bought
Prob(0 winners) = QN
Prob(1 winner) = N * P * QN-1 = Prob(0) * N/1 * P/Q
Prob(2 winners) = C(N,2) * P2 * QN-2 = Prob(1) * (N-1)/2 * P/Q
...
Prob(K winners) = Prob(K-1) * (N-(K-1))/K * P/Q
This < Prob(K-1 winners) when (N-K-1) / K * P/Q < 1
-> N - K - 1 < K * Q/P
-> N - 1 < K * (1 + Q/P)
-> (N - 1) / (1 + Q/P) < K
If there is only one possible ticket that wins, then Q/P + 1 = the number of possible tickets, so Prob(K) decreases when K > (tickets bought - 1) / (number of possible tickets), which means the K with the highest probability = (tickets bought - 1) / (number of possible tickets) rounded down.
Quote: WongBoi am not sure what the states' rake is from the mega millions, i don't think it has been discussed.
Does anyone know, so I don't have to dig for it?
About 50% for prizes, 15% for administation and retailers, and 35% for the state.
Where does the 3,904,701 number come from? It is shown on the official mega millions website. The only way I can come up with anything close is to divide 175,711,536 by 45 (one less than the number of megaballs as far as I can tell) = 3,904,700.8 which might round up to 3,904,701.
Is there a mistake on the official website, or do I not understand something?
Quote: epaulsonI don't understand something about the math. Why are the odds of getting 5+0 matches 1 in 3,904,701? There are 56 different (non mega) balls, and you have to pick five. 56!/(5! * 51!) comes out to 3,819,816 by my calculation. 3,819,816 * 46 = 175,711,536 which is the listed odds for the jackpot.
Where does the 3,904,701 number come from? It is shown on the official mega millions website. The only way I can come up with anything close is to divide 175,711,536 by 45 (one less than the number of megaballs as far as I can tell) = 3,904,700.8 which might round up to 3,904,701.
Is there a mistake on the official website, or do I not understand something?
There are 45 ways to not match the mega ball.
If 340 million tickets are sold, then the expected win amount, assuming somebody wins and taking into account other winners, is about 221 million, or 159 million in cash.
If 500 million tickets are sold, then the expected win amount is about 165 million, or 119 million in cash.
epaulson: The probability of winning second prize is 5!*51!/56! * 45/46. The other 1/46th of the time, you hit the jackpot.
Your probability of getting those 5 out of 5 correct and also getting the megaball wrong is:
(1/3,819,816)*(45/46) = 2.561015687 x 10^-7 = 1/3,904,700.8 or 1 in 3,904,700.8, rounded off to 1 in 3,904,701.
Edit: Guess I was once again typing too slowly.
Quote: CrystalMathI estimate 340 million tickets to be sold, although we are in uncharted territory, and it could go as high as 500 million. Doing some reverse math on the lottery's estimated jackpot of 500 million, they also expect about 340 million.
If 340 million tickets are sold, then the expected win amount, assuming somebody wins and taking into account other winners, is about 221 million, or 159 million in cash.
If 500 million tickets are sold, then the expected win amount is about 165 million, or 119 million in cash.
epaulson: The probability of winning second prize is 5!*51!/56! * 45/46. The other 1/46th of the time, you hit the jackpot.
If you want to set the line on ticket sales at 500,000,000, I'll take the over...
Quote: FleaStiff... for those who live in Florida where the similarly named Mega Dollars are offered the next drawing is 500,000. So save yourself the trip to the convenience store.
I was curious if the 7 states without lotteries added up to more population than Florida. They do not.
563 626 Wyoming
710 231 Alaska
1 360 301 Hawaii
2 763 885 Utah
2 700 551 Nevada
2 967 297 Mississippi
4 779 736 Alabama
15 845 627
18 801 310 Florida
2010 population
Still not enough to buy the LA Dodgers, apparently.
Quote: IbeatyouracesNows the time to buy every possible combination if you could.
Suppose you could borrow 176 million dollars for four days. Would you really buy those lottery tickets knowing that you have absolutely no control how many other people could pick the correct combination?
Terrance Watanabe lost $127 million in Vegas in about a year.
Quote: pacomartinSuppose you could borrow 176 million dollars for four days. Would you really buy those lottery tickets knowing that you have absolutely no control how many other people could pick the correct combination?
Terrance Watanabe lost $127 million in Vegas in about a year.
I feel like it would be a logistical problem. Paying people to purchase the tickets for you would seriously cut in to your winnings. And you would have to fill out the little slips manually to actually get all of the combinations.
Quote: TiltpoulStill not enough to buy the LA Dodgers, apparently.
It wouldn't even get you on the Forbes 400 which Elaine Wynn managed to do by divorcing Steve.
Speaking of sports franchises, did you see where Madrid's soccer team is opening a billion dollar resort in the middle east for their Arab and Asian fans? There is a stadium, so presumably they will do exhibition games there.
Since there's two draws a week, you have 3 days to fill out slips. So, I think working 16 hour days, it would be possible for a person to fill in 14,352 slips, and cover all the combinations with 12,243 people!
That's all!
I always assumed that Quick pick used a RNG, like a slot machine. After reading a previous post in this thread i am not so sure now.
Can someone clarify this?
For those who like to pick numbers look here.
http://finance.yahoo.com/news/mega-millions--by-the-lucky-numbers-.html
Quote: conoI will buy one ticket. When I do this I always use the Quick pick, it is fast and convenient.
I always assumed that Quick pick used a RNG, like a slot machine. After reading a previous post in this thread i am not so sure now.
Can someone clarify this?
