Jack by the hedge
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I wonder what the actual odds were.
"If Ginther's winning tickets were the only four she ever bought, the odds would be one in 18 septillion, according to Sandy Norman and Eduardo Duenez, math professors at the University of Texas at San Antonio.
Exactly how often Ginther plays is unknown. But Norman and Duenez said that a habitual player winning four times over a 17-year span is much less far-fetched.
At the Times Market, Bae and store regular Gloria Gonzalez said they've certainly watched Ginther buy her share of tickets over the years. And not just for her.
Gonzalez said when her elderly father would sit at the store's window booth and scrub through dollar scratch-offs, Ginther would surprise him with a $50 ream of tickets."
"If Ginther's winning tickets were the only four she ever bought, the odds would be one in 18 septillion, according to Sandy Norman and Eduardo Duenez, math professors at the University of Texas at San Antonio.
Exactly how often Ginther plays is unknown. But Norman and Duenez said that a habitual player winning four times over a 17-year span is much less far-fetched.
At the Times Market, Bae and store regular Gloria Gonzalez said they've certainly watched Ginther buy her share of tickets over the years. And not just for her.
Gonzalez said when her elderly father would sit at the store's window booth and scrub through dollar scratch-offs, Ginther would surprise him with a $50 ream of tickets."
The fact that this woman is a former math professor makes me wonder if she somehow detected a bias in the distribution of winning jackpot tickets, and bought accordingly.
Jack by the hedge
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It's a thought that has to cross your mind when you read the headline. Generally though, lotteries are kept simple enough as to avoid any such possibility. Do you know anything about how that particular lottery works?
rwguinn
Penultimate Amazing
you buy a ticket. The clerk pulls the next one off the roll, hands it to you. You scratch off the foil covering with a coin, and see if you match the winning combination.
Jack by the hedge
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So it's an instant win, and there's no way of selecting your combination. Do you know anything about the odds of any one ticket winning? The article kinda hints that it's a little under 1 in 2 million. Do you know how the prizes are calculated?
ZirconBlue
Sole Survivor of L-Town
One of them was not a scratch-off:
That still means that statisitical analysis is unlikely to be involved.
rwguinn
Penultimate Amazing
"Winning" means anything from a $1.00 bill up to and including the jackpot.
Beerina
Sarcastic Conqueror of Notions
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Her four were 3 scratch-offs and one draw. Let's ignore non-pure chance the latter for now, as that would involve dishonesty on the part of lottery officials far more likely than some subtle, non-random influence on the ping pong balls.
Does anyone know how the scratch-offs are randomly generated? If they are done by computer, and by the standard rand() type algorithm (which is very well-known), you could, in theory, buy a ream of tickets and try to find out whereabouts in the massive, but ultimately repeating, stream of random numbers you are.
I actually toyed with a theory about this back in my old EverQuest days, wherein some chain of hits and misses, recorded, could gain insight on the position to where you were in the random number generator's sequence. It would have been exceedingly difficult, given "your fighter" would only receive some of the random rolls, with the others going to other players or god knows what processes on the server. But if it had worked, you could wait for a string of 20 "hits" to come up, then run up to the deep red monster and slaughter it.
Back to the lottery: With that info, you could the map the serial numbers on the ticket to the random stream of rand() numbers generated by the state's computer, and make an excellent guess as to what the "big win" ticket's serial number would be. Then go conveniently position yourself to buy the block of tickets around that one. You'd have to hoof it a bit to find out which stores have which blocks of serial numbers, or the equivalent, if they're covered up. Details left to the field mathematician.
ETA: Hmmmm. If you could get this info:
1. Random number algorithm.
2. Method to encode them on a ticket and a sequence of tickets. i.e. how to turn a block of random numbers into a ticket.
3. Some knowledge of serial numbers on the tickets
You could do it. The first one, one would start with the standard rand(), and then through alternative rand-style algorithms.
The second could probably be deduced from examining the tickets.
The third could be as easy as looking on the backs of a ream of tickets, or a ream of scratched tickets, and the rest creative social engineering. Don't go doin' nuthin' illegal, people!
One other thing occurs to me. For a given series of tickets they'll have, say, 1 ten million dollar winner. So they can't just generate, say, 10 million tickets and assume they have exactly 1 winner. They may have 0. They may have 2 or more. So there must be some algorithm in there to throw out other winners that get generated. Or maybe they randomly (!) place a deliberately-crafted winner somewhere when printing.
