Powerball at $550 Million
I find that the optimal jackpot size to play is $475 million. After that the hysterical demand increases the competition, lowering value.
At a jackpot of $550 million I find the value of a $2 ticket to be $2.11, before considering taxes and annuity. If we assume that 50% of the jackpot is lost to taxes, and another 50% to the annuity, then the value of that $2 ticket I show to be $0.80.
I must say that I'm hoping nobody wins on Saturday. If this happens, I think a jackpot exceeding a billion would be possible for May 22, which would be interesting to see.
ZCore13
Quote: WizardI must say that I'm hoping nobody wins on Saturday. If this happens, I think a jackpot exceeding a billion would be possible for May 22, which would be interesting to see.
How about buying Powerball tickets as a WoVCon ]I[ activity, if th ejackpot reaches $1 billion? I seem to recall it can be bought in Arizona, which is about a very loud shout away from the Strip, right? ;)
Quote: Zcore13I'd even prefer 1010 winners of $500,000
They wouldn't sell as many tickets though. $500K just doesn't sound as 'sexy' as $500 million.
ZCore13
Quote: Zcore13That would be insane. I wish there was a way to do it so that 550 winners could win 1 million rather than one winner winning 550 million. 1 million to 550 people would be life changing and probably a huge boost to the local economy. 550 million to one person is overkill and seems like a waste to me. I'd even prefer 1010 winners of $500,000
Be careful what you wish for.
In this interview with ER physician Doctor Doug McGuff, winning the lottery is listed as a risk for winding up in the ER:
http://www.philosophyinaction.com/archive/2013-05-08.html
Here's a text lisitng from Dr. McGuff's blog: http://www.bodybyscience.net/home.html/?p=740
Briefly:
Quote:12. Don’t play the lottery…you might win. Any unearned wealth, or wealth that is disproportionate to the objective value you provide will destroy you. Lottery winners and Sports/Movie stars share a common bond of disproportionate rates of depression, addiction, and suicide.
Yes, I know I proposed buying lotto tickets.
Quote: Zcore13That would be insane. I wish there was a way to do it so that 550 winners could win 1 million rather than one winner winning 550 million. 1 million to 550 people would be life changing and probably a huge boost to the local economy. 550 million to one person is overkill and seems like a waste to me. I'd even prefer 1010 winners of $500,000
That is, of course, very logical. However, the average lottery player can't conceive of the difference in odds between the 1 in 175,223,510 of winning the current Powerball and something more attainable, like 1 in one million. However, it is easy to visualize the difference between one million dollars and 550 million. One million would be nice, don't get me wrong, but lots of people have a worth over a million. However, anything in the 9 figures is really rich. So, I think your way would definitely result in more happiness, but less ticket sales.
Quote: NareedHow about buying Powerball tickets as a WoVCon ]I[ activity, if th ejackpot reaches $1 billion? I seem to recall it can be bought in Arizona, which is about a very loud shout away from the Strip, right? ;)
Count me OUT. Before considering the bad value, the lines at the places near the Nevada border can take hours to wait through.
Quote: rainmanI always prefer to win more than less. Am I mistaken or is Wizard rooting against me winning?
Give me a new ivory back-scratcher if you win and I'll pull for you, and only you, to win.
ZCore13
Quote: WizardCount me OUT. Before considering the bad value, the lines at the places near the Nevada border can take hours to wait through.
Sure, but it's a holiday. People will be vacationing in Vegas. Oh, wait...
How about Tuesday 28th early in the morning after the holiday?
Quote: NareedHow about Tuesday 28th early in the morning after the holiday?
The drawings are Wednesdays and Saturdays. The probability nobody hits this Saturday is 26.8%, based on the current jackpot. If nobody wins I think ticket sales will really skyrocket for the 5/22 drawing. If we assume a billion dollar jackpot on 5/22, I estimate a 17-way split, and the probability of no winner at 1 in 27 million. Actually, it may physically be impossible to sell as many tickets as my analysis suggests (3 billion tickets) given a billion dollar jackpot. This isn't even getting into the May 25 drawing. My point being that by May 28 this will all be over.
