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Statistician Cracks Code For Lottery Tickets
Hugh Pickens writes writes "Lottery Post has an interesting story about Mohan Srivastava, an MIT educated statistician who became intrigued by a particular type of scratch-off lottery ticket called an extended-play game — sometimes referred to as a baited hook — that has a tic-tac-toe grid of visible numbers that looks like a miniature spreadsheet. Srivastava discovered a defect in the game: The visible numbers turned out to reveal essential information about the digits hidden under the latex coating. Nothing needed to be scratched off — the ticket could be cracked if you figured out the secret code. Srivastava's fundamental insight was that the apparent randomness of the scratch ticket was just a facade, a mathematical lie because the software that generates the tickets has to precisely control the number of winners while still appearing random. 'It wasn't that hard,' says Srivastava. 'I do the same kind of math all day long.'"
"Lottery Post has an interesting story about Mohan Srivastava, a *millionaire* MIT educated statistician" Fixed that for you
This just in, MIT-educated statistician Mohan Srivastava has retired suddenly at a young age and is not taking questions.
This is a hacked account, for which the owner can not be held responsible.
Now that's *sunglasses* the ticket.
YEAAAAAAAAAAAAAAAAAAAAAH!
my wife used to play these and i would take them to the store to redeem the winners. the people behind the counter never looked at the results scatched off. they just scanned the UPC code on the back into the lottery machine and it told them if it was a winner or not
Lotteries are a tax on people who are bad at math. And people who are very good at math.
I used to work in a convenience store, and one of the employees told me of a a trick that I didn't believe until I saw it in action: simply find a winning ticket (~1 of 3) and taking every third in sequence (they all had serial numbers; adjust occasionally for non-winning tickets). No, it wasn't perfect, but I watched more than once as he quite legally turned a profit with scratch tickets: one of those "no f-ing way" moments, but in draw out over 5-10 minutes.
When was the last time you were allowed to look through and then pick the scratch off tickets you wanted from a spindle of tickets behind the counter.
While the game is flawed, there is no real way to get only the winners.
This was in Wired Magazine earlier last month.
http://www.wired.com/magazine/2011/01/ff_lottery/all/1
The same article appeared in Feb 2011 issue of Wired even though Lottery Post doesn't seem to go out of its way to attribute the author and cite the issue properly.
This is nothing special... This information is told to many people that cash in lottery tickets in order to verify that they are legitimate. Obviously it is a well established fact that the codes are not random, they are in fact a mathematical formula that ensures that the state who issues the ticket will ultimately make money. Plus this information is still not helpful to figure out how to "beat" the lottery. Yes, you could discover if it is a winner or not without scratching but you can't pick and choose lottery tickets. I wish I had published these discoveries when I turned 18 and figured this stuff out for myself. Good work for going to MIT though.
FYI, I think this is a Wired story by Jonah Lehrer:
http://www.wired.com/magazine/2011/01/ff_lottery/all/1
If so, please modify the post to direct traffic where it ought to go.
Cheers!
They must be dumbing the explanation down. You don't have to be non-random to control the number of winners. You can use a deterministic process to generate all the tickets in a series, and then a true random process to control the order in which the tickets are printed. If they're not doing that, they're really screwing up. Even a fairly dinky computer should be able to store patterns for all the tickets in a Big F'n Array, and use real random numbers to shuffle the Array. Then hit "print".
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
Who's there?
Lottery Commission.
DOH!
lawsuit coming in, 5, 4, 3 ....
After calculating that his average winnings would come out to $600 a day:
"People often assume that I must be some extremely moral person because I didn't take advantage of the lottery," he says. "I can assure you that that's not the case. I'd simply done the math and concluded that beating the game wasn't worth my time."
Moral of the story for those who play the lotto: Even if you figure out how to break the game, it still isn't worth playing.
I read this a week or so ago in Wired Magazine. /. really needs to get better about getting articles out when they happen...
"To prevent this day from getting any worse, I'll just read ERROR as GOOD THING" 1GJU8xLuDKDxEs4KLf8fAGyptoDsqvEsBT
Android App in 3 2 1.
I think the issue is that there is in a lot of these tickets there is visible data and hidden data and you win if they match up somehow. Apparently for a lot of these tickets, the process used to generate the tickets is biased in that certain visible data was highly correlated with a ticket being a winner. This is not surprising, as generating random sequences of anything is hard, and I would imagine it is even harder when you want a random sequence of pairs (visible data and hidden data) that meet certain conditions with a given probability distribution so that the correlation of (any type of visible data pattern) to (any type of hidden data pattern) is tiny. The surprising bit in the specific case in the article is that the visible data pattern giving the high correlation, the presence of singletons, was relatively easy to spot.
