How the Powerball rules were tweaked to make the game an even bigger ripoff | Hacker News Reader

How the Powerball rules were tweaked to make the game an even bigger ripoff

latimes.com

108 pointsparadygm201 comments

I found this statistic to be the most interesting: "In 1999, researchers at Duke University reported that American households spent an average of $162 per year on lottery tickets, but low-income households spent $289 and those with less than $10,000 in income spent $597. Higher lottery purchases also were associated with lower educational attainment and ethnic minorities."

I didn't find the fact that poorer people were more likely to play surprising but just how much more. Nor would I have guessed that the overall average was anywhere near $162 a year. I don't think I've spend that much on the lottery in my 20+ years of being old enough to play the lottery.

Part of it could be explained by how the lotteries are marketed. For example, in the south side of Chicago (not exactly known for its manicured lawns and gated communities) there was a billboard advertising the lottery: "Your ticket to easy street." As more anecdotal data, it has been my observation (without actually recording my finds in an organized manner) that one will see considerably more lottery advertisements in low-income neighborhoods than in more wealthy neighborhoods.

I'm not saying that advertising is the explanation, but I'd be surprised to find that it had no bearing at all. I also kind of wish that state governments would, well, cut it out.

I have found the advertisements to be very interesting in Denver too. They more or less imply that you are going to win. Some of the claims are along the lines of "How are you going to spend your millions?" Here they would never let the casinos put an ad like that up. I guess that's the wonderful part of state sponsored gambling is that it gets to ignore state consumer protection controls.

I think that advertising is more likely an effect rather than a cause. The lottery knows their market.

It's probably a symbiotic relationship to some degree.

To a degree. But it would be silly to think Lotto would avoid marketing to a higher income demographic if they thought there was a chance they could get the same return from it. (Especially since the higher income demographic would have more money to spend).

But marketing to a higher income demographic is considerably more expensive (per eyeball/impression). High income demographics are targeted with ads for high-margin goods (cars, vacations, fashion goods), which have 3- to 5- digit margins that can be used to advertise them, so there is more competition to target ads towards wealthier people.

The higher income demo would rather gamble on Wall St, where the odds are much better.

Sometimes they fund startups and hunt for unicorns.

I think the median numbers (in combination with mean) would be very interesting. I am suspicious that numbers like that are not spread anywhere close to evenly through those demographic groups.

It's like a redistribution of wealth scheme. Welfare checks go to the poor who use their welfare to purchase lotto tickets. Some ends end back in the governments hands and some lands in the lottery operators coffers. Anyone know how much lottery officials and employees earn/make?

Then add on top of it the scandal that happened in the past where a lottery official was selling the winning numbers to certain people in return for a kickback from the winnings.

http://www.seattletimes.com/nation-world/with-14b-lottery-ja...

https://www.washingtonpost.com/news/post-nation/wp/2016/01/0...

And the wiki article explains a little bit more on how he did it[1]: "When his trial began on April 13, 2015, evidence was introduced by the prosecutors to support allegations that Tipton had rigged the draw in question, by using his privileged access to an MUSL facility to install a rootkit on the computer containing Hot Lotto's random number generator, and then attempting to claim a winning ticket with the rigged numbers anonymously."

[1] https://en.wikipedia.org/wiki/Hot_Lotto_fraud_scandal

Yeah, it makes me want to look at the numbers. We as a family spend maybe $20; so are there households that are spending tens of thousands?

Perhaps, but I think it more likely that there are tens of thousands that spend a little more than the average.

I was shocked the first time I realized how big some lottery-playing communities are, and to what extent it's actually a social activity.

Oh yes. There's a customer at my local 7-11 who spends a couple hundred bucks on every powerball draw. That's a twenty grand over the course of a year, and that's assuming she doesn't play other games.

I have no idea how much money she has, but she doesn't spend much on her clothes or car.

get rich or die trying

I find it puzzling that the reaction to the lottery here on HN and among many tech people I know is very different to say... fantasy sports betting.

With sports betting, not only do you have the prospect of wasting lots of time, but you end up getting hooked to obsessive watching of ESPN and tracking player stats, wasting lots of time. With lotto, I drop $2 and I'm done.

Yet the consensus seems to be the the millions of people buying lotto tickets are all rubes, but the folks flouting the law and running bookmaking operations on the internet are disrupting staid government regulation?

Probably because fantasy sports betting is not a 100% game of chance and that application of data science ostensibly increases your chances of winning.

As with poker versus slots, one may require more time/work to become a reliably winning player, but the payoff is larger. With slots, you pull the lever and you're done.

Ultimately, though, gamblers of all kinds find these sorts of things fun in some way, otherwise they wouldn't continue to throw away money. It's addictive because it triggers some sort of reward center in the brain, and simply participating provides not only fantasy but also a sense of drama and unknown in an otherwise very predictable life.

full disclosure: not a gambler and rarely play the lotto

Lots of gambling isn't "100% a game of chance": Poker, Blackjack, Horse Racing, etc. That doesn't seem like a very good rationalization for fantasy sports over lottery... and I agree with GP: Lots of fantasy sports folks waste insane amounts of time tracking and updating their rosters. You could justify it as "more fun for the same $$", but that definitely wouldn't be true for me.

Blackjack is not like horse racing and poker -- in the latter, the player can use information that is available to them to have a positive expected outcome. In blackjack, no matter how good you are you cannot create a positive expected outcome, you can only minimize your negative expected outcome.

Actually you can in blackjack, it just involves playing outside the individual game of blackjack and employing card counting techniques across multiple tables. Although, at that point, I can understand if you distinguished between playing that "game" and playing a table of blackjack.

Yes, you can do that. In Nevada that's cheating and in New Jersey it isn't (but if they see you doing it they can make your life very difficult), but at that point you're operating outside the norms of the game so I didn't count it.

It's not against the law unless you're using a device, but you can bet your ass that Casinos will kick you to the curb if they figure out you've been doing it. They'll also tell all of the other Casinos to blacklist you too.

And they will figure it out, too. It's not that hard for me to spot card counters, and I'm not a pro.

Seems like over the years the way they've dealt with card counters is by tweaking the game, though. They've added decks, they shuffle sooner, they shuffle when you increase your bet or when a new player sits down and plays for nontrivial amounts, and lately with continuous shuffling machines.

It's not cheating in Nevada. But you can be bounced when they catch you.

It also depends very strongly on the rules of the game. There are variations where you can get a slightly better than 50% odds just by playing "correctly" if the rules are in your favor. (single deck, hit on 16, etc etc)

Actually the best casino game to play from an odds perspective is craps at a table that meets these conditions:

1. Field has 2 or 12 pay triple and the other pays double

2. 5x odds bets or better allowed.

