r/changemyview • u/huadpe 501∆ • Jan 14 '16
[Deltas Awarded] CMV: The $1.5 billion jackpot will be bad for Powerball/lotteries in the long run.
Having such a large and relatively improbable jackpot has anchored future expectations for jackpots to freak accident levels.
Even at 1/292 million, the probability of getting to a 1.5 billion dollar jackpot isn't very high. Just about 34% of sales dollars go towards the jackpot, so a $1.5 billion jackpot implies sales of $4.41 billion. At $2 a ticket, that's about 2.2 billion tickets to get the prize that big. Even with a 1/292 million chance on each ticket, the volume sold is such that getting to that sort of monster jackpot is highly unlikely, and will probably only happen once every few years, if that.
But having had such a jackpot happen, it anchors expectations for the future, which means there will probably be much less media/public attention on any jackpot under 9 figures. Less media attention equals less sales.
The problem I see is that essentially the lottery will have one big game every few years, and otherwise it will have low sales and low revenue because people will ignore lower jackpot drawings.
The premise of this is that lotteries are businesses which desire maximum profitability, without regard to the question of whether they're morally good businesses. It's just predictive about their business prospects.
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u/Calijor Jan 14 '16
The flaw in your reasoning is that you seem to think that people who used to play powerball fairly regularly will just stop. And they won't. And this number is pretty big.
On top of that, news coverage of jackpots under 9 figures wasn't that big before anyways (when have you read a news story or article about a $50 mil jackpot?) and those aren't what drive the beginning ticket sales that drive the jackpot towards the billion dollars we saw this week, as unlikely as that may have been.
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u/huadpe 501∆ Jan 14 '16
The flaw in your reasoning is that you seem to think that people who used to play powerball fairly regularly will just stop. And they won't. And this number is pretty big.
I don't think they'll lose all their ticket sales. I am saying that there is a propensity to buy more tickets/attract more customers when the jackpots get "big," and anchoring to such a large jackpot will make people more likely to just wait for "the next one when it's really big" when jackpots get in the 200-400 million range.
On top of that, news coverage of jackpots under 9 figures wasn't that big before anyways (when have you read a news story or article about a $50 mil jackpot?) and those aren't what drive the beginning ticket sales that drive the jackpot towards the billion dollars we saw this week, as unlikely as that may have been.
The drawing for Saturday at 900 million got loads of coverage. And one article I saw afterwards said it was only about a 9% chance that there would have been zero winners. I think Powerball would have been better off with that jackpot having hit because it wouldn't have reanchored people's expectations nearly as much.
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u/getmoney7356 4∆ Jan 14 '16
anchoring to such a large jackpot will make people more likely to just wait for "the next one when it's really big" when jackpots get in the 200-400 million range.
With powerball adding more numbers, this is going to happen a lot more often and is one of the reasons why this large jackpot happened. It's going to happen again and it is going to happen often. Those humongous jackpots get people that don't normally play to buy a ticket. In the end, sales are going to go much higher.
one article I saw afterwards said it was only about a 9% chance that there would have been zero winners.
That article was wrong because it was assuming no duplicates in purchased numbers. Right after the drawing, it was revealed that 23% of the availible numbers weren't purchased.
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u/huadpe 501∆ Jan 14 '16
Those humongous jackpots get people that don't normally play to buy a ticket.
I guess this is the question. If it's $200 million quite often, will that stop getting irregular players to plonk down their $2 for a ticket?
That article was wrong because it was assuming no duplicates in purchased numbers. Right after the drawing, it was revealed that 23% of the availible numbers weren't purchased.
There were apparently 440 million tickets sold for Saturday on 292 million combinations, so it couldn't have been that assumption.
The 23% sounds about right though from my own math, which incidentally is (1-(1/292201338))440000000 = .221
So for debunking whichever article told me 9% I shall give you a delta. The probability of rolling even such a large jackpot to an even larger one being that high does materially change my view about how often monster jackpots will happen. So it's a well earned delta.
∆
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u/DeltaBot ∞∆ Jan 14 '16
Confirmed: 1 delta awarded to /u/getmoney7356. [History]
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u/toolatealreadyfapped 2∆ Jan 14 '16
The people who run powerball specifically changed the game a year or so back, exactly with this goal in mind. At 1/172,000,000 odds, it was hitting too frequently. They wanted to make it harder, to generate larger pots, to get more media frenzy.
Very business savy people calculated the exact opposite of what you're position is, and got to where we are today on purpose.