The problem is that he reverse engineered their deterministic process for generating winners and losers and then was able to pick out the winning cards based on the partial information they revealed. The order in which they are printed doesn't really matter. Given any random subset of the cards he could pick the winners out of them at a much higher % than he should have been able to if they were actually random.
Sounds to me like they should figure the game out in such a way that a real random number generator will generate winners and losers at the desired rates on average and then just rely on the law of averages / large numbers to give them their desired take.
Here's the link to an article about this in Wired. A very interesting read.
http://www.wired.com/magazine/2011/01/ff_lottery/all/1
- Joenonymous Howard
The problem is that he reverse engineered their deterministic process for generating winners and losers and then was able to pick out the winning cards based on the partial information they revealed. The order in which they are printed doesn't really matter. Given any random subset of the cards he could pick the winners out of them at a much higher % than he should have been able to if they were actually random.
... :(
Sounds to me like they should figure the game out in such a way that a real random number generator will generate winners and losers at the desired rates on average and then just rely on the law of averages / large numbers to give them their desired take.
Forgot to login, sorry for the dup
TFA on Lottery Post was plagiarised from Wired.
Original story: http://www.wired.com/magazine/2011/01/ff_lottery/all/1
You can use a deterministic process to generate all the tickets in a series
If you started at the time of the big bang, such a process wouldn't have finished yet.
Even a fairly dinky computer should be able to store patterns for all the tickets in a Big F'n Array
Ha ha.
Because I am calling you from my boat, BITCH!
Even still. In the tic-tac-toe game, it seems like you should be able to generate a set N of truly random tickets, and then randomly select exactly M of them to be winners by choosing the hidden numbers after you've picked which tickets should win and which should lose? The only quirk would be having to validate each loser to verify that you don't accidentally make a winner, but that should be sufficiently rare to not through a wrench into the plan.
They are scratch off tickets, not drawing tickets. So each round of each game (the different games are just different gimmicks, for marketing) has a fixed number of tickets and a fixed number of winning tickets, and both those numbers are 'small'.
Nerd rage is the funniest rage.
I read the Wired article; the amazing thing is he did this with sample size of two.
I think you hit on the problem he found; if it was truly randomized (ie. just order), there'd be far more winners than they actually have. This means the set of cards that are likely to win are underrepresented. If there is a pattern they have in common, then you simply need to look for it. This guy figured out that winning tickets are likely to have a high frequency of singleton numbers and chose those.
Surely they just need to hide both sets of numbers so that they can't be seen before you buy? Then in order to play you have to scratch off both sets of numbers?
The problem isn't the order of the tickets, its that the tickets have visible info on them that gives away the hidden info. Of course, you're still right that you don't need to be non-random to control the number of winners. Just use a true random process to generate the tickets, and a separate process to analyze the tickets created and hold back any winning tickets once you pass a certain quota (and re-introduce them to the stream at a random point if you fall too far below quota).
The North American lottery system is a $70 billion-a-year business, an industry bigger than movie tickets, music, and porn combined.
Wow... that IS big!
lotto and big slot wins are tax-free within Canada
How do you tell the difference between an MIT mathematician and a smart MIT mathematician? One talks to the media, the other is a millionaire.
If you'd read the fine article, you'd have seen that he calculated how much he'd earn by using his system and how long it would take - and found that it was far lower than his consulting pay rate. So if he spent time doing it rather than his day job he'd be taking a pay cut.
Sounds to me like a GOOD mathematician - one who applies math to ALL the aspects of the problem and comes to the right conclusion.
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
Numb3rs was a tv series that focused on the FBI solving crimes with the help of a mathematician. One of the episodes centered around a plot very similar to this.
A person who worked with the state lottery commission tried to and succeeded in cracking the code for one of the scratch off tickets. However, they never cashed in the small winners. The end goal was to find and cash in a ticket worth 10 million. It seemed like one of the more farfetched ideas until i read about this
the vast majority of tickets are purchased by about 20 percent of the population. These high-frequency players tend to be poor and uneducated, which is why critics refer to lotteries as a regressive tax.
And yet a Massachusetts auditor for the lottery says of people gaming the lottery system:
The problem is that when there's a lot of money involved, unscrupulous people are always going to be looking for new ways to game the system, or worse.
Exactly. So why don't I feel sorry for them?