3. Minimal / no restrictions on place bets. ( some table don't let you do place bets on 6 or 8 )

And then follow these rules:

1. Only do field, place, or come bets

2. Always have your place and odds bet "working" - you will have to tell the dealer

3. If a number is rolled that you have an existing place bet on convert it to a odds bet.

4. Limit the total amount of money on the table - one 7 will wipe everything.

5. If you feel nervous, take all the money off the table that you can. Let the last few remaining bets play out and then walk away.

6. Lastly, and most importantly limit yourself to a specific amount of time or rolls. This is especially important if you are winning.

> Field has 2 or 12 pay triple and the other pays double

> Only do field, place, or come bets

The house edge on the field with those rules is 2.78%, which isn't bad, but isn't great. Ideally you want one that pays triple on both 2 and 12 (good luck finding that!) because then the house edge is 0.00%

All the rest of your bets are either 0% or 1.4-1.6% house edge.

Also, if you're really worried about one seven wiping you off the table and don't mind being contrarian, play the don't. While the odds are basically the same (slightly better actually) in the long term, I find the short term odds much better (because of the aforementioned deadly seven).

However if you value the social aspect of the game or your casino player rating, don't play the don't. :)

Yeap on the odds. In other words, best game if you want to have a reasonable chance on being a lucky winner.

Also impossible for the casino to make a subtle rule or behavior change that negatively affects the odds.

I personally don't know why casinos bother worrying about card counting. All they really have to do is increase the number of decks and/or increase the reshuffle frequency.

Or if they really want to stop it but some house rules that say that the next bet can't be any more than 2x the previous bet.

Sure they might miss that person that is going to go all in on one last draw. But whatever. Besides gambling revenues are down and non-casino revenues (like shows) are up. So maybe Las Vegas will stop being a gambling mecca and just be an entertainment hub.

I would love it if Vegas started shifting the rules back into the player's favor so us degenerate gamblers could come back more.

I got so angry when I see a blackjack table with a 6 for 5 payout on a blackjack and the lack of surrender.

I heard if you play perfectly on a totally random round, the dealer has less than a 0.5% edge (depending on the rules) which is very good for the player, compared to other games.

If you count cards on a small hand shuffled shoe, even with a basic system it is relatively easy for a player to have a fraction of a percent edge. Good players can have a few percent edges.

However, most casinos nowadays use large shoes and frequently (or even constantly) machine shuffle the cards. This effectively almost completely negate card counting.

Large shoe is actually more advantageous to card counting, and mechanical shuffling doesn't make a difference (but the frequency of shuffling does).

It's perceived the smaller shoes are better since they are easier to county, but with a smaller shoes the count can't swing as far one way or another, so with a large shoes there is a high probability of getting better odds.

The main thing they do is not play through the whole shoe, i.e. they shuffle before they get all the way through. This prevents the count from being allowed to swing as far as possible.

It's not just that, though. They will also shuffle if you substantially increase your bet, or if you're a new player coming in with larger bets. So even if you get a good count you won't be able to exploit it.

Interesting. Counterintuitive but it makes sense.

I think the guy who explained it to me was talking about a combination of counting, pattern recognition and other such strategies, hence my confusion.

I don't see how you're disagreeing with me. I'm positing that HN may be more amenable to games that allow you to employ skill/knowledge to your benefit (racing/poker/blackjack/sports betting) over games that rely entirely on chance (lottery/slots).

> Yet the consensus seems to be the the millions of people buying lotto tickets are all rubes, but the folks flouting the law and running bookmaking operations on the internet are disrupting staid government regulation?

I agree with you, but I also gamble when I go to Vegas. I think when people say lottery players are dumb they are mainly pointing to the 'spend a large percentage of my paycheck each week on the lottery' group. When the jackpot is this big and is dominating pop culture, buying a ticket is just part of being entertained by the whole thing.

With the lottery, you are expected to lose. I would the lottery in the same box as slots, blackjack, and other games where you play against the house. The house will always win. They spend a lot of money making sure the odds are in their favor.

Fantasy sports is more like poker. Yes, it is a game of chance, but it is primarily a game of skill. Maybe most people don't have enough skill to make a difference, but given enough time, it can be acquired and you can have +EV.

Also, in poker and fantasy sports, you don't play against the house. They just take their cut, and you play against other people.

Note, I'm excluding blackjack from skill-based mainly because you are playing against the house, so its by their rules, and if you start winning, they'll kick you out.

A minor quibble with this argument, both in poker and fantasy sports, while you do compete with others, the house also always wins, because of the rake.

TBH, the whole "game of skill" thing (notice how obsessively often this particular phrase pops up) is just a way to sneak fantasy sports through a loophole in anti-gambling laws. For your average Joe, it's indistinguishable from gambling - including all the addiction and collateral damage that causes gambling to be heavily regulated in the first place.

But it is a good game for bored STEM undergrads, just like online poker is a good game for bored computer science undergrads. I had a few guys on my year who lived completely off online poker games while in university. They deployed custom-made scripts to automate playing on multiple tables at the same time, and probably did some other things that they didn't tell me. It's the same thing with fantasy sports, except you spend most of the time maintaining complex spreadsheets.

Recent article posted here in HN shows that fantasy sports are not a game of skill, since a very few people win all the money (millions) and everybody else loses. Because those few have written software to game the leagues. So essentially just a money pit.

What?

If very few people win all the money, it is most definitely a game of skill and not a game of chance,

It's a zero sum game, so the applicability of your skill is relative to the other players. The average bettor understands the mechanics of the bet and has an intuitive understanding of what he is betting on. The 25th percentile bettor is clueless or worse (I like green, go Jets!) and is operating a reverse ATM.

Look at horse racing. At an off-season harness track where the purse is low and horses all suck, the professional handicapper loses a lot of his edge, as you never know when one horse is going to have a great day.

At the Belmont/Preakness/Travers/Kentucky Derby, a pro has a huge edge, as they generally can call the winner with precision -- the pros are betting on the finishing order via exacta bets. The crowd tries to picks the winning horse, and in the event of a win, makes a lousy $0.50 on a $2 bet :)

It's negative-sum, because of the rake.

...or the game is essentially fixed, so that your skill is irrelevant.

I'm curious how you arrive at the conclusion that using software to help you win a game means it's not a game of skill.

That's like the definition of self-contradiction.

Your skill is irrelevant against the automated betting bots.