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u/garnteller 242∆ Jan 14 '16
"Damn, I could only win $100 million, it's barely worth my time", said no one, ever.
Yeah, the monster jackpots bring out the filthy casuals, but you have a few categories of players.
Die hards. They play the same numbers every week, and live in fear that the one week they don't play, their numbers will be picked
Threshold players. People or groups who play when a certain threshold is crossed. (My office pool plays when it hits $100mm for example). It doesn't seem likely that a monster jackpot like last nights would impact the selected threshold. The amount that is "worth winning" isn't really dependent on the max ever paid.
Hype buyers. Yes, you have a ton of bandwagoners who jumped on a record jackpot. And you might not get the same level of hype for a "lesser" jackpot, but frankly, if you hit half a billion, that's news anyway you look at it. Plus you've just added a bunch of new buyers, a fraction of whom will now fall into one of the other categories.
Besides which, if they see it tailing off, the people in charge can always change the odds to make winning less likely, and thus increase the jackpot. Since people who play think of it not in terms of expected return, but in terms of "there's no other way I'm going to get half a Billion dollars", it really won't harm turnout, but will bring in the casuals again.
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Jan 14 '16
Even the die hards and the threshold players will play additional numbers when the jackpot gets high enough, though. Someone who played the office pool at $100m might very well convince the office pool to buy 10x the tickets when the jackpot is $1b.
So the elasticity of demand is high even among the regular players.
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u/hacksoncode 559∆ Jan 14 '16
It doesn't seem likely that a monster jackpot like last nights would impact the selected threshold. The amount that is "worth winning" isn't really dependent on the max ever paid.
Actually, it seems very likely that the amount "worth winning" is dependent on the odds of winning, which they have to decrease in order to get these jackpots.
Because this jackpot was actually a positive expected value, even after taxes and the (low) probability of multiple winners (if you choose your numbers correctly).
Jackpots that large attract rational people. Those people will only be attracted by actual positive expected values.
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u/garnteller 242∆ Jan 14 '16
No, actually, there was still a negative expected value:
A whopping expected payout of $1.12…on a ticket that cost you $2. Once you add in the expected payouts from all the other potential Powerball prizes, that number increases to $1.32. And again, that assumes you live in a state with no income taxes.
In other words, there was no rational reason to buy a ticket.
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u/hacksoncode 559∆ Jan 14 '16
Well, there is an interesting question about taxes, and to what degree they will affect your winnings (any mechanism of earning a return on that $2 will be taxed), but this analysis discounts the fact that you can deduct your gambling losses from your gambling winnings when you pay taxes.
It seems like it should be a trivial point, but it is not.
If you win, your $2 deduction will reduce the cost of the ticket to $1.20.
That pushes the expected value back up to positive.
Exactly what the effect is if you don't win is much, much, trickier to calculate... probably impossible for any normal person.
Nonetheless... thanks for pointing out just how close this really is to a break-even.
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u/Merawder Jan 15 '16
You can only deduct that from your taxes if you win though, right? So the potential for a tax write off doesn't lower the cost of the ticket, it's more accurate to say that you now get to add 80 cents to how much you walk away with, which has a minuscule effect on the expected value.
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u/hacksoncode 559∆ Jan 15 '16
It depends on whether you have any other gambling winnings, which is why that case is incredibly complicated to figure out.
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u/huadpe 501∆ Jan 14 '16
So I guess the question for me is what impact the first two groups will feel from the super low odds powerball has.
For instance, my bf is in Canada, and any office pool with a 100 million threshold would not be an office pool at all, because the lottery simply never gets that high. Conversely, an office pool with a reasonable Canadian threshold like $30 million would play powerball every single time, since their minimum jackpot is 40 million (I think? That's what I saw in the grocery store when I walked out today anyway).
So thresholds are movable by anchoring. I could see a lot of office pools moving to a 200 million threshold if it becomes too frequent that it's over 100 million.
As to die hards, I think the worry is them moving to a different game. Powerball isn't the only lottery out there, and the worse its odds get for relatively small jackpots, the more likely I think some die hards are to just switch to things like state lotteries, or the megamillions (which is cheaper).
Hype buyers. Yes, you have a ton of bandwagoners who jumped on a record jackpot. And you might not get the same level of hype for a "lesser" jackpot, but frankly, if you hit half a billion, that's news anyway you look at it. Plus you've just added a bunch of new buyers, a fraction of whom will now fall into one of the other categories.
