Powerball at 400 Million
Poll
 | 30 votes (48.38%) | ||
| | 7 votes (11.29%) | ||
| | 15 votes (24.19%) | ||
| | 4 votes (6.45%) | ||
| | 6 votes (9.67%) |
62 members have voted
It is a good thing I did, because I was unaware the lottery changed the rules again, on October 7, 2015, making it yet again harder to hit. The previous rules had 59 white balls and 35 red balls. The new rules have 69 white balls and 26 red balls. To review, the player must predict the draw of five white balls and one red ball (the Power Ball).
Previously, the probability of winning was 1 in 175.2 million. It is now 1 in 292.2 million.
The number of Powerball players who I think will care about this rule change is probably near zero. Nevertheless, I thought it I would be remiss in my duties as an actuary to consider sales data before the rule change. Considering drawings only since the rule change I still find an exponential relationship between sales and jackpot size. To be specific, sales (in millions) can be estimated as 8.3112 * exp(0.0051*j), where j is the jackpot (in millions).
Based on this new formula and rule change, I find the optimal expected value to be at a jackpot of 630 (edited) million. If it gets greater than that, it induces too much demand, resulting in splitting the jackpot among more competitors. The expected return at that jackpot is 91.09% (edited), before considering the annuity and taxes.
At the current 400 million jackpot, I find the expected return to be 75.28%, again before factoring in the annuity and taxes. The probability of at least one winner in the next drawing on Jan 6 I calculate to be 19.65%. I hope nobody hits it. I must that I enjoy watching the hysteria and appreciate the tax revenue.
The question for the poll is will you play at 400 million?
Links:
Wikipedia
Powerball official web site
Ask the Wizard questions on the lottery
I'm waiting for day when one of these jackpots hits $1 billion!
Quote: GWAEI laugh at people who run out and buy because it is 400 million. What about 20 mil, I guess those people are too good to only win 20 mil.
Years ago, the NY Lottery did a commercial about this. A couple were looking out their apartment window, watching money fall from the sky. The husband said, "Yeah, but it's only about $_ million...."
I think the tag line was, "What are you waiting for?"
Quote: IbeatyouracesI'm waiting for day when one of these jackpots his $1 billion!
So am I. With this new rule change that is much more likely to happen. If we can go four or five drawings without anybody hitting it (a big "if"), then we should get there.
Quote: Wizard
The question for the poll is will you play at 400 million?
To misquote "Jerry McGuire":
"You had me at 337 million"
FYI: The lottery billboard at my local liquor store had the prediction for Tuesday's draw at 477 million.
Quote: DRichWhen did the price of a powerball ticket go from $1 to $2?
January 15th, 2012
Quote: DRichWhen did the price of a powerball ticket go from $1 to $2?
Jan 15, 2012.
I know I've said this before, but I think it bears repeating; I think there should be a single-ticket cap on jackpots - say, 100 million. (For example,. if the jackpot is 450 million, and three tickets win, each gets 100 million (instead of 150) and the remaining 150 million rolls over; on the other hand, if there are five winners, each gets 90 million.)
Quote: zoobrewFor all the people who say they will never buy a ticket, would you chip in $10 for an office group pool? When it gets this high, I wonder how many people buy-in just so they are not the last person working at the job. If you though your job sucked before......
I don't, and if by some chance they happen to win, I remind myself that they bought Quick Picks, so even something as insignificant as having to take my money would have affected the timing with which the tickets would have been bought (it would have taken a fraction of a second longer for whoever was punching the tickets to count the money), and, as a result, the numbers almost certainly would have been different.
When somebody asks me, I always decline with the statement, "My money's the curse" - and if they do happen to win, the first words out of my mouth will probably be, "I was right about that curse, wasn't I?"
I am not a lottery expert but in WA where I live, there is a web site for scratch tickets that shows all the prizes paid and remaining for each game. I am sure a clever bear could create a program to analyze these and there might even be times when a scratch game becomes +EV. It would still be guessing because you have no way of knowing when there are winning tickets that are not yet claimed. Such situations would also be most likely when only a small percentage of tickets are left remaining, so good luck finding them.