For those who like to pick numbers look here.
http://finance.yahoo.com/news/mega-millions--by-the-lucky-numbers-.html
Yes, it's random like a slot machine. The part about it that's odd is that the RNG picks 5 "balls" from a list from 1-56, and then the system re-orders them to appear from lowest to highest on the ticket. So if the RNG comes up with 1/9/7/3/5, it will appear as 1/3/5/7/9 on the ticket.
Quote: conoI always assumed that Quick pick used a RNG, like a slot machine. After reading a previous post in this thread i am not so sure now. Can someone clarify this?
What rdw4potus said is correct.
First, remember the difference between a combination and a permutation: in a combination, the order of the individual items does not matter; in a permutation, it does.
Now think of it like this: the RNG is not picking 5 random numbers from 56, it is picking a random combination of 5 numbers from 56, and since order does not matter, the lottery terminal sorts the individual numbers corresponding to that combination before it prints the ticket.
So I learned something new, thx
I would say if you buy more than one ticket you are an idiot.
Chances of being killed by parts falling from a plane: 10,000,000 to 1
Chances of being killed by a lightning strike: 2,290,000 to 1
Chances of getting a royal flush in poker with first 5 cards dealt: 655,750 to 1
Chances of lightning striking you: 587,000 to 1
Chances of being killed in an airplane accident: 355,318 to 1
Chances of being murdered: 19,000 to 1
Quote: pacomartinI would say if you buy more than one ticket you are an idiot.
It is unreasonable to think that any particular ticket will win the lottery. At the same time, it is unreasonable to think that no ticket will ever win the lottery.
Quote: JBIt is unreasonable to think that any particular ticket will win the lottery. At the same time, it is unreasonable to think that no ticket will ever win the lottery.
I didn't say it was stupid to have the fantasy of winning. I just think it is stupid to try and increase your odds by buying multiple tickets. They only increase to the point that they still far exceed anything else that will logically happen in your life.
Quote: pacomartinI didn't say it was stupid to have the fantasy of winning. I just think it is stupid to try and increase your odds by buying multiple tickets. They only increase to the point that they still far exceed anything else that will logically happen in your life.
Understood; I don't disagree. I just like paradoxes so I thought I would post the one I described above.
Quote: pacomartinI didn't say it was stupid to have the fantasy of winning. I just think it is stupid to try and increase your odds by buying multiple tickets. They only increase to the point that they still far exceed anything else that will logically happen in your life.
I disagree. Yesterday an employee at my work came in a bit early for his swing shift. A group of us were talking about the lottery and someone told the early guy he should go get a ticket before work starts. I told him he should get several. The nearest place he could buy a ticket was several miles away. Given the roughly 1.4 deaths per 100,000,000 miles traveled, if he only got one ticket he'd be more likely to die on the trip there and back than to win the lotto. At least if he bought several tickets he'd be slightly more likely to win the lotto than die.
Here's a little bonus exercise: If there's 1.4 million deaths per 100,000,000 miles traveled, how many miles round trip to buy a ticket would it take before you had an equal chance of dying as winning the Mega Millions?
Quote: PopCanI disagree. Yesterday an employee at my work came in a bit early for his swing shift. A group of us were talking about the lottery and someone told the early guy he should go get a ticket before work starts. I told him he should get several. The nearest place he could buy a ticket was several miles away. Given the roughly 1.4 deaths per 100,000,000 miles traveled, if he only got one ticket he'd be more likely to die on the trip there and back than to win the lotto. At least if he bought several tickets he'd be slightly more likely to win the lotto than die.
Here's a little bonus exercise: If there's 1.4 million deaths per 100,000,000 miles traveled, how many miles round trip to buy a ticket would it take before you had an equal chance of dying as winning the Mega Millions?
That would be 715 yards. I think that makes my point as succinctly as the other probabilities. You could say something good or something bad might happen to me. Good would be winning the lottery, and bad would be dying while driving my car 715 yards. But you know they are equally probable.
Quote: pacomartinI didn't say it was stupid to have the fantasy of winning. I just think it is stupid to try and increase your odds by buying multiple tickets. They only increase to the point that they still far exceed anything else that will logically happen in your life.
At the risk of opening a can of worms, did you mean to say buying multiple tickets increases your chances, not your odds? The odds are still 175-ish million to one. Buying one ticket gives one a single chance, buying two tickets gives one two chances. Please, if I am incorrect, correct me.
Quote: pacomartinOdds are 176 million to 1.
I would say if you buy more than one ticket you are an idiot.
Chances of being killed by parts falling from a plane: 10,000,000 to 1
Chances of being killed by a lightning strike: 2,290,000 to 1
Chances of getting a royal flush in poker with first 5 cards dealt: 655,750 to 1
Chances of lightning striking you: 587,000 to 1
Chances of being killed in an airplane accident: 355,318 to 1
Chances of being murdered: 19,000 to 1
Aren't you comparing the odds of winning this single fixed lottery drawing with the odds of being murdered ever? There's a 1:176MM chance that I'll win $500MM between now and 10pm EDT on Friday night. What are the odds that I'll be murdered between now and then?
Quote: pacomartinOdds are 176 million to 1.
I would say if you buy more than one ticket you are an idiot.
Let's do a thought experiment.
Suppose I print one million and one hundred tickets for a drawing (that's 1,000,100 tickets) and give one to each of 1,000,000 people. To you I give 100 tickets. Are you or are you not more likley to win the drawing than a person who received only one ticket?
On other matters, if you buy the same combination ten times (for the same drawing), by how much do you reduce the expected loss from the jackpot if someone matching your combination? Related, do you increase the expected win for smaller prizes? Is it worth it to buy ten of the same number?