Quote: WizardMy point being that by May 28 this will all be over.
Good! Then the lines will be shorter. <she said with a straight face>
Quote: Zcore13That would be insane. I wish there was a way to do it so that 550 winners could win 1 million rather than one winner winning 550 million. 1 million to 550 people would be life changing and probably a huge boost to the local economy. 550 million to one person is overkill and seems like a waste to me. I'd even prefer 1010 winners of $500,000
ZCore13
For Powerball, the second place prize (picking the 5 numbers correctly, but an incorrect power ball) is 1 million dollars (before taxes). There are several of these winners for every drawing.
Quote: cclub79I wonder if the addition of California to the Powerball last month (and Florida to the Mega Millions yesterday) will cause the jackpots to get larger quicker. It definitely will fuel the frenzy when we get to these levels, as this is the first time California has been involved in a Jackpot this size with Powerball.
Yeah larger jackpots will occur more frequently now due to a larger volume of ticket sales. But the sizes of the jackpots will be similar though unless they change the payout matrix because more sales will speed up the jackpot hitting as well.
Me, I sure hope I win. Played last night for the first time since the last winner. Alas, as you can tell, I did not win. I will continue to throw good after bad until the jackpot is won.
Same goes for MegaMillions, but have played the last two drawings on it, since the last winner, and hope to win it tomorrow night. Hey, there's a question, what are my odds of winning both, in consecutive nights. No, don't attempt to answer that. I will let you all know after tomorrow/Saturday.
Quote: tringlomaneYeah larger jackpots will occur more frequently now due to a larger volume of ticket sales. But the sizes of the jackpots will be similar though unless they change the payout matrix because more sales will speed up the jackpot hitting as well.
True except when we are in a window like right now. Since there are three/four days between drawings, there are now more terminals selling tickets in that window. So when you get to a superhigh number and media attention, you'll get a larger jackpot.
Quote: Zcore13That would be insane. I wish there was a way to do it so that 550 winners could win 1 million rather than one winner winning 550 million. 1 million to 550 people would be life changing and probably a huge boost to the local economy. 550 million to one person is overkill and seems like a waste to me. I'd even prefer 1010 winners of $500,000
ZCore13
From http://www.powerball.com/pb_contact.asp
I HAVE A GAME IDEA; YOU SHOULD GIVE 100 PEOPLE $1 MILLION EACH.
We do get mail from persons offering ideas that promise to double or triple our sales in the game. We also get a lot of mail that starts - "Everyone I talk to agrees that Powerball should pay more and smaller prizes, who needs $XXX million!!!" In this new game we are going to give away hundreds of $1 million prizes - but we cannot convert the jackpot to all $1 million prizes. These writers usually get extremely angry when we try to explain why their idea won't work - so we prefer to use this standard response. Please accept this response with our apologies for not recognizing how very right you are:
(3) If you believe that we should pay out $1 million prizes to lots of persons: After players told us that in focus groups, we actually started that game. No one played. Lotteries need to create a variety of games that appeal to different players. Powerball is a game that appeals to those players who want to play for large jackpots. There are other games that offer better odds (and so, lower jackpot amounts). Sales for a Powerball drawing can vary from $16 million to $200 million. You might guess which jackpot levels bring the most sales. Players vote with their dollars on the jackpot levels they prefer and we must listen to our customers. Powerball is actually two games in one – a big jackpot game and a big Cash 5 game. Now, a player will win $1 million just by matching the five white ball numbers. We know folks don't really get excited about that, but it is just something we want to do. By adding the Power Play option, a player can even increase the Cash 5 part of the game to a $2 million cash prize.
Quote: sodawater(3) If you believe that we should pay out $1 million prizes to lots of persons: After players told us that in focus groups, we actually started that game. NO ONE PLAYED. Lotteries need to create a variety of games that appeal to different players. Powerball is a game that appeals to those players who want to play for large jackpots. There are other games that offer better odds (and so, lower jackpot amounts). Sales for a Powerball drawing can vary from $16 million to $200 million. You might guess which jackpot levels bring the most sales...