Only because their skill is much higher than mine. That makes it a game of skill, just one in which the top percent is MUCH better than most.

That's not entirely true.

They game the system by automating lineups that allow them to play multiple games a day.

you end up getting hooked to obsessive watching of ESPN and tracking player stats

For many people it's the other way around. They were already obsessively watching ESPN - fantasy sports betting just gives them an additional reason to do so.

The difference between playing fantasy football and playing the lottery are like the difference between playing an RPG and running an UPDATE script on a database.

In the end, grinding out your characters stats are just running scripts with a nice GUI on top. It's the experience that provides the value, not the result.

The difference between lottery and playing fantasy football is like the difference between betting against a random number generator, and playing Eve Online part-time, respectively. In the former, you lose consistently. In the latter, you lose to people who spend most of the time in Microsoft Excel and are better at it than many a corporate accountant.

The lottery is a government subsidy to bog, established, non-tech-industry, non-startup firms. HN, naturally, dislikes it.

DFS, OTOH, is a quasilegal (at best) industry with new, rapidly scaling, tech-heavy firms.

The fact that both are gambling is really a side issue to how they relate to HN's focus and biases.

So DFS is literally Uber for lottery? That would explain quite a lot about why there's a split on HN between the people who hate it and the people who love it.

> you end up getting hooked to obsessive watching of ESPN and tracking player stats, wasting lots of time.

I kind of thought that was the point. If you just want to win money their are, as you said, lots of easier ways of doing that. But that would be less fun.

That's certainly the reason the major sports leagues have invested in DFS.

That's kind of the point.

If someone without a lot of skills is wasting his money on the lottery and that's bad, why is it ok to bet on college basketball? It's a zero-sum game.

Especially with this new model of "take my money, and sell my eyeballs". Old time bookmakers just took their vig, the corporate version wants you soul too (consume media = buy subscriptions + watch ads).

It's really an insidious business!

as per the top post I think the main issue that people have with the lottery is that it is a stupid/poor tax. Low income and less educated people spend the most on lottery tickets anywhere between 1.5 times to 3.5 times more than those with a higher level of education or a higher income. Notably this spending is also a significantly higher % of their total income than it is for those on middle/higher income levels.

Structurally, this seems similar to thinking that drugs should be legal, but taking drugs is silly.

I think the difference is the fantasy sports betting are small companies whereas lotteries are typically run by the government. There is also the difference in that winning fantasy sports betting is far, far more likely than winning a lottery jackpot.

Seems pretty different to me enough to illicit different reactions.

Is it? I.e. winning small on lottery is not that improbable. It still has negative expected value, and so do fantasy sports. The difference is that winning big in lottery is uniformly unlikely, while winning big in fantasy sports is mostly tied to your Microsoft Excel skills. Which:

a) makes me believe that your assumption that "winning fantasy sports betting is far, far more likely than winning a lottery jackpot" is incorrect, and in fact for an average Joe, the reverse is the case;

b) suggests that the biggest advocates of fantasy sports will be people who believe they're good enough with Excel and statistics.

> Is it? I.e. winning small on lottery is not that improbable.

Yeah I know meant winning the big jackpots not the few dollars here and there many people win.

You are probably biasing the prominence of the voices that disagree with your position.

Most of the comments on this story are pretty straightforward attempts to apply some analysis to the problem (with no real hostility behind them)

If all you want to do is to take a random bet, you can do that with the sports games too... but at least you have the opportunity to increase your odds by doing some research.

Yeah, but to some people all of the things in your second paragraph are FUN - not a waste of time. Pretty condescending attitude man...

And so is most of the gambling. Whether poker, roulette or slot machines, a lot of people would tell you they're doing it for the pleasure.

But in a way, a lot of things are gambling - up to and including investing, particularly in startups. The desirability of a particular form of gambling in society is tied to the negative effects it has on people (e.g. how easy is it for a player to get addicted), and how exploitative the organizations operating a given game are. Under those metrics, fantasy sports are very much like lottery or one-armed bandit, and very much unlike investing.

And hell, it's not just about being condescending to people. I'm perplexed by how people tolerate, and even vocally support companies that intentionally fuck over poor people.

GP wasn't condescending at all but was merely pointing out how it's condescending and hypocritical to look down on people playing the lottery when the attitude is different wrt sports bets.

They are two very different things though. Even the OP acknowledges that's less about the outcome and more about the experience (which is the opposite for lottos).

Cutting right to the more meta part of the discussion, it's just false equivalency constructed that hits both a desire to dump on sports fans and find a way to make an absurdly irresponsible habit practiced mostly by lower income people more palatable.

(all of this is based on an idea from another poster in a different thread, which I cannot find at the moment)

odds of winning: 1 in 292,200,000 (approx)

miles between LA and NYC: 2,800 (approx)

feet in a mile: 5,280

inches in a foot: 12

US dimes in an inch: 1.4 (approx)

2800 miles * 5280 feet * 12 inches * 1.4 dimes = 248,371,200 "dimes" between LA and NYC

Summary:

Assume that someone drove from LA to NYC at stopped at any point of their choosing along the way and threw a dime onto the ground. Starting from LA you drive the same route, you have better odds of stopping your car at the exact spot that that person dropped their dime than you do of winning this Jackpot.

With all the usual caveats about not being evenly distributed. I find this a little easier to explain to people, such that they can reasonably understand that it's not just "unlikely". Stuff like 10 times as likely to be hit by a meteorite or other super rare events just doesn't seem to get the point across as well. It's also easier to break it down into smaller pieces (throw dimes on the ground and have people try to pick the right one, guess a mile marker just in Colorado, etc)

For people who care more about their units:

2800 miles/distance_between_LA_and_New York * 5280 feet/mile * 12 inches/feet * 1.4 dimes/inch = 248,371,200 dimes/distance_between_LA_and_NYC

People go to casino's every day and for every winner there is a looser, and in the middle the house takes a cut. The Lottery is no different except that the pot is a little larger as in the case of Powerball. It is entertainment pure and simple, so if someone spends $200 per year entertaining themselves, I can't see a problem with it. The -odds- are that someone is going to win, and if you don't play at all, it is impossible to win.

I'm all for people having fun. I'm also all for people really understanding their odds. In my experience, 'pick a dime' works better than 'struck by a meteorite' in the limited time I've used the example. It seems that people around me have a harder time grasping the wide gulf between abstract stuff like "struck by lightning" vs "10 times as likely to be struck by a meteorite", and something they can measure/visualize and break down in to pieces.