When writing this post, I thought making an app to give you the best scratcher games to buy could be a fun idea. As usual with my business ideas, a clever bear beat me to it:
http://scratchoffodds.com/washington/best/
Quote: ThatDonGuyI know I've said this before, but I think it bears repeating; I think there should be a single-ticket cap on jackpots - say, 100 million.
If you did that, then ticket sales would go way down. Lottery players just don't care what the odds are -- but they do like to see big jackpots.
This sounds like me. I will spend maybe $10/yr on lotto games, only when it gets big. I voted 'Maybe' in the poll. I might wait to see if it gets even bigger.Quote: jml24About once every year or two I buy a ticket for entertainment value when the jackpot starts getting big.
I will likely be the only one at work in the office on Thursday morning if the office pool hits the jackpot. At first my co-workers thought I didn't want to take part in the lotto pool because I had religious objections to gambling! :D No, just mathematical objections! I also know they will want to take the lump sum. :P I'm pretty sure $400 million 25 ways is better as an annuity, at least tax implications-wise.
I do sometimes buy scratchers as Christmas gifts. I like to give "Guaranteed Winners" as presents -- buy a handful of tickets and scratch each one enough to show if it is a winner or not, but make sure not to scratch too much as to reveal the amounts. Trash the losers and stuff the winners in a loved one's stocking!
Quote: Wizard
Previously, the probability of winning was 1 in 175.2 million. It is now 1 in 292.2 million.
Crap, I guess I can scratch that off my list.
No hope of winning now..
Fun Part: If the odds are ~1 in 300,000,000... and the jackpot is 400,000,000... then while perhaps not "optimal" from Mike's view, it's still a good bet, no? =P It's just like any other game (LOL) where the variance is ALWAYS LOSE or WIN A COUPLE HUNDRED MILLION!
Quote: RomesNot Fun Part: This just reminds me of the slim filled offers of a casino. Up the min bet, up the house edge/hold, and let the sucker just keep on giving their money away...
Fun Part: If the odds are ~1 in 300,000,000... and the jackpot is 400,000,000... then while perhaps not "optimal" from Mike's view, it's still a good bet, no? =P It's just like any other game (LOL) where the variance is ALWAYS LOSE or WIN A COUPLE HUNDRED MILLION!
But you are paying $2, not $1, and at those giant figures you must count the actual cash value and then subtract the taxes. No where close to + EV at a meager $400 million.....
Quote: SOOPOO...a meager $400 million.....
Hehe... While I could take my $10 and put it on "banker" for almost 50/50, that wager doesn't come with a couple of days of dreaming about how to spend a wheelbarrow full of cash. That fun is worth a couple of bucks.
Quote: AyecarumbaHehe... While I could take my $10 and put it on "banker" for almost 50/50, that wager doesn't come with a couple of days of dreaming about how to spend a wheelbarrow full of cash. That fun is worth a couple of bucks.
I agree 100%. The +EV for me of dreaming about the really big jackpots outweighs the negative feelings about making that grossly negative EV bet.
Quote: CA Powerball site (Highlight mine)
The last draw under the previous Powerball field of numbers was October 3, 2015. The first draw under the new field of numbers was October 7, 2015.
Field of numbers
Players previously chose 5 numbers between 1 and 59, now they choose numbers between 1 and 69.
Powerball number
Players now choose 1 number between 1 and 26, previously they choose a number between 1 and 35.
Odds
The overall odds of winning any prize changed from 1 in 31.85 to 1 in 24.87.
The Jackpot odds changed from 1 in 176 million to 1 in 293 million
Does this change the break-even?
I don't think you should be allowed to get away advertising jackpots that aren't in today's dollars, even if there's a required disclosure. The false-jackpot number does make sense for the estimated number of winners calc since that's the number people see when deciding to purchase a ticket. Additionally, taxes are a different issue, as it is convention to list monetary compensation pre-tax in this country (but I still think of it post-tax).
Here's to a $140m jackpot, post state tax.
Quote: AyecarumbaDoes this change the break-even?
I'm sure it does. Break-even is now $251,868,314, before factoring in the annuity, taxes, and jackpot sharing. After factoring in just jackpot sharing, there is no break-even point -- it is always negative.
Quote: AyecarumbaFYI: The lottery billboard at my local liquor store had the prediction for Tuesday's draw at 477 million.
They are probably right. I suspect the 400 million is what is in the bank and doesn't include sales for the next drawing.