So I guess there really wasn't a frenzy after all to win a bunch of small prizes? As I said earlier, $500K isn't nearly as sexy as $500 million.
I have recently grown very angry about advertising jackpots by annuity rather than immediate value, it's straight up lying. I tried explaining this anger to a friend of mine who has a masters in chemical engineering and he just didn't get it, he said something along the lines of "but you'd get all the money with the annuity" when I tried explaining the time-value of money. I have a handful of little things I get angry about, this and JJ-douchebag-Abrams ruining Star Trek are my current beefs.
Off to see Star Trek.
Quote: Zcore13That would be insane. I wish there was a way to do it so that 550 winners could win 1 million rather than one winner winning 550 million. 1 million to 550 people would be life changing and probably a huge boost to the local economy. 550 million to one person is overkill and seems like a waste to me. I'd even prefer 1010 winners of $500,000
ZCore13
The Canadian government hosts a number of lotteries, the biggest one right now is called Lotto Max. It's only a few years old, and has a max jackpot of $50 Million. If the jackpot pool keeps building, they give away the rest in $1 Million prizes in redraws, one for each $1M. Not too long ago there were about 50 side prizes as well. There is a reasonable frenzy when the 'maxmillion' prizes start to climb in #.
Quote: ahiromuI bought a few tickets, also the "rule of thumb" I use is 1/3 of the advertised jackpot amount is what you'll see after immediate payment and taxes.
I see the Powerball web site says the current $550 million jackpot has a $350.1 "cash value." I assume that is the lump sum option.
The highest tax rate is 35%, except if you're single it is 39.6%. Assuming one is not single, the ratio of money received after the lump sum and taxes would be 41.4%. However, that doesn't count state taxes, which vary by state. In California, the highest rate is 10.3%. All things considered, 1/3 sounds like a good rule of thumb. Assuming that figure, I show a $2 ticket for the May 18 draw has an expected value of 94.2 cents.
I agree that it is indeed deceptive.
When New York first started their lottery the rules were not well understood. One "Million Dollars a Year for Life" winner submitted the ticket in the name of his two year old kid figuring he would have the longest life of anyone in the family. The lottery people told him: You get absolutely nothing and the kid gets his first check at 18... and thanks because now we can fund that price for a fraction of what the ticket was worth before you put a minor's name on it.
A lottery ticket is considered "an expectation" but once the results are announced it can become "property" and the subject of fraud upon creditors, so treading carefully is required. I'd certainly see a tax lawyer or cpa before opening a bottle of champagne.
Quote: sodawaterIf you believe that we should pay out $1 million prizes to lots of persons: After players told us that in focus groups, we actually started that game. No one played.
The problem is that if you think about lotteries rationally you would never play them. What kind of investment has a lot of people give you money, the investment group keeps half the money, and then it gives most of it to a small number of people.
Lotteries are all about fantasies. The bigger the fantasy, the more popular the game. People say things with their rational mind, but that isn't what reacts.
Quote: slytherI have my 2 tickets. Rational or not, it's still fun.
Yup. The cure for a lotto addiciotn is to make it not fun anymore. It's one thing when you buy your tickets once a week, and involve family and friends, and you spend the weekend daydreaming about buying a Caribbean island or a private jet. That's "fun." It's less so when there are three drawings bunched up together, which drives up the price. And take palce twice a week, so you're rushing to get your mid-week tickets. And if you can't manage to get tickets for one drawing, youa gonize at recognizing your usual numbers when the results are posted.
That's not fun.
Upon winning, I plan to donate $10 mil. to establish a Trust Fund for the express purpose of keeping Mike in the Wizard of Odds/Vegas business for the rest of his lifetime.
Quote: slytherI have my 2 tickets.
So does that mean I'm five times the loser you are?
(Can you guess how many tickets I got?)