The driving example is exactly the same as saying "put 250M dimes in a big pot, then pick the exact one randomly". However, restating the problem, in a way that breaks down naturally into individual units that people can grasp, can help prevent it from becoming too abstract.

> The -odds- are that someone is going to win, and if you don't play at all, it is impossible to win.

The odds are that if you play, you're going to lose, and if you don't play at all, it's impossible to lose.

And while it doesn't do to be mean and judgmental towards individuals or even populations who do things like play lotteries, we can make normative judgements. For instance: "enterprises which promise riches while delivering poverty are dystopian, wrong, and practically fraudulent", and "entertaining yourself with dreams of unearned riches runs counter to all the values which will help people achieve real, meaningful value in life, and as such ought not be celebrated."

Right, people spend all sorts of money on silly entertainment, the lottery isn't much different. Now, if you drop your life savings on it, that's a different story.

For the curious, at the current jackpot level, with a cash lump sum payout of $930 million, the expected average return on a $2 ticket is $3.50.

Unfortunately, that's before tax. After tax (45% for estimation purposes, this will vary by state) it's $1.93. After taxes, the lump sum payout would need to be around $970 million for it to average a $2 payout on a $2 ticket.

This doesn't include the possibility of you splitting the money with another winner, but it also doesn't include the additional value of the money if you invested it wisely, etc.

According to [1] the expected average return on a $2 ticket is $1.34. That's accounting for the almost certain chance you'll have to share the prize, the lump sum payout and taxes.

1: http://fivethirtyeight.com/features/billion-dollar-powerball...

> the almost certain chance you'll have to share the prize

What are you basing that on? I don't know what you mean by "almost certain", but to me that phrase means at least 90%, and the chance of two people hitting the powerball jackpot are substantially less.

During the last drawing they estimate that 75% of all possible numbers were chosen. This time there will be even more tickets sold and the possibility of doubling up is probably going to be higher than ever.

Currently, they're projecting 85% of all combinations will have been purchased for this upcoming drawing.

Wow, that drops it more than I would have thought.

There's an estimated 97% chance of a shared prize.

You're misreading. 538 says 97% chance of at least one prize. The EV calculation comes from the Federalist, which doesn't give an exact probability for a shared prize, but reduces the payout by 37% to account for it. This is based on another source, which also doesn't give a probability that I can see. (That probability might not be super helpful - you want the probabilities of one winner, two winners, three winners, etc. At some point it becomes rounding error, but I wouldn't be surprised if you want to go at least to three.)

But 538 guesses twice as many tickets sold as the Federalist does.

An expected loss of 7 cents is not a bad price for the entertainment value of imagining what you'd do if you won big. But never buy more than one ticket...

I can imagine winning without buying any tickets at all! Expected value: indeterminate

My friend Bob says he's waiting for the winning ticket to blow into his hand as he walks down the street. Only microscopically different odds than buying a ticket.

> Only microscopically different odds than buying a ticket.

If that were the case, then approximately one winning ticket would blow into someone's hand every week. Alternatively, literally no one ever would have bought a winning ticket.

(I'm guessing here that nobody has ever won by having the winning ticket blow into their hand. Correct me if I'm wrong.)

Buying a winning ticket is incredibly unlikely, and having the winning ticket blow into your hand is incredibly unlikely. But the difference between these two is very large.

Both are less than one in 100M. Indistinguishable from where I stand.

A handy random statistic from https://what-if.xkcd.com/19/ for anchoring the discussion:

"Astronomer Alan Harris calculates that a person’s lifetime odds of death from a comet or meteorite impact are about 1 in 700,000."

With an estimated 1 billion tickets sold, one should expect splitting the jackpot 2, 3, or 4 ways. Making the expected average return much much worse.

You'd think that, but I get the idea that you're figuring that there's a relatively even distribution of picked numbers across the entire available set.

Historically there's a higher than average representation of numbers 31 and under (birthdays, anniversaries, special events), which means that there are going to be gaps; especially now that the highest possible white number drawn has been increased to 69.

I imagine that there are lots of duplicate tickets out there, for certain number combinations, and lots of (potential) tickets with combinations that haven't been purchased.

That's precisely why you should always let the computer pick your numbers for you - your expected value is (slightly) higher because the odds of a shared jackpot go (slightly) down.

Even better, instead of letting the lottery sales computer pick your numbers let your computer pick them, and filter out combinations that human pickers favor.

Also, once your computer has generated a set of numbers for you only play those once. If you want to play again later roll a new set of numbers.

The reason for this is that if you get into the habit of playing the same numbers every time you play, and you do not play every time, you face the possibility of seeing your numbers win a drawing you did not enter. It could be really annoying to know that you would have won if only you had bought a ticket that week.

No. Don't do that. Sharing a jackpot is still better than not winning. Your EV would drop more by abandoning that part of the probability space than it would drop by the possibility of splitting the pot.

The only valid reason not to use the lottery computer's random picks would be mistrusting its random number generator.

How does a bad random number generator or a smaller probability space change the EV?

The numbers 1-2-3-4-5-6 are just as likely to be the winning numbers as the output of a perfect random number generator. The only remaining variable in the EV is the liklyhood of sharing the winning numbers, and that probability can be reduced by decreasing the probability space in smart ways.

Deleted comment

If I use a ticket generator that always generates the ticket "1 2 3 4 5 6", I've excluded 292201337/292201338 of the probability space, so by your argument I'm lowering my chances from 1 in 292 million to approximately 1 in 85 quadrillion.

You argument applies to any particular ticket, and thus if right would show that the odds of any particular ticket winning are 1 in 85 quadrillion.

Your EV would increase if you removed numbers that are picked more often.

Your chance of winning is still the same but the expected payout is higher because the expected number of identical tickets is lower.

Your chance of winning is not the same if you never pick a number that could be drawn with the winning combination.

If you never pick 7, the winning combination could still have a seven in it. By never picking seven, you are voluntarily abandoning 1/69 of the white balls and 1/26 of the red balls. There are (68 C 4) x 25 + (69 C 5) such combinations out of the (69 C 5) x 26 possible combinations, or 31598138 out of 292201338. You lower your chances of winning in the first place to 89% of normal by avoiding just one number.

What you've actually shown is that someone who bought all possible tickets that do not contain 7 has less chances of winning than someone who bought one each of all possible combinations that do not contain 7 has less chance of winning that someone who bought one each of all possible combinations.

For someone buying a single ticket excluding 7 has no effect at all on their chances that their ticket will win.