My favorite buzzkill is to ask, "If you get two quick picks, what chance do you think there is you will get the the same numbers on both tickets?" The usual response is, "That's impossible." The conversation usually ends abruptly when I point out it's actually the same chance as winning.
Quote: WizardI just wrote up a formal page on the Powerball. Please click the link and let me know what you think.
As always, I welcome comments, questions, and especially corrections. Thank you.
Nice update, thanks! The tables are right-truncated without a scroll bar when viewed in portrait orientation on my iPhone. Also, the table headers and footers could be better aligned with the column data. Those picky details aside, the wealth of information should answer about every question people might have.
Quote: BleedingChipsSlowlyMy favorite buzzkill is to ask, "If you get two quick picks, what chance do you think there is you will get the the same numbers on both tickets?" The usual response is, "That's impossible." The conversation usually ends abruptly when I point out it's actually the same chance as winning.
Yes. A similar question is "On 9-11-01 the draw of the New York Lottery's Numbers game (where they pick three digits from 0 to 9, with replacement) was 9-1-1. What are the odds of that?"
The answer is the same as any other outcome, 1 in 1,000. The date has nothing to do with it.
While you are correct, what about two identical quick picks on the same ticket? In a paper saving method, you can get up to five games on the same ticket. Is the system programmed to prevent that kind of duplication? You'd think that such an occurance would get some media attention...Quote: BleedingChipsSlowlyMy favorite buzzkill is to ask, "If you get two quick picks, what chance do you think there is you will get the the same numbers on both tickets?" The usual response is, "That's impossible." The conversation usually ends abruptly when I point out it's actually the same chance as winning.
Quote: WizardI just wrote up a formal page on the Powerball. Please click the link and let me know what you think.
As always, I welcome comments, questions, and especially corrections. Thank you.
Here's how the Powerball payouts work in California:
| Numbers | Powerball? | Percentage of pool |
|---|---|---|
| 5 | Yes | Varies |
| 5 | No | 8.5558% |
| 4 | Yes | 2.1903% |
| 4 | No | 1.0951% |
| 3 | Yes | 1.1380% |
| 3 | No | 1.3109% |
| 2 | Yes | 1.2405% |
| 1 | Yes | 5.6536% |
| 0 | Yes | 10.8027% |
The percentage of the pool that goes into the jackpot pool is:
68.0131% if the jackpot is less than $120 million
64.0131% if the jackpot is between $120 million and $250 million
60.0131% if the jackpot is more than $250 million
The pool consists of $1 per $2 ticket bought.
Note that there is no PowerPlay option in California.
Source (which also includes the breakdown for MegaMillions)
Quote: ThatDonGuyHere's how the Powerball payouts work in California:
Thanks; I added that information to my page.
The possibility of duplicates is a function of random selection. I think using something other than random selection would be a problem Two duplicates on the same ticket, however, would easily be handled by providing two slices of the pie in case of a shared jackpot.Quote: DJTeddyBearWhile you are correct, what about two identical quick picks on the same ticket? In a paper saving method, you can get up to five games on the same ticket. Is the system programmed to prevent that kind of duplication? You'd think that such an occurance would get some media attention...
Quote: DJTeddyBearWhile you are correct, what about two identical quick picks on the same ticket? In a paper saving method, you can get up to five games on the same ticket. Is the system programmed to prevent that kind of duplication? You'd think that such an occurance would get some media attention...
This is a great question DJTeddyBear. I suspect the answer would be a potentially embarrassing State Secret since it would reveal how the supposedly random picks are actually bunched in a less than random fashion.
Quote: WizardI just wrote up a formal page on the Powerball. Please click the link and let me know what you think.
As always, I welcome comments, questions, and especially corrections. Thank you.
Two of the column headers on the, "California Prize Allocation" table need to be corrected. They should read "White Balls Match" and "Power Ball Matches", instead of "Multiplier" and "Weight".
Otherwise, an excellent "pearl". Unfortunately, the "fever" is pretty compelling amongst us "swine".
Quote: AyecarumbaTwo of the column headers on the, "California Prize Allocation" table need to be corrected. They should read "White Balls Match" and "Power Ball Matches", instead of "Multiplier" and "Weight".
Thanks; I fixed that.