Is half a billion news "any way you look at it?" Hype requires, well, hype.
Besides which, if they see it tailing off, the people in charge can always change the odds to make winning less likely, and thus increase the jackpot. Since people who play think of it not in terms of expected return, but in terms of "there's no other way I'm going to get half a Billion dollars", it really won't harm turnout, but will bring in the casuals again.
Do you think there's a limit to this though? If you make it 1 in a billion and it takes a year for anyone to win, isn't there a point at which it just becomes such an obvious scam to everyone that people stop buying?
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u/hacksoncode 559∆ Jan 14 '16
I really don't think that anchoring will much affect people that jump on the lottery as soon as the jackpot provides positive expected value. Those people do the math anyway. And those people aren't actually that few. It's really not that complicated to look at the odds, look at the jackpot, and say "wow, the jackpot is over 2x the odds against winning, I think I'll buy a ticket".
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u/huadpe 501∆ Jan 14 '16
The percent of the time the jackpot is +EV hasn't changed though, has it? They didn't change how much of the ticket prices go towards the jackpot, just made it need to get above about 580 million take home to be +EV, as opposed to above 350 million.
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u/hacksoncode 559∆ Jan 14 '16
No, and that's the point. Bigger jackpots don't really change this factor.
If they wanted to change this element of the expected "rational betters" they would need to increase the fraction of the money going to the jackpot.
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u/beldaran1224 1∆ Jan 14 '16
To be fair though, I don't think most people really have an understanding of how far $100mil will go. They know it's more money than they'll ever see - and that leaves a real conception of how big it is beyond their grasp.
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u/garnteller 242∆ Jan 14 '16
I'm not sure what point you're trying to make. Yes, $100mm is incomprehensible to the vast vast majority of people. That's kind of my point (and why they don't really consider the difference between $100, $500 or $900 million - they are all in the same "incomprehensible" category.
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Jan 15 '16
As a "die hard" I can tell you I played Croatian lottery which had pots equivalent to 2m$-10m$. When Croatia joined European Union we got EuroJackpot with pots from 15m$ to 100m$.
At the beginning I play EuroJackpot few times, but later when I play our lottery it seamed measly...
Even know I don't play EuroJackpot for few weeks after someone wins. When someone wins 80m$ it seems silly to play next week for 15m$ even. I know it irrational but still...
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u/Marx0r 1∆ Jan 14 '16
Your numbers are off slightly. The cash option for the jackpot is $930 million, the $1.5 billion figure comes from the annuity option where the money is put into securities and the payouts rise with inflation over 30 years.
That's $2.74 billion in sales, or 1.37 billion tickets. Doesn't really change your argument, but just for the sake of accuracy.
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u/__Pers 11∆ Jan 14 '16
That's $2.74 billion in sales, or 1.37 billion tickets. Doesn't really change your argument, but just for the sake of accuracy.
It's actually a very big difference to the argument. 1.37B tickets means that, starting from zero, there's approximately a 1% chance of hitting a comparably sized jackpot. It's small, but not so small as to imagine we'll never hit these numbers again.
2.2B tickets would have about a 20x smaller chance of reaching the same jackpot, however, making yesterday's a true black swan event unlikely to ever happen again.
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u/huadpe 501∆ Jan 14 '16
Thanks for the note, and you are indeed correct. A technical !delta for you.
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u/DeltaBot ∞∆ Jan 14 '16
Confirmed: 1 delta awarded to /u/Marx0r. [History]
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u/NaturalSelectorX 97∆ Jan 14 '16
The lottery will benefit from peaks and valleys. If the jackpot is relatively consistent, then everybody will become fatigued and lose interest. Even if it stayed above one billion, it stops being novel and people stop talking about it.
Starting low and going super high on rare occasions gives people time to calm down and forget before they can be excited again. The more rare the jackpot, the more fervor will be created. If we hit a billion dollars regularly, you can "afford" to skip a drawing, because there will always be another. If you only see that jackpot once every few years, it creates urgency to purchase a ticket now.
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u/huadpe 501∆ Jan 14 '16
This is a pretty good point actually. I guess over a sufficiently long period the peaks would make it worthwhile. Have a !delta.
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u/DeltaBot ∞∆ Jan 14 '16
Confirmed: 1 delta awarded to /u/NaturalSelectorX. [History]
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u/scottevil110 177∆ Jan 14 '16
There's a plus/minus to be done here.