Checking the math:

  P(7) = 31598138 / 292201338 ~= 0.108
  P(~7) = 260603200 / 292201338 ~= 0.892
  P(win|7) = 0
  P(win|~7) = 1 / 260603200 ~= 3.84e-9
  
  P(win) = P(win|7) * P(7) + P(win|~7) * P(~7)
         = 0 + 260603200 / 292201338 * 1 / 260603200
         = 1 / 292201338

You are correct, sir. I withdraw my incorrect statement.

Nevertheless, I presume that most of the surge players, who only buy tickets for very high jackpots, will not have favorite numbers, and thus you would only be avoiding splitting the pot with the regulars playing their usual numbers.

If someone plays his birthday every week, but bought an extra 10 tickets for the record jackpot, those extras are likely to be completely random draws. Judging by the increase in the pot from the last draw, there are a lot of people buying more than the usual amount of tickets.

So in the EV calculation, if the amount attributable to not splitting the pot is not greater than the actual value of your time in filling out the form to play specific numbers, you are better off taking the random draw.

Wow! Your comments on the site are usually great, and higher in this thread is the first time I've read something you've written and said "no, that's completely wrong!". Coming to the bottom and finding that you've already done the math to prove yourself wrong is wonderfully enheartening. I hope that I can have the grace and ability to do the same the next time I make a similar mistake.

Your complimentary comment made me slightly uncomfortable, for reasons that I can't quite discern. Rather than allowing myself to pretend it never existed....

Thank you for recognizing in me a quality you would wish to nurture in yourself. It takes some of the sting out of being wrong.

> abandoning that part of the probability space

this is hogwash. ALL numbers are equally likely to come up.

Then thats precisely why you should always pick your own numbers, and specifically choose combos containing numbers above 31. You would get (slightly) better EV than even the RNG-generated ones, because those can include both +/- 31

I prefer quick picks but for a different reason. I used to have a set of favorite numbers, but then I heard a story - urban legend most likely - about someone in Ireland who forgot to play their lucky numbers. Of course, those numbers won that time, so the now distraught Irishman committed suicide.

>but it also doesn't include the additional value of the money if you invested it wisely

I don't understand how this could be brought into the argument at all. Surely we are just speaking about present value of the money and ignoring how it's spent? Money that gets invested instead of spent wasn't different in quantity in any way. Investing the money you spent on the ticket instead of buying the ticket was also a possibility-- presumably we didn't account for that since we called it a $2 ticket.

My instinct is that the increased likelihood of splits with increased prize size keeps the EV from ever crossing over into positive territory, but I haven't done the math.

since you can also invest the $2 wisely, isn't future value irrelevant in this equation?

The key fact here that in fact you cannot invest $2 wisely.

Vanishingly few lotto players buy one ticket (or very few) ever.

As another poster noted, players tend to gamble $100-500 annually (inversely proportional to their income). Investing that can be done wisely (even just leaving it in an interest-bearing bank account gives an assured average net profit).

Sure, probably, but it's also easier to earn more on $200 million than on $2, but then I guess I'm really splitting hairs.

I bought a ticket last night - expected cash value at that time was $969.7mm so it was right at expected average return. It will probably go up more today.

Kidnapping & being held for ransom would be a very real threat for the winner. If someone could plan to kidnap the one of the president's dogs [0], a multi-millionaire and their family is totally plausible as a target.

[0] http://edition.cnn.com/2016/01/08/politics/secret-service-je...

The smart winner would not claim the prize themselves, but instead find a huge law firm to set up a trust and then claim it for them, so no one will know who the winner was.

Also, why would this person be any more of a target than the publicly known shareholders of public companies that have more than a billion?

> Also, why would this person be any more of a target than the publicly known shareholders of public companies that have more than a billion?

Because rich people have (sometimes multi-generational) experience at being rich. They have multiple layers of security that include lawyers, armed guards, armored vehicles. Also, they invest most of their assets in not easily transferable ways.

A jackpot winner is just a middle class joe with a big pile of cash and a target on his back. If you were a lion, wich prey would you pick? The tame cow of the wild buffalo?

I'm not sure if i'm foolishly answering a rhetorical question, illustrating your point or just extending the metaphor too far..

but I would attack the wild buffalo instead of poaching an owned cow and triggering a lion hunt by the local police department.

That would be very valid if you believe the local police department would respond more promptly to a report by an average job, than a case that involves someone the city major goes to golf with every Tuesday.

But still, I consider your comment valuable. The point is not just how much meat/money is there to be had in the prey/jackpot. There are risks, opportunity costs and tradeoff that should be evaluated. Probably nothing extremely complex, but not trivial either.

Winners are required to declare their identity to the lottery commission to claim the prize--but they do not have to agree to have their identity publicized in most states.

Many winners choose not to be publicly identify. As I recall, one of the winners of last years bigger jackpots chose to remain anonymous.

Most states have rules that you have to declare your identity to claim the prize. So no shell corporations, LLCs, law firms, etc. allowed. AFAIK, only Delaware, Kansas, Maryland, North Dakota, Ohio and South Carolina allow you to keep your identity private.

Bill Ford has corporate security protecting him. Mary Barra at GM does too. They probably get whackos coming after them all the time for concealing the existence of the 100 mpg carburetor, etc.

If I took home $500m from the lottery I'd hire a security firm, too. It's not really an option, at that point.

> Most states have rules that you have to declare your identity to claim the prize.

But there are ways around that. You can transfer the ticket to the lawyer and then have a contract that says the lawyer will pay your trust $908 million. Or whatever your $1000/hr lawyer tells you to do. :)

I'm pretty sure Bo wasn't a dognapping target for a ransom:

    Stockert also claimed he was the son
    of John F. Kennedy and Marilyn Monroe
    adding that he had come to the District
    to go to the Capitol to advocate for $99
    per month healthcare and to announce
    that he was running for President.

    After his arrest, Stockert stated he
    was Jesus Christ, and that this could
    be verified on his license.

Does that include the fact that the money is paid out over time, and apply standard discount rates to that future money? Because that makes it even worse.

The $1.5 billion figure is paid out over time. There's also a lump sum option that gives you $930 million right away. That's what the calculations are based on.

I didn't realise the $1.5B was paid out over time. Does anyone know what that period is by chance? Just curious.

i believe it's an annuity paid out over 29 years (payment annually). First payment comes up front.

If you do the TVM calculations, you have probably never seen a lottery payout schedule that works out to have greater current value than the lump sum for any reasonable annual rate of investment returns.

The $1500M is actually a 30-year annuity due with payments of $50M. In order for it to be worth $930M in present value, the assumed rate of return can only be about 3.7%. If you have even a bare inkling that you can invest at a rate better than 3.7%, you should take the lump sum. For reference purposes, the worst historic 30-year rolling rate of return on a S&P500 index fund is 8%, for a period including the entire Great Depression. Mostly, people get at least 10% over that span of time.