Quote:Otherwise, an excellent "pearl". Unfortunately, the "fever" is pretty compelling amongst us "swine".
Thank you for the compliment. Your penance will be five push-ups for every ticket purchased.
Hehe, I am going to do them as a 25 year annuity...Quote: Wizard...Your penance will be five push-ups for every ticket purchased.
When I was with KCAL about ten years ago our newsroom pool hit 5 of 6 numbers in the weekly California lottery and we each got something like $87.
When I was with KTTV here in LA I was buying a weekly lottery ticket at a 7-Eleven. My cameraman Mike was in the store with me and when I bought mine he said "I'll buy one too. If I win, Alan, I'll give you ten percent ."
That night in the newsroom we all watched the drawing. Mike had five of the six numbers for about $3500. He screams with joy and announced "I bought this because of Alan and I said I would give him 10% if I won -- but I meant only if I won the jackpot."
My buddy.
Quote: Wizard...Your penance will be five push-ups for every ticket purchased.
Quote: AyecarumbaHehe, I am going to do them as a 25 year annuity...
No, the 25 push-ups is the annuity price. You just have to do 2 now and be done.
Spent $2.
I assume the jackpot will now be $400,000,001.25.
Hey, I'm a lucky guy ;-)
Quote: BleedingChipsSlowlyTwo duplicates on the same ticket, however, would easily be handled by providing two slices of the pie in case of a shared jackpot.
Didn't a player do that one time? I could swear I heard about a player deliberately picking the same numbers on two tickets, then getting 2/3 of the jackpot when he was one of two grand prize winners.
Mike, would you say there's any credence to the suggestion that picking at least one number higher than 31 gives you slightly better value since you're less likely to share the jackpot with birthday-pickers?
Quote:Mike, would you say there's any credence to the suggestion that picking at least one number higher than 31 gives you slightly better value since you're less likely to share the jackpot with birthday-pickers?
Yes, it would. Very marginal. It would make a good Ask the Wizard question if I could get some data on frequency of each number picked.
Quote: AyecarumbaHehe, I am going to do them as a 25 year annuity...
Quote: DeucekiesKicked my $10 into the kitty.
The punishment for buying Powerball tickets for all forum members per ticket shall be either:
A) Five push-ups payable immediately.
B) One push-up per year for each of the next 30 years.
You may pay other forum members to serve them. I think Miplet works pretty cheap.
Quote: TwoFeathersATLOK, had to go to the store anyway...
Spent $2.
I assume the jackpot will now be $400,000,001.25.
No, it's $400,000,000.63 - the prize pool is $1 per ticket, and (at least in California) about 63% of the pool goes into the jackpot.
Quote: DeucekiesDidn't a player do that one time? I could swear I heard about a player deliberately picking the same numbers on two tickets, then getting 2/3 of the jackpot when he was one of two grand prize winners.
I remember a story about a 7-11 clerk accidentally creating 6 tickets with the same set of numbers for somebody who only wanted one; the purchaser didn't want to pay for the other 5, so the store's policy was that the store would pay for them...and when the numbers hit, the original purchaser tried to sue for the 5/6 of the jackpot that the store won.
Quote: ThatDonGuyI remember a story about a 7-11 clerk accidentally creating 6 tickets with the same set of numbers for somebody who only wanted one; the purchaser didn't want to pay for the other 5, so the store's policy was that the store would pay for them...and when the numbers hit, the original purchaser tried to sue for the 5/6 of the jackpot that the store won.
I hope it got laughed out of court.
Quote: WizardThe punishment for buying Powerball tickets for all forum members per ticket shall be either:
A) Five push-ups payable immediately.
B) One push-up per year for each of the next 30 years.
You may pay other forum members to serve them. I think Miplet works pretty cheap.
But, one physical ticket can have multiple plays on it - so, is it per ticket or per play?
Also, as an aside, what would be the probability that the 3 numbers chosen in a Pick 3 would correspond with the date of the drawing?
Quote: aceofspadesBut, one physical ticket can have multiple plays on it - so, is it per ticket or per play?
Per ticket.
Quote:Also, as an aside, what would be the probability that the 3 numbers chosen in a Pick 3 would correspond with the date of the drawing?
Per my earlier post about the 9-11 New York Lottery result, 1 in 1,000.