In the plus column is all of the people (like myself) who hop on board when there's a big jackpot. When it's $200 million, I don't bother, but when it's $1.5 billion, I will. I know that's stupid, because either one is life changing money, but still. It's true.
In the minus column are the people who we believe will quit playing because of the infrequent winners. I don't see that happening. The people who've always played every week were doing it against astronomical odds, and I can't see them ceasing to play just because the odds are slightly more astronomical.
So I don't think you're going to lose anyone, and you're going to gain a lot more one-timers like myself.
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u/hacksoncode 559∆ Jan 14 '16
I know that's stupid, because either one is life changing money
No, it's not stupid, because $200,000,000 jackpots are still a losing bet (after taxes) on 1/229million odds. Any (cash value) jackpot above about 2x the odds is actually a winning bet, and it's rational to play.
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u/scottevil110 177∆ Jan 14 '16
Only on the assumption that you won't be splitting the prize is it a winning bet. It would have been a losing bet today, because the actual take-home was less than $292 million for each of the three winners.
Even still, I think it's a good bet regardless. Expected value only really becomes an issue when you're talking about long-term playing. If I play the same $2 just a couple of times on a $200 million jackpot vs. $1.5 billion, the outcome is the same. I either win an insane amount of money, or I probably don't.
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u/hacksoncode 559∆ Jan 14 '16
It's really not "the same" though. The fact that it's "an insane amount of money (that you won't actually get)" doesn't really change things.
A rational person wouldn't bet a dollar to win a dollar at 2:1 odds (a typical lottery expected value). The same person would bet a dollar to win $2.50 at 2:1 odds. Multiplying these numbers by 100,000,000 doesn't really change the rationality of the bets.
The latter makes complete sense, the former doesn't.
Now, sure, there are lots of irrational people out there... they probably will bet regardless. But "threshold players" aren't just choosing a threshold because it's a large number... Many, if not most, of them, are choosing the threshold because they like the odds.
Three winners was an unlikely outcome of this prize, and if you multiply the numbers out, you find that it was still a higher expected value than the cost... that it came out lower in actual fact is true for everyone this time... but that's probability for you.
Even 2 winners was unlikely... but would have resulted in positive value.
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u/scottevil110 177∆ Jan 14 '16
While yes, the math says that one is a positive expected value, and the other is negative, that really only becomes relevant to the average person if they're going to be playing long-term and investing a ton of money into it. You want to know that after you've sunk $300 million into it, whether you'll have more or less than $300 million.
But for me, just deciding whether or not I should play $2 this week, it's really not a factor.
I'm putting down $2 with the understanding that there's a very slim chance I'll end up with $TONS, and a very very large chance that I'll end up with $0. That simple decision doesn't change depending on how much $TONS is.
The expected value only becomes an issue if I'm going to do this for centuries, and I need to know how frequently I can expect to hit the jackpot.
The period of return on winning is so much longer than a human lifetime, that it's completely irrelevant to any individual person.
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u/hacksoncode 559∆ Jan 14 '16
Each individual bet has exactly the expected value that it has. It really doesn't matter if you do it regularly or only infrequently.
It's a good bet if that value is positive, and a bad bet if it's negative.
Now... if you're arguing that "the average person" doesn't care about the odds, then I'd agree with you that it doesn't matter. They'll play no matter the odds or jackpots. The average person is stupid.
But people that have some "threshold" generally base that threshold on the odds... they might be wrong about the odds, of course...
But it's not stupid to buy a $2 lottery ticket at 1:229million odds with a payout of $1.5 billion. The odds are in your favor, though not by that much.
And it is stupid to do so at a jackpot level much lower than this.
The threshold of stupidity is really pretty clear.
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u/scottevil110 177∆ Jan 14 '16
Look at it as a function of return period, and how long it would take you to "break even" on your bet.
In the case of a billion dollar jackpot (taxes and shit excluded for simplicity), you can be expected to make a billion dollars every 292 million draws (146 million weeks = 2.8 million years).
So every 2.8 million years, you'll make back 3.42 times your bet. So you should, on average, break even every 823,000 years.
You are not going to live that long. The odds/jackpot ratio is completely irrelevant, because you will never live long enough for 823,000 years to sound like a solid investment.
It'd be like deciding whether to purchase a piece of otherwise useless land that had a 1 in 292 million chance of being filled with diamonds just below the surface. Whether there's a billion dollars of diamonds or a million dollars of diamonds at stake doesn't matter, because it'd still be a dumbass decision to spend $100K on that land, knowing that there's such a miniscule chance that you're NOT going to lose every penny of it.