Quote: midwestgbJust bought my five tickets. Upon winning, I plan to donate $10 mil. to establish a Trust Fund for the express purpose of keeping Mike in the Wizard of Odds/Vegas business for the rest of his lifetime.
Thanks! After I just lost much of my money in Cyprus, I could use it right now.
Quote: chickenmanJackpot now at $600 million, cash option $377 million. So now the largest Powerball jackpot ever and second largest after the Megabucks $656 million in March
It may pass $656M by the drawing. I'm surprised the media hasn't been trying to find me this time. Usually whenever there is a huge jackpot I get asked lots of odds questions.
Quote: WizardI see the Powerball web site says the current $550 million jackpot has a $350.1 "cash value." I assume that is the lump sum option.
The highest tax rate is 35%, except if you're single it is 39.6%. Assuming one is not single, the ratio of money received after the lump sum and taxes would be 41.4%. However, that doesn't count state taxes, which vary by state. In California, the highest rate is 10.3%. All things considered, 1/3 sounds like a good rule of thumb. Assuming that figure, I show a $2 ticket for the May 18 draw has an expected value of 94.2 cents.
except most people should take the annuity, not the cash value.
the annuity provides two things you can't get with the cash value:
1. a government guaranteed return on investment
2. no taxes on the profit of the investment
which means that if you take the annuity, the lotto uses the lump sum cash to buy annuities, then guarantees your return. and you only pay taxes once on the annuity, instead of twice on the lump sum + investment return
Quote: WizardI'm surprised the media hasn't been trying to find me this time. Usually whenever there is a huge jackpot I get asked lots of odds questions.
They probably are ringing Ahigh's phone off the hook, having been tipped off by casino executives who can't stop talking about him.
Quote: WizardThanks! After I just lost much of my money in Cyprus, I could use it right now.
It may pass $656M by the drawing. I'm surprised the media hasn't been trying to find me this time. Usually whenever there is a huge jackpot I get asked lots of odds questions.
Maybe they dont want to hear to actual odds and value of a ticket.
Quote: WizardIt may pass $656M by the drawing. I'm surprised the media hasn't been trying to find me this time. Usually whenever there is a huge jackpot I get asked lots of odds questions.
Do you give them any tips, like, "If you want a better chance of winning the whole thing - and let's face it, if you didn't want the whole thing, then why didn't you play on Wednesday - then pick three numbers 32 and higher, as couples with one child will tend to play "birthdates and ages", where the three birthdates and the child's age will be less than 32"?
Quote: WizardAssuming that figure, I show a $2 ticket for the May 18 draw has an expected value of 94.2 cents.
Does that mean it's worth more than the paper it's printed on?
Quote: sodawater....
2. no taxes on the profit of the investment
which means that if you take the annuity, the lotto uses the lump sum cash to buy annuities, then guarantees your return. and you only pay taxes once on the annuity, instead of twice on the lump sum + investment return
NOPE
Quote: Maverick17NOPE
Annuity distributions are treated as income, not captial gains correct?
Quote: 1arrowheaddrAnnuity distributions are treated as income, not captial gains correct?
This is getting out of my area, so I could be wrong, but I think lottery winnings are treated as gambling winnings, which are taxed at the same rate as work income.
Quote: sodawater2. no taxes on the profit of the investment
Let's say you can be paid $100 today or $105 next year, wherein the market would make you 5% interest (let's talk expected value here) and a flat 20% interest rate.
$100 today * 1.05 interest * .8 tax = $84
$105 next year * .8 tax = $84
Admittedly, with a progressive tax system, you'll be paying a lower rate on the annuity. With the max rate kicking in at 400k or so... you're talking a negligible amount and I believe it's fair to not even consider income tax progressiveness here. If this was something like $5m total over 20 years, this would be a completely different story.
I had a lot written, but in the end the following is how I found the interest rate at which the annuity and immediate payouts were equal... with the assumption of a flat 40% tax rate (cancels out).
x=interest rate
.6*377*x^29=.6*20*sum(x^n,n,0,29)
x = 1.03585
Or an interest rate of 3.6% - logic dictates that this inflection point is when the immediate payout overtakes the sum.