For years I've said the the lottery is a tax on those who don't know math. Now I realized that it's a boon to those really know their math.
"Love is a familiar; Love is a devil: there is no evil angel but Love." --William Shakespeare ('Love's Labors Lost')
it could have broken relationships.
I work for another provincial lottery in information security and one of my colleagues met this guy following OLG's tic tac toe incident in 2003. There was indeed a problem with that game. That game was entirely created by the OLG and printed without further analysis according to OLG's own specifications. The printing companies usually create the logic behind a lottery ticket. It's not a mistake that they would do. The guy later got a contract for a year by the OLG and given full access to other ticket's printing specs. He was never able to find a flaw with another scratch game...
There are people who say that Claude Shannon, of 'Shannon's Equation' fame, made more money by winning lotteries using his statistical knowledge that in his day job as inventor of information theories. Maybe the key is to keeping it quiet?
They are probably doing exactly the sort of thing you suggest, and it turned out to be highly correlated to winners instead of "should be sufficiently rare".
One problem is that saying "should be sufficiently rare" isn't an analysis: it's a guess based on your personal expectations. "This system is so complex it must be equal to random" has never worked out well for cryptography, either. The lottery algorithms really need to be vetted by experts.
John
A real geek would have built an iPhone app and let it do the work for him... or her.
The eternal struggle of good vs. evil begins within one's self.
Sure. So that's why they use algoritms for generating winning and losing tickets. The GPs suggestion of generating all possible permutations and then picking winning and losing tickets from that selection is impossible, at least for the ticket design discussed in the article.
After playing quite a few of these games, I have seen this pattern too. I can look at a ticket (I'm a fan of the crossword game), and look for the less-common letters, and know basically whether or not I stand a good chance of winning. The problem here though - let's say I buy 5 tickets and don't scratch them because they all appear to be losers. What gas station have you been to that will take them back, or exchange for other tickets? None. You're buying the next 5 tickets off the roll. So what if you know that 1 out of the 5 has a really good shot at winning - you already paid for the other 4 and lost.
I had to do the same thing for a bingo game. (5x5 grid). However in this case it was a for a short-term game (One night)
Basically I just chose the numbers that would win, created all the possible permutations of winning numbers (12345,13245 etc.) for each axis (up, down, diagonals) then, from that array, randomly selected winners until I got the desired number of winning cards.
Fill in the blank numbers for the cart then randomly created the losing tickets and make sure that none of the lines match a winning line from the original winner array.
It worked for me. sure, there might be some collisions which means I have to regenerate the ticket again but with 10,000 winners are a HUGE number of possible losers it didn't exactly increase the generation time by anything noticeable.
The real humor from TFA comes from reading the comments that follow it. A quick read through tells you that the lottery commission has nothing to fear.
If I were him, I might have gone down to the local soup kitchen and told a couple homeless people about it, and given them each a few tickets to demonstrate it. That community could have benefited for a few weeks or months before the lotto figured it out.
Well, it is somewhat reasonable to infer that the O.P. meant enough permutations for the game, not all the possible permutations.
Nerd rage is the funniest rage.
When I said "series", I meant "series of tickets" as in "series of games to determine who is the champion of baseball". In the case of the former, the number is at most 7. In any case, the word "series" does not, to me, imply astronomical numbers.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
1. Notice non-random numbering on lottery tickets
2. Research lottery tickets and crack the code to money
3. Call press conference
Don't we all know what step 3 should be?
-Matt
--- Need web hosting?
The trick is stringing people along so that they'll keep buying as they try and chase a winner. $2 here, $10 there, the small winners are spread throughout the book fairly evenly with the hope that people will come back and rather than collect their winnings, buy more tickets.
After reading TFA (it was actually quite interesting) I think you hit the nail on the head. The scratch-off material was opaque; but the singletons leaked data past the physical barrier.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
So I can make a web page full of Mickey Mouse cartoons and stuff? And it's all ok if I say "Copyright by Disney" way down at the bottom of it? I don't need to ask permission or anything? Wow, that's great! Thanks for the info!
You sir are poor at Math.
Actually $150K puts you in the top 15% of US income and $215K puts you in a group numbering less than 7% of US households. Everywhere, but especially in the US, people like to think they are richer than they are and that their potential to be rich is greater than it is. This is why so many Americans vote against their class interests - they all think they might one day be millionaires so they don't want an estate tax for when that happens, and they think they won't get sick and old like everyone else.
Stupidity is its own reward.