Accounting for federal taxes, which I assume to be 39.6% for a sum that large, the lump sum winner takes $930M and keeps $562M. For tax reasons, you arrange for your ordinary annual income from the low-risk investments to be $400k, on which you pay $116k in tax, and spend $284k. So you set aside $13.3M at 3% for this. With the remaining $549M, you invest at an average 10% over 29 years, occasionally paying 15% long-term capital gains tax, to get $5850M.

The annuity winner pays $19.8M in income tax every year, resulting in a net annual payment of $30.2M. If you subtract $284k as expenses, and invest the rest at 10% with occasional 20% long-term capital gains tax (the tax reason from the previous paragraph), you end up with $3390M after 29 years. This is almost 7 years behind the lump sum investor.

Conclusion: take the lump sum payment.

On the other hand, most people who take the lump sum end up declaring bankruptcy after 2-4 years. The annuity at least prevents them from spending it all in one place.

does your EV calculation adjust for subtracting all the minor wins as well ?

Saying the game is a bigger ripoff after odds change without discussing changes to expected values and then going on to say:

> people don't understand odds

Is quite ironic.

As a kid in the 80s I wrote a program in Basic to randomly pick lottery numbers and print them as fast as it could and stop when it matched a predefined number.

Watching the program spin for hours disabused me of any notion that the lottery could be won. It was a good way to get a feel for the ridiculous odds involved and to this day I've never felt tempted to play the lottery.

I also like comparisons to the chances of other things happening as a way to get a feel for the odds, for example you're (apparently) more likely to be killed by a vending machine (1 in 112,000,000), become US president (1 in 10,000,000), or become an astronaut (1 in 12,000,000), than win the powerball.

Of course, just because your program never found the right numbers, doesn't mean it couldn't. People do win...

I'm curious about some of those numbers. In particular, it seems unlikely that one is more likely to become US President than an astronaut given that we have an order of magnitude more astronauts than presidents. Are the populations different?

the chance of becoming POTUS is ridiculous. that chance goes way up if you're a white Christian male lawyer with an Ivy League education, and go way down if you're anything but.

"Dec. 23, 2015: A prominent lottery official who has run the Powerball game since its inception was quietly removed from his 28-year post leading the Multi-State Lottery Association after a jackpot-fixing scandal inside his organization had spread, according to a document obtained by The Associated Press."

http://bigstory.ap.org/article/63f14f1932164832a7f571d0c1b4e...

Certainly interesting timing.

How could they fix it? Aren't the numbers randomly selected using a spinning drum?

I wonder if someone with sufficient access would be able to inject a record of sale of a ticket with the winning numbers and create an authentic ticket stub showing them.

The same group runs many other lottery games besides Powerball.

Wow - they're handling this with kid gloves. No FBI escorting him handcuffed from the building. Just an exit interview about "how they could improve security". He stole millions!

That's because the person fired has not been charged with a crime. Nor does it seem anyone even suspects him of a crime. Strutt, who this article is about, was the executive director of the lottery. Tipton, the security director, has been convicted of fraud. Tipton stole millions. There seems to be no evidence that Strutt stole anything. (If there was, I assume they would have also charged him.)

This is a typical "heads will roll" situation. Strutt was the leader, a serious crime happened during his watch, and he's being replaced because of it.

Ok I see that now. But I wouldn't be so sure nobody suspects him of a crime. His good working buddy for years suddenly has millions of dollars, and he's clueless?

I have no idea what people suspect, but I'm confident in saying the prosecutors don't have enough evidence. I also don't know if Tipton is "his good working buddy for years". There are other possible narratives.

He isn't accused of that, his security director was convicted for the $millions in theft.

It seems like term limits on critical lottery employees would be a good idea, regardless.

No one wants a hoo-haa on these levels.

I think that is demonstrably not true, as the person who committed the fraud has been convicted: http://www.nydailynews.com/news/national/lottery-fixing-scan...

Experts aren't entirely sure why "those who can least afford it play the most," as German sociologists asked in a 2013 paper. The pessimistic, and perhaps condescending, view is that the poor and less-educated don't have the intellectual gifts to appraise the odds, but middle-class and rich people play the lottery too.

This perspective is deeply flawed. If humans obeyed a risk adjusted rate of return strategy and rationally discounted for the future, human behavior across the board would be profoundly different. The lottery is only one example of many.

Any portfolio of early stage startups is destined to perform worse than the S&P500, as is any portfolio of series A startups. As is any portfolio of lottery tickets... but there is always that winning ticket, that Facebook, that Google.

There have been very few big homerun startups. The rest would fail to lift the average above the S&P.

In an environment where the future seems fairly certain (poverty, affluence, whatever) there is lots to be gained by rolling the dice and experiencing a bit of risk. Lotto is less fun than a startup, but it scratches the same itch. It lets you ride the emotional roller coaster and imagine the greatness that will one day be yours.

Startups are a superior version of lotto because you get to be the CEO or the CTO and someone invests their money to help you build a team and get traction, etc. So your bet with destiny is being underwritten by others. You get advisors, board members, and metrics, and essentially spread the thrill of the tumbling balls across however long your runway lasts. The superiority of startups is why young affluent people do them, and why poor people play lotto.

The urge to take on risk is what got humans onto ships, rockets, and bathyspheres. It's the unique human ability to reason probabilistically and take a leap, to undertake a calculated risk, and to engage in an exciting dance with destiny.

For centuries and in pre-enlightenment times, people believed that all of life was fated and that one's lot was destined from birth.

When we appreciate the emotional thrill of risk we start to see that it's part of the glorious awakening of the human sprit birthed in the enlightenment. When a dejected person puts his last quarter into a slot machine, we are not seeing hopelessness, we are seeing hope in its most unfettered form. Even if he loses that person will pick himself up and dust off and be ready to try again, for fate is on his side. This stands in stark contrast with the previous worldview in which the quarter would be saved and a prayer offered up, which has far smaller odds of success than the slot machine.

I think it's more that if your life really sucks you are a lot more likely to try to escape from it (even if the odds of it happening are pretty low), if you have a comfortable middle class lifestyle you can debate pros/cons and odds.

If you are on fire and there are a bunch of extinguishers for sale but only one of them works, you are not going to debate the price/odds, you are going to buy as many as you can afford to

I think the cause and effect are reversed. Having destructive financial habits are going to cause you to have "life that sucks." Whether it's buying too many lotto tickets, smoking, driving buzzed drunk on a regular basis, ect.