I would always, always choose the immediate payout. The only thing that should keep someone from not taking it is if they don't have the self control to have a ridiculous amount of money dropped on their lap at one time. I believe the risk of losing a bunch in the market is perfectly acceptable, you'd be able to live (quite well) through any market downturn and be around when the markets rebound.
Edit: Assumption that lotto (annuity) winnings are taxed at the same rate as an immediate payout)
Quote: Wizard
It may pass $656M by the drawing. I'm surprised the media hasn't been trying to find me this time. Usually whenever there is a huge jackpot I get asked lots of odds questions.
Okay, so here's an odds question: What's the formula you used to determine the chances of someone winning, based upon the jackpot? (You stated earlier that, based upon the jackpot size at the time, there was a probability of .268 that no one would win. How did you arrive at that?)
Quote: EdCollinsOkay, so here's an odds question: What's the formula you used to determine the chances of someone winning, based upon the jackpot? (You stated earlier that, based upon the jackpot size at the time, there was a probability of .268 that no one would win. How did you arrive at that?)
It's based upon sales for that draw to estimate the number of tickets sold.
Currently the est. jackpot is $600M annuity ($376.9M cash).
The previous jackpot was $360M annuity ($229.2M cash).
The states will take roughly $1 per $2 ticket, so at this point they estimate 376.9M - 229.2M = 147.7M tickets will be sold.
If this is the correct amount of sales, then the chances of no winner are:
(175,223,509/175,223,510)^147,700,000 = 0.43045
If the annunity matches the record annuity of $656M (50/50 likely, imo):
Powerball's cash option is currently (~63% of annuity value) which leads to a cash value of $413.28M.
This would imply that 413.28M - 229.2M = 184.08M tickets will be sold.
If this is the correct amount of sales, then the chances of no winner are:
(175,223,509/175,223,510)^184,080,000 = 0.34975.
My numbers don't match the Wiz's exactly, but it's clearly because we are making different estimations with regard to contributions to the prize pools.
Quote: tringlomane(175,223,509/175,223,510)^184,080,000 = 0.34975.
I prefer to use the Poisson distribution instead when such huge numbers are involved. I think a lot of calculators would freeze up on that calculation. If we assume 184M tickets sold, then the expected number of winners is 184000000/175223510 = 1.05. The probability of zero winners, with a mean of 1.05, is e^-1.0500874 = 0.359907, which is very close to your number.
To update, the jackpot is 600M now. I assume 307M in tickets sold, for 1.75 winners. Probability of no winner = 17.4%.
Over my objections I called my parents, who live in California, and handed her the phone. She requested to buy ten tickets. After returning from the store my mother had evidently become excited about the whole thing and suggested that we split any winnings, and our $10 share would be their gift. In the unlikely event we win there is sure to be protests from my two brothers about why they weren't given a free share.
I'd say "wish me luck," but I don't believe in luck.
If you make a trip just to buy the tickets, you are far more likely to die on the trip than to win the jackpot.
So if you buy them when you're already at the store, you are freerolling w/r/t untimely death.
Quote: WizardWouldn't it be ironic if I, the one always trying to ruin everybody's fun with how lousy a bet the lottery is, won the Powerball? As usual, whenever the jackpot gets big enough for the local media to report on the long lines to buy tickets in Primm, my wife gets excited and wants to play. We had the exact same debate this morning we've had many times before. My mathematical explanations about how a $2 ticket has a value of 90 cents. Her argument is simply "you have to be in it to win it."
I’m with Mrs. Wiz on this one. Yes, buying a ticket is probably going to be worthless. But it costs, what, $5? How much entertainment does a $5 Pass Line get you? A few seconds / minutes? A lotto ticket at least gives you hours if not days to dream, dreams that often show you where your heart is pointed. I wouldn’t do it every day / week, but sometimes a reminder of what your heart wants is worth the $5.