I meant to cite this table:
http://en.wikipedia.org/wiki/Household_income_in_the_United_States#Household_income_in_the_U.S.
Stupidity is its own reward.
From my read of TFA, it looks like they didn't generate random boards and then picked winners, but generated winning board/hidden tickets and losing board/hidden tickets from different distributions, yielding the easy crack.
If you generate all random boards with a full set of 72 symbols (to guarantee no repeats on a ticket), then you can uniquely identify a winning streak anywhere on the board and write it in the hidden spaces. I'll buy that my guess about sufficient rarity with a reduced set of 39 symbols may be BS, but I don't think they were trying to do what I suggested.
heh "...mathematicians... can be as petty as anyone"
Reminds me of some recent news along those lines.
This issue is a bit more complicated than you think.
Yet again, Slashdot links to some parastic site that copied the original story rather than the source: http://www.wired.com/magazine/2011/01/ff_lottery/all/1.
Sounds to me like they should figure the game out in such a way that a real random number generator will generate winners and losers at the desired rates on average and then just rely on the law of averages / large numbers to give them their desired take. (
The companies that print the lottery tickets would love to - but in most Canadian provinces at least, this is expressly forbidden. The payout must be guaranteed, not theoretical - and the people who write the laws are not generally the people who know anything about statistics/probability/mathematics, so it wouldn't do much good to explain the math works out in the end. Also, the kind of tickets he broke is a very specific type - games where some info is revealed (think a crossword puzzle where you have some letters already). So the really easy solution is to not have these types of tickets, and only sell "blind" lottery tickets - where it's all scratchable area.
He's a consultant. The first thing I though reading this article was that he's fishing for customers. Why break the lotto for $600 a day when you can get yourself hired by the lotto companies to check their work by showing them how weak their current auditors are?
"You saved 1968." - Ms. Valerie Pringle to the crew of Apollo 8
600$ a day, 5 open day a week, that's 12000 to 15000 a month. Maybe that guy earn more than that per month, and maybe on slashdot this is the median salary (I doubt it) but for most of the people 12K to 15K a month is enormous. Try telling the same sentence "not worth playing for 600$ a month" to your average person. Most of the people I know earn arround 2000 (low end) to 4000 $ a month... And I earn before tax about 10000$ (I don#t even want to mention what's after tax).
C. Sagan : A demon haunted world:
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visit randi.org
People who are bad at math play the lottery badly, people who are good at math avoid the lottery, and people who are really good at math figure out how to play the lottery intelligently. :)
I listen to both RIAA and non-RIAA stuff if I like the music, tangential business/politics nonwithstanding.
Trying to figure out where to stop or keep going in the first place (when there's a lower or higher expected value for the next ticket) is a problem, and so is a lack of fine-grained control over when to stop or keep going. Having to buy the tickets off the stack in sequence helps lead to the latter problem. However, buying my tickets one-by-one helps. (I bring a large stack of $1s with me to the Lotto retailer to help enable this logistically.)
I too have figured that the scratchoffs aren't truly random independent trials because they have to be machine-printed en masse, and for regulation and/or business reasons, it may make sense to ensure that the prizes aren't clumped.
The whole idea is to find ways to increase your odds; some games and play options may give you better odds to begin with in addition to whatever advantage gained through your stratagem. Check your local listings. :)
I listen to both RIAA and non-RIAA stuff if I like the music, tangential business/politics nonwithstanding.
A typical assignment for Srivastava goes like this: A mining company has multiple samples from a potential gold mine. Each sample gives a different estimate of the amount of mineral underground. "My job is to make sense of those results," he says. "The numbers might seem random, as if the gold has just been scattered, but they're actually not random at all. There are fundamental geologic forces that created those numbers. If I know the forces, I can decipher the samples. I can figure out how much gold is underground."
Given that his day job could easily be replaced with a 3-D plotting program.
Also wouldn't you be putting a geologist in his position rather than a statistician?
Charged with what exactly?
OK, so one brain hasn't punched out.
At a casino, you get busted for counting cards because it's essentially a private facility and they are free to enforce house rules.
The retailers are bound by retail agreements. Sifting before you sell would get you into serious hot water.
In some games of chance, large winnings are taxable, so you can get into big hot water by failing to report your earnings.
In this scenario, had he taken that path: he's not entering the premises of a lottery corporation, he's not conspiring with retailers to break the retail process, and (from what others have said) the winnings from these tickets in Ontario are not taxable.
Changed with what exactly? Charged with bogus charges that don't stick, most likely, just to uphold the common sentiment that winning at games for losers is unethical.