I grew up in low class area/family and saw that there is a pretty clear difference between a lower class and middle class mindset.

I think it's reasonable to argue that it's less of an either/or and more of a self-defeating cycle.

Lower class life -> desire to escape -> worse habits -> lower class life

and so on.

I think it has more to do with society being class segregated, and the habits that could raise your class (or raise your chances of getting out anyways) are not the social norms in the lower classes.

Then desire to escape step isn't even necessary.

There's a confirmation bias in that kind of logic, since people who start out poor and work their way into the middle class (or higher) don't "count" any more.

>Any portfolio of early stage startups is destined to perform worse than the S&P500, as is any portfolio of series A startups

Serious question: what's the point of angel investing?

Counterpoint: The true value of a lotto ticket is dreaming about hitting the jackpot. Bigger, less winnable jackpots increase the dream-value of the tickets.

This is true, for many people playing the lottery is a means to attach a nonzero probability (no matter how small) to a fantasy.

For myself, I'm uncertain how much of a fantasy it would really be to suddenly hold ~$1B (though I obviously wouldn't hesitate to try..). But have you ever played a video game, then discover an exploit or cheat code to give you everything you want, then realize how boring and pointless it became relatively soon afterwards?

Part of me wonders if shuffling all the way across Maslow's hierarchy of needs in the real world would have the same psychological effect. I think we crave a certain comfortable level of struggle.

There is some research on this. Assuming you make ~75+k winning the lottery would probably have minimal impact on your long term happiness. Sure, work is a non issue, but you get a whole new set of concerns.

I think that's probably true for most people, but not a given.

`Mo Money Mo Problems` is true if you use your money to buy things, celebrity, social/political status. It's not true if you start an incubator with no expected returns, start a charity, etc.

> But have you ever played a video game, then discover an exploit or cheat code to give you everything you want, then realize how boring and pointless it became relatively soon afterwards?

I don't think that's a great comparison. You've removed the point of the game by cheating, but the point of life isn't "accrue $1 billion".

No doubt, but it's a problem I'm willing to struggle with :)

I think it's part of the worry people have had for ages and ages: what do you do idle? Do you find things to do? Or just stop doing things? Or do you create and/or learn a skill? Do you work harder to leverage it all for power?

Well, do you have hobbies? Interests? Things that you think about wanted to do when you're at work? Things you have to stop doing because gosh darnit you need to get up for work tomorrow even though you'd rather carry on until morning? If you have those, then why not do them more?

All those things you enjoy and do without question or thought, or wanted to try, those are the things that you do.

Yup. I suspect I (with likely a large number of people who tend to sites like this) would have no problem filling our time well. And for those that don't, I'd bet a good number of them could learn to :)

> I think we crave a certain comfortable level of struggle.

For years, my greatest fear has been to win the lottery because of that reason exactly. I don't know what I would do with my life. And it would cause all sorts of stress among friends, family members and potentially strangers.

Regardless, I still bought a ticket.

If possible I'd claim it in secret. I've heard that you can create a trust to do so but I'm not sure if there's truth to that or not. I'm also not sure how I'd be able to secretly help friends and family so it may be moot or just a temporary measure.

http://www.forbes.com/sites/deborahljacobs/2012/02/11/10-thi... Looks some good first steps.

But real life has an infinite amount of unlockable content.

> for many people playing the lottery is a means to attach a nonzero probability (no matter how small) to a fantasy

Probably the same reason people found startups.

Exactly. I'll buy a ticket on my way home because it'll be a fun game for $2. I think this will be my third or fourth ticket I've ever purchased. I know I will not win, but it is still exciting. It is the same reason I play craps when I go to Las Vegas - entertainment.

Totally agree.

Calling the game a ripoff is unfair. Ripoff is a deception, yet Powerball is completely honest about its mechanism.

Participants understand that they are playing a game with a low chance of winning, but they do get a lot of value out of the ticket. Otherwise, with so much information available, why would they play?

If we worry about participants not being able to "understand" these sorts of large odds, we might be better off worrying over much graver yet common situations. Do we understand the price of not paying attention in elementary school math class? The pitfalls of not having various kinds of insurance? Or even driving on the freeway?

> Participants understand that they are playing a game with a low chance of winning

I see poor people lined up at my local convenient store, spending considerable amounts of their money on scratch offs and lottery tickets. They actually don't understand or are addicted, and the gov doesn't care, so long as they're getting money out of it. Who's going to regulate the regulators? It's not like the State limits how many you can buy.

Are we assuming we should care? Yes, the behavior is not in their best interest by the metrics we use, but if they are adults who are fully consenting to the transaction, and they are not be lied to, should the government care?

If the government should stay out of the bedroom of consenting adults, why not stay out of their wallets as well?

That's all good in theory, but then what do we do when we have people suffering because they spent all their resources on this ridiculous "game"? I'll tell you right now the answer won't end up being "let them wallow in the steets". It ends up just being wildly inefficient. If we care enough to help these people after they are down on their luck, metaphorically and literally, then we should just cut out the middle man and stop having it as an option to waste money on. Alternatively we could stop changing the lottery so it's less efficient at extracting money from people and is closer to a random chance wealth redistribution.

I agree, but the government is already in our wallets via taxes used for social programs to help the poor. I happen to disagree with these programs, but here we are. We abdicate to the State with the idea that they're going to help the poor, not take advantage of them. Lottery tickets exploit the poor, so I'm left with the notion that the State is more concerned with its bottom line than helping the poor.

Why do you say they either don't understand or are addicted? Have you asked them, or are you just assuming that there's no possible alternative? And are you sure that the money would be better spent if it couldn't be spent on lottery tickets?

I'm pointing out the hypocrisy in government, how they crack down on illegal gambling because of its vice, yet exploit the poor with State endorsed gambling.

What are the alternatives? I'm sure they enjoy it, but that's part of addiction -- not being able to delay pleasure in the present for future rewards. They could save their money, buy new clothes, get some dental work done, etc. I'm not saying we force them or that we should deny people ostensibly-wasteful pleasures--a drink is fine every now and then, but when someone goes over the edge into full-blown alcoholism, I think society should extend a helping hand.

Counterpoint(s) to this theory: http://lesswrong.com/lw/hl/lotteries_a_waste_of_hope/ and http://lesswrong.com/lw/hm/new_improved_lottery/

Care of ikeboy on the lottery simulator thread.

https://news.ycombinator.com/item?id=10868702

The new American dream now that social mobility is demonstrably low.