Same applies to the lesser prizes, too.
It occurs to me they could just throw out the 2nd and further computer-generated "winners", as the 1st would be properly distributed across the whole run, assuming the run is exactly the right amount to statistically have precisely 1 big winner.
And even if they "inserted" a hand-carved winner somewhere, that would make a 1-off vs. the random number sequence-to-serial number mapping, unless they replaced one with the winner instead of inserting the winner. If the former, you could kind of triangulate on whereabouts the winner would be, in the serial number sequence, by buying various tickets around the state and seeing if their spot in the random sequence was accurate or 1-off from where it "should" be, when compared to their serial numbers.
This type of analysis would also be good for fraud detection on the part of lottery officials.
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ponderingturtle
Orthogonal Vector
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If you had enough data from the makers of scratch off tickets you could know exactly where any winner was. It does not seem like enough to be fraud, or she has a lot of will to prevent winning too much to get looked into.
patchbunny
Graduate Poster
Makes me think of the McDonald's Monopoly game, which for years had been rigged by the person in charge of security.
On the other hand, she's not the only lottery winner to have won more than once. There have been two others, IIRC.
On the other hand, she's not the only lottery winner to have won more than once. There have been two others, IIRC.
Dr.Sid
Philosopher
Or it is all scam ..
Jack by the hedge
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I suspect they've thought of that. The cover material you scratch off seems to be metallic (maybe aluminium powder in some kind of soft plastic?) which I presume makes it practically impossible for anything to see through the cover unless it's so energetic a wavelength it has no hope of seeing the printed ink underneath.
They don't just have to guard against stealthy customers using some discreet scanning apparatus, they have to guard against unscrupulous shopkeepers, who could spend hours privately examining their rolls of tickets any way they please before they go on sale.
I'd speculate that there may be several non-random elements to the Texas Lottery. For example, let's suppose the powers-that-be at the Lottery decide it's a good idea to have:
(1) Jackpot winners distributed geographically, so that if there is such a winner in the Dallas area this month, that won't happen again until there have been such winners in the Houston, San Antonio, Galveston, etc. areas;
2) Jackpot winners distributed by type of game, so that if there has not been a jackpot winner in a 2010 baseball scratch-off game with only a small percentage of tickets in that game remaining to be sold, there will be such a winner in the near future;
(3) A maximum time limit, such as X months, on not having a jackpot winner.
I'm sure that there are many other opportunities for bias to creep in, if someone decides that some goal or constraint should override randomness.
paximperium
Penultimate Amazing
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I love speculations that don't require any evidence or math to back up.
There are three basic possibilities here. The lady math professor has:
(1) Paranormal powers;
(2) Been incredibly lucky;
(3) Detected bias in the Texas Lottery and devised a system to make money off of that bias.
I'm simply throwing out some speculations -- i.e., "reasoning based on inconclusive evidence; conjecture or supposition" -- that (3) may be the most likely. If I had solid evidence, I would not be inclined to post it here.
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Dumb luck
or a case of a divine intervention?
Science doesn't like these "miracles," coz it doesn't have the tools to set things apart - providing those were fair winnings. Actually, there is a tool with dull edges that is being used again and again to prop the mere luck: Project the existence of the scratcher game into the future - add some 10 trillion years - and the chance that a person gets lucky the way Joan Ginther did becomes more than realistic. The math holds that the distribution of a rare event is randomly spread over the duration of trials. In other words, if there is on average just one expected event to take place in the course of 10 trillion years, it has the same chance to take place in 2010AD or in 10^9AD.
Suppose that the event was a case of a divine intervention. Was it a dumb intervention or not? Why would the divinity bless that particular person?
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valis
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Correct me if I am wrong but.....
Here in Florida there are a set number of each prize for each run of scratch off tickets. So IF the winners cashed in so far is public knowledge AND you could somehow take an educated guess at how many tickets are left in circulation you then could possibly spot instances were the odds of winning were increased.
I don't know that you could gain that much of an advantage but it would be similar to card counting in black jack. I suppose you could check multiple stores and take note of how many tickets they had left for a particular game....
Here in Florida there are a set number of each prize for each run of scratch off tickets. So IF the winners cashed in so far is public knowledge AND you could somehow take an educated guess at how many tickets are left in circulation you then could possibly spot instances were the odds of winning were increased.
I don't know that you could gain that much of an advantage but it would be similar to card counting in black jack. I suppose you could check multiple stores and take note of how many tickets they had left for a particular game....