Thankfully, I haven't been charged when making winning picks on the stock exchange. It's not actually illegal to use a formula which gives you an edge, only if the information required is insider information.
Speaking of brains on dialtone, I have it on good authority from Michael E. Mann that geological statisticians from Ontario don't know their sigma from a shaft in the dirt.
Fortunately, no lotto ticket designers were terminated with cause, and no peer reviewed studies (where peer is defined as people as bad at stats as you are) were formally repealed as a result of these crackpots.
Now all we need is an iPhone app that uses the camera to find winning tickets...
Should have put together a team, ala the earlier MIT group with the Black Jack system.
As long as you're sure the visible data is fully random you can tailor the invisible data as much as you want and generate deterministic winners or losers anyway. Any algorithm where the visible data cannot, in some cases, be turned into a 'winner' or 'loser' by tailoring the desired hidden content gives away the same knowledge to any observer and is automatically flawed.
Dispense the cards in a way where you cannot cherry pick.
Oh, and just a heads up for everybody... turn off javascript in your browser before going to the website with the article. I don't know what it's doing, but it hangs Chrome something terrible.
File under 'M' for 'Manic ranting'
That's one of the reasons some contests have a "If you're an employee of..." clauses in the terms.
So the really easy solution is to not have these types of tickets, and only sell "blind" lottery tickets - where it's all scratchable area.
You're assuming that (1) the lottery organisers care -- they don't, they're spending the same on prizes whichever way the prizes are won -- and (2) that the partial information tickets don't sell significantly better than blind ones (I don't know whether this is the case or not, but I suspect they actually do). So that may be an easy solution but as it solves a problem that they don't care about, probably at a significant expense, it isn't going to happen. They'll carry on churning out these tickets, and gullible schmucks will keep buying them randomly, while people who know will watch for ones that are guaranteed wins.
The problem is that he reverse engineered their deterministic process for generating winners and losers and then was able to pick out the winning cards based on the partial information they revealed.
The problem is that the lottery people didn't hire the right statistician.
This dude out-thunk a bunch of municipal employees.
Ah, so you think the problem is not with the particular numbers on the tickets, but with the order of printing of those tickets. But in the article that's not the case. He knows whether a ticket is a winner or loser by looking at the ticket, not by the sequence of the tickets.
Back in (Greek) Junior High we went for a one-day school trip to an island (Poros IIRC). The day plan consistend of letting a few dozens of 14-15 year-olds roam around the town unattended. Obviously, one of my group's first stops was at an Arcade, to spend some coins on things like Cadillacs and Dinosaurs or NBA Jam. Another group of friends called us to a back room to check something out. There was an electronic (electromechanic?) gambling machine that had a roullette (but with fewer segments than the classic) and you could bet on outcomes. I hadn't seen such a machine since my usual Arcades in the city were just, well, Arcades, so I was intrigued and stood by to watch some of my friends play. Born a geek, even before any formal statistics training, I started analyzing the game and the betting possibilities and I soon realized that - woops - the designers allowed for multiple bets per cycle, but had not calculated the combined odds properly, so there was a combination of bets that would give the player an advantage. So I told my friends to stop betting randomly and I showed them a winning strategy that would give them on average something like a quarter (the equivalent 20 or 50 drachma coin that arcades accepted back then) for every 4 or so (don't remember specifics) plays. After explaining, I oversaw a few rounds and then left. Yes, money was useful for me as well, but I had calculated the expected payout and judged that I had stayed enough at the arcade, so spending the rest of the day outside (and finding a good restaurant) was worth more for me than that amount.
Sure enough, after several hours, we all met back at the boat. The 3-4 kids that had stayed at the arcade had each made around 2-3k drachma (I guess something like $20 of early 90's USD), which was not insubstantial for us back then (since I remember I felt about 20% regret for not staying myself, given the fact that I had not found such a great restaurant - hehe).
Anyway, the moral of the story is that gambling games are not usually designed by PhD's, although I would have expected at least big lotteries like those in TFA to be designed by groups of excellent statisticians. And also that winning a gambling game is not always worth your time.
Violence is the last refuge of the incompetent. Polar Scope Align for iOS
so the lotteries predetermined 'random number generator' for the actual scratched off space, and a closer to random number generator for the numbers on the outside? sounds like a simple fix yes?