"Never tell me the odds!" -Han Solo

Odds are you're about 10x more likely to die while driving to buy the ticket than you are of picking a winning one.

They did this so that the lottery overall was less of a regressive tax on the poor. It's not a rip-off at all, it's actually much fairer. We desperately need something similar with our tax code as a whole.

That may be the result, but that is not why they did it. If you read the article, they did it because sales were down and altering the odds so as to end up with some crazy high jackpot was a known way to get sales back up.

What do you mean?

My guess is that as the pot increases people of a higher income get interested. I can see an argument that if the pot increases from $1M to $10M in likelihood of someone that makes $100k/y buys a ticket will increase by more than 10 times while someone that makes $10k/y wont. Part of it is the hype and part the impact to your life being large enough to override reason.

It would be interesting to see if there are any studies that show that trend and where it cuts off.

I think the GP means that odds of getting a small win -- i.e. $4 -- went up and odds of winning big went down. So you are more likely to get your money back in small wins. Since poor people play more, they are disproportionately likely to benefit from the increase in small wins, thereby defraying their costs a bit.

How on earth have they arrived at odds which aren't an integer result for a lottery? http://www.trbimg.com/img-56954025/turbine/la-fi-mh-powerbal...

Not only do you have match n numbers, you must also not match n+1, n+2, etc., otherwise you win a different prize.

> Experts aren't entirely sure why "those who can least afford it play the most,

Is this that irrational?

With 1000 trials, probability of winning at least one time is 3*10^-6 which is low.

But what are the odds of becoming a billionaire given that your annual income is below $10,000?

Assuming that one's goal is to become a billionaire, maybe Powerball is rational for people with low incomes. But is that a rational goal to have? Wouldn't a person be better off prioritizing more modest improvements to one's finances through other strategies with a high probability of success?

That being said, not everything in life must be rational. If there are people out there who get a lot out of dreaming of becoming a billionaire and playing Powerball, I have no problem with it.

But I do have a problem with governments praying on these aspirations to raise money.

> But what are the odds of becoming a billionaire given that your annual income is below $10,000?

Much much worse when you're spending all your money on lotto tickets.

Its probably not a good idea to try to become a billionare. A millionare is within the realm of possibility, especially if you set your expectations to produce a millionare in your family over the next generation.

By the way, as of Wednesday morning, Powerball reports "only" 85% of all number combinations have been sold.

So still a 15% chance no-one wins.

I spent almost 300k in that simulator and only won ~7k. I thought I'd hit big. I still put up 2 bucks for tonight though :(

Anyway, the cheeky FAQ on the PowerBall site is worth money down the drain http://www.powerball.com/pb_contact.asp#odds

Off-topic question:

Here's a past (yesterday's) submission: https://news.ycombinator.com/item?id=10891465

Linked URLs are identical, so how did it pass the 'previously submitted' filter?

This is interesting because the UK lottery made a very similar change, with the same effect - higher odds of winning any prize, lower odds of winning. They also doubled the entry price to £2.

They changed the numbers to choose from 1-49 to 1-59, and added a prize for matching any 2 (apparently 1 in 10.3 odds) of a free lucky dip (ie another play).

It'd be interesting to know the distribution of people's picks now - I know that my parents use the same numbers they always have, all in the 1-49 range. Obviously lucky dips are more fair, I'm not sure which is more common though.

It's mentioned that some states were looking at dropping Powerball because the jackpots were won too often and didn't grow big enough to generate excitement. Maybe this points to the fact that people are playing -- and paying -- for the excitement? After all, if your goal was to actually win the jackpot, it seems like you'd be one of the ones playing every week. But there obviously weren't enough of those people to keep the game going.

There will likely be a winner, or multiple winners today. If not, it'll be +EV to play in the next drawing, and might be already.

It's $2 * 292M, $584M minimum payout, for the odds to be in your favor. Expected payout is now up to $930 * (1 - 0.395), so $562M after federal taxes. Depends on state taxes, and if the estimate is a little low, only about $20M short this morning.

While it's technically +EV numerically, it's not really +EV functionally, due to the high variance / extremely low odds and the value of a dollar when you have none vs the value of a dollar when you have half a billion.

At +EV, it would mean, if I put in $60,000, I would expect to get more than $60,000 back, and on average that's correct, though odds are still that the $60k will go to waste.

Furthermore, after the first $100 million, the next $100 million isn't really going to change much in utility, and each dollar becomes worth less as you go further out, so at odds of 1 in 200m, it doesn't really pay off unless you already have the $200m to place the bet. When you take into account that the pot might get split with multiple winners, that's a massive risk you take.

I don't think this is really viable until you have odds of 1 in 5 or 10 million with +EV, but at that point, you've got multiple people, hedge funds, etc, that can get together and buy the winnings.

It's never positive EV, once you account for taxes and the odds of multiple winners.

It may, of course, have positive utility.

Ah, the split. Yeah. seems like the jackpot went up $400M, so i'll guess around that many tickets sold. each number has been sold around 1.4 times, blowing the odds.

The ticket price is $2, so there's more room than you think.

Some lottery setups do go to positive EV when the prizes get really large, and I expect that even the powerball would if nobody wins today.

For example, the Canadian 6/49 goes to positive EV at around $40M. But Canada has higher payout ratio, no taxes and no lump sum silliness.

Some do, usually because of some structure in the secondary prizes. In Powerball, the top prize is basically everything, and the likelihood of a split jackpot increases very fast as the jackpot grows.

It has nothing to do with the secondary prizes, at least for Canadian 6/49. Most of those are fixed value, so are a increasingly small ratio of total payout as the jackpot goes up.

It's because of those people who bought tickets in the many preceding weeks when there wasn't any winners. Those tickets are contributing to the jackpot, but have exactly 0% chance of winning, increasing the odds of the tickets for the current week.

If someone finally wins, the best part will be a temporary moratorium on people who think themselves clever telling me how I won't win. Yes, the odds are clearly published and I can do basic math, but I bought a few tickets anyway. Now shut up about it. Even NPR isn't immune, as evidenced while I listened on the ride to work yesterday. YES, I KNOW!

So why didn't they decrease the odds even further? The change of a factor of two or so doesn't seem like much and I don't see a real downside until it actually gets to the point where everyone 'knows' that winning is actually impossible since no one does it.

Larger jackpots will sell more tickets. When half the country is buying tickets for a historic jackpot, Powerball (and therefore the States) will take in much more money than if this same jackpot was split over several drawings.

Personally, I see the lottery as an opt-in tax on hope geared towards the poor.

I've always thought of it as a tax on people who are bad at math.

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