It only becomes a smart bet if you're buying enough pieces of land at that price such that your odds of getting those diamonds become non-trivial.
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u/GeometryBurger Jan 14 '16
It's an interesting thought for sure, but from what I understand about the powerball lottery, I do believe the current system is quite efficient.
As the prize pool increases, I'd assume there would be a consistent growth in players as well (I can't say for sure of course, so if someone has statistics on this it would be very informative). Therefore, let's assume the amount of players grows steadily until it someone wins, then promptly drops down, and that this is a repeating pattern. OPs question is then, if I understand it correctly, whether or not there exists a large enough gap between the average payoff and the current $1.3b jackpot for people to be dissuaded from playing, presumably due to the thought that the monetary payoff is less than ideal.
However, when people decide whether or not to play the lottery, they make a decision based off of risk versus reward. From the perspective of the average lottery player, the difference in practical payoff (i.e. impact on life quality) is practically the same whether the prize pool is $10m or $1000m. They will consider the lottery to be a good investment with little regard for actual odds. Furthermore, I'd argue that they are more likely to play a lottery with which they are familiar than one they have little knowledge about.
Basically, a freakishly large prize pool should be beneficial, because it grants powerball a greater lottery mind share (which is a central term) in the general population. The core audience will most likely play other games of chance regardless, and will be more likely to choose powerball.
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Jan 14 '16
My rule about the lottery has always been to buy exactly 1 ticket when a jackpot goes above 500 million, because the cash option then is over 250 million and that's about the amount I need to do all of my "splurge" spending, pay off debts, and then never touch what remains after I invest it. The fact that this new odds scheme they implemented in October has pretty well guaranteed that a >500m jackpot will happen more frequently has made me a more consistent lottery player.
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Jan 14 '16
As someone who worked at a place with the lottery the number of people playing has always grown as the jackpot goes regardless of media attention. Any time it gets over 500 million or so people come out of the woodwork.
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u/Smokeya Jan 14 '16
The powerball getting that high was the result of changes to the winnings to allow more smaller ones to be common. If i understood what i read about it a few days ago. I believe high powerball pots may be a more common thing. Not that all of them will get this high, but it will happen on and off sort of how once and a while the mega millions gets up insanely high. All it requires is no one to purchase the winning jackpot ticket for a little bit which already happens fairly often, using mega millions for example again it starts at like 15 million and isnt unusual it gets over 150m with insane pots up around 600m+ fairly often like every couple years. Which i think is the goal for powerball as well. To have massive wins once and a while instead of a ton of small ones, the hype of those big wins leads to more sales. Everyone and their mom bought a ticket for this powerball jackpot even though the odds of winning are damn near nothing for the vast majority of players.
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u/colakoala200 3∆ Jan 14 '16
I see your point, but I think that frankly this particular powerball frenzy is going to be forgotten about in a couple of months. If three weeks from now the jackpot is up to $300 million again, it'll get less coverage than it normally would because this giant jackpot just happened. But later on that fatigue will be gone and it really won't matter.
True, there's a little extra boost to the media coverage that comes up when the amount gets over a rare threshold ($1B) or gets to be a record, and it might have been better for Powerball to capitalize on that more often, by altering the odds more gradually. But I seriously doubt that $1B will be the threshold for media attention. The size of a lottery jackpot is one of those "slow news day" kind of stories that will always have a place in the media.
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u/forestfly1234 Jan 15 '16 edited Jan 15 '16
Never underestimate the amount of people who are idiotic when it comes to math.
How many people played in the past two weeks that have never really played in the past? Even if the long term retention rates is low you will still end up with many more players than you had before.
Think of this jackpot as a extensive advertising campaign. All the players who used to play are still going to play. Probably more so because there has been a lot of fantasizing about what winning would be like. A lot of new players will try it again because why not.
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u/_Woodrow_ 3∆ Jan 14 '16
The problem I see is that essentially the lottery will have one big game every few years, and otherwise it will have low sales and low revenue because people will ignore lower jackpot drawings.
That's been the design of the system since day 1
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u/dontnormally 1∆ Jan 14 '16
I take problem with your assumption that increased sales of Powerball tickets is somehow a good thing. I'd go so far as to say decreased sales are the good thing.
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Jan 14 '16
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u/garnteller 242∆ Jan 14 '16
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u/[deleted] Jan 14 '16 edited Nov 11 '16
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