Having actual experience with how lottery works behind the scenes I'd say this particular place was not run by people who knew what they were doing. You can't be so stupid to print something that is correlated to the outcome. This is something that would need statistical evaluation beforehand. Anyways, the way around it is to print independent serial numbers from a totally different random sequence or some strong crypto hash based on this other independent sequence. You can use these independent codes if your sales places are online so that a server can check ticket outcomes stored in a database. One would still want to test for proper stats before the series gets printed.
"Lots of people buy lottery tickets in bulk to give away as prizes for contests," he says. He asked several Toronto retailers if they would object to him buying tickets and then exchanging the unused, unscratched tickets. "Everybody said that would be totally fine. Nobody was even a tiny bit suspicious," he says. "Why not? Because they all assumed the games are unbreakable.
Step 2) Take all the scratched tickets that people throw away onsite, and scan them for hints as to how to pick winners.
By virtue of having already been scratched, the information needed to find the pattern of winners has been removed. What you would need to do is buy a few tickets, photograph the unscratched surface, scratch the tickets, and then go back to the reference photos of the known winners and try to find a pattern.
Now if you'll excuse me, I have an erection to attend to.
Just completely wild-assed guessing here, but I'm wondering if they developed just one algorithm to "fill in the blanks with interesting but guaranteed non-winning numbers". The algorithm looks at the starting condition of the board, selects random numbers that do not correlate with any values already on the board to ensure they don't create extra winners, then fills in the blank spots. TFA's statistician guessed that this algorithm seeds the cards with several two-in-a-row kinds of things in order to make it more exciting. So I'm suspecting that because they want all cards to be equally intriguing to the buyers, they start with the winning sequence of numbers, then run that same algorithm to fill in the rest of the digits. Very non-random, and he spotted it.
I think their problem is in their whole approach to preventing "extra" winners. They appear to be taking the safest route to guarantee that only known winning cards are produced by completely avoiding the winning numbers in the random fill-in data. If they instead reused all numbers (including winners) to fill in the empty spaces, and added a final one-winner-only check (discarding any game card with winners other than the intentional winners) they might be able to avoid this problem. But again, that's a "might". Study would be needed before I'd run down there and say "here's a statistically random algorithm to generate interesting game cards."
Actually, it being a lottery, a whole pile of cash would be needed before I'd run down there and say anything at all! :-)
John
Because it's a complex game. It's sort of like playing 10 bingo cards at the same time. You need a way to mark what spots on each card have been drawn. To do that, you scratch off the spaces to mark them. If you have to scratch off the entire game board, then you have no way to mark the spaces on your cards (since lottery tickets are designed so that you don't need anything but your scratching device to play).
It's nothing of the sort; it's not an actual tic-tac-toe game in which you mark spaces to win. From the article:
On the right were eight tic-tac-toe boards, dense with different numbers. On the left was a box headlined "Your Numbers," covered with a scratchable latex coating. The goal was to scrape off the latex and compare the numbers under it to the digits on the boards. If three of "Your Numbers" appeared on a board in a straight line, you'd won.
The tic-tac-toe part of the board is already revealed, it's the "Your numbers" part that is scratched, no marking of boxes was involved. And the purpose?
One important strategy involves the use of what lottery designers call extended play. Although extended-play games — sometimes referred to as baited hooks — tend to look like miniature spreadsheets, they've proven extremely popular with consumers. Instead of just scratching off the latex and immediately discovering a loser, players have to spend time matching up the revealed numbers with the boards. Ticket designers fill the cards with near-misses (two-in-a-row matchups instead of the necessary three) and players spend tantalizing seconds looking for their win.
The design of the game is pure busy work meant to "extend" the time it took a person to figure out if they won, thus giving them the impression that the game is more involved than a regular scratch ticket. A secondary consequence of this "hunt for all of your numbers in a grid of 72 squares" game is that it makes it a lot easier for players to accidentally overlook a win, thus reducing the number of payouts made by the State Lotto commission
Couldn't the company just separeate the two printing processes. Why even let the same computer print the two? If you first print the result, then add the latex, then print the visible numbers whitout them having anything to do with the original print. You could still keep track of the number of winning tickets, and be safe from this kind of trick.
Sorry for the misunderstanding, I just reread your previous post, clarified it in my mind, and realized I've just parroted exactly what you suggested in the first place. Damn, where is that "remove stupid post" button when I need it? :-)
John
No, he figured out that the singletons on the eight tic-tac-toe boards had a high frequency of showing up in the list of numbers scratched off. He would buy a ticket if the singletons showed up in a winning combination on the tic-tac-toe boards. The system had nothing to do with the frequency of the singletons and everything to do with the placement of the singletons.
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