So this Pennsylvanian named Nadine Vukovich “a Mechanicsburg veterinarian, has claimed 209 scratch tickets, each worth $600 or more, over 12 years. Collectively she’s won about $350,000.”

This streak caused the bushy appurtenances perched atop certain supraorbital foramens to incline northwards at oblique angles. *Could it be*, some wondered, *that Vukovich cheated*?

The C-word is a harsh word. A legal word. It stimulates the greed juices in the people who carry actual briefs in briefcases. And nobody wants that. Let’s use the newspaper *Penn Live’s* *questionable activity*, instead. Especially since Vukovich wasn’t alone.

The question becomes: if Vukovich didn’t win the “normal” way, *how* did she do it? Did she figure a way to shade the odds in favor or was she just lucky?

#### Figuring the odds

To shade the odds means first being able to figure the odds.

There is a substantial difference in types of lottery, which broadly fall into two groups: lotto and treasure hunt. The bouncing numbered balls kind are lottos, and scratch-offs are treasure hunts.

Calculating probabilities, or odds, for lottos is, for those equipped with training in advanced combinatorics, child’s play. All we have to know is that we can’t know what causes those little numbered balls to pop out of their plastic holes in the sequences they do. The bopping and bumping are so complicated no physicist can model the exact movements.

But we can express the uncertainty that any sequence shows given assumptions we hope hold in the actual lotto machines. For instance, given usual assumptions, the odds to win the jackpot in Mega Millions are a bit under 1 in 260 million. Ouch.

#### Scratching the itch

Scratch-offs are a whole ‘nother story. They are like treasure hunts. It’s here where the story becomes interesting.

Suppose you had a map with 100 X-marks-the-spots and told that under 10 of these X-marks was buried treasure, and that under the other 90 are slips of paper on which are bad jokes.

If you had time to visit only one spot, and knowing only the possibilities, the odds are easy to figure: 10 in 100. What if you visited two spots? At the first spot you discover a slip of paper on which is written, “One snowman said to the other, ‘That’s funny, I smell carrots, too.'”

So what are the odds you find treasure at the second spot? They have increased, albeit modestly, to 10 in 99. The same is true if you didn’t visit the first spot but heard your friend did and came away empty.

#### Arrr, matey

Scratch-offs are like treasure hunts because like with cached pirate booty, fixed dollar amounts are allocated among a known number of tickets.

If you were to hang around a lottery retailer and watch the comings and goings of gamblers, you can like card counters in Las Vegas shade the odds your way. If everybody is buying the Treasure Hunt scratchers (I have no idea if this is real) and nobody wins, the odds have increased in your favor if you know this.

Not much, though. Because there’s lots of tickets and not so many prizes. On the other hand, there are web sites that track how much has already been claimed for certain scratchers. If the big money was already paid out, the odds of you winning big are, of course, *nada*. But they’re *higher* if you know nobody’s yet taken the major loot.

And again like with pirate booty, if you knew the Crimson Pirates’s habits you might guess he’d prefer certain hiding spots over others. Why sail to the Antipodes given Crimson’s notorious loathing of crocodiles? Best stay in Caribbean.

Same with scratchers. The lottery people have to print winning tickets, so if you can figure anything about either (A) how they choose which tickets get the money and which don’t, or (B) where the winning tickets are more likely to be sent, you can really boost the odds in your favor.

It’s been done, too.

#### The not-so-lucky winners

Once by Toronto statistician Mohan Stivastava who figured a way to tie in the visible information on a certain scratcher to the numbers under the latex coating. He boosted the odds in his favor to about 9 in 10 *or more*.

Stivastava figured how to decipher other scratch-off games, too. In the *Wired* story about him, one lottery official hinted that decipherable information was found in the visible bar codes on certain other scratchers. And that in many instances in many places there were suspiciously many multiple-winners.

Then there’s Joan Ginther, another mathematically minded person, who won tens of millions with scratchers—though she had to pay a lot out, too. Authorities surmise she pegged to the distribution system used in the State lotteries, which is just like knowing where the Crimson Pirate likes to sail. This dramatically altered the odds in her favor.

#### A bet is always a gamble

These clever schemes make formal calculations of probabilities true academic exercises. The real odds are always calculated on what *you* know, not on what others *think* you know.

Are there still ways to game the system? Nobody knows. The easy loopholes identified by Stivastava and others have been filled. But given the amounts of money involved, it’s a good bet new ones will be discovered.

*Thanks to Dan Hughes for pointing us the way.*

Around 25 years ago one of my kids was in the high school marching band. The band-parent’s auxiliary had a regular money-making gig at the local bingo parlor at which the parents of band members were expected to take a turn helping run the “pickle” counter. “Pickle” is what they called the scratch tickets that were available for sale between bingo games. I only did my part one time because I was so disgusted by how much money was being lost by people buying pickles that I never did it again. However, that one night I was there, one lady won big (somewhere around $1000, IIRC) on four tickets from the same pickle bin (there were many different bins with different pickle games, each consisting of about 3,000 pickles. Each packet of pickles came with a poster showing how many winning tickets of each dollar amount there were. The buyers weren’t able to put their own hands in the bins to choose their pickles, but they could direct me or one of the other band-parents which part of the bin to pull from. I was convinced that lady was cheating, but couldn’t figure out how. If she wasn’t cheating maybe she was increasing her odds in one of the ways you described. But to win as big as she did in one night seems way too lucky even for someone with the mind of a savant.

I think one of the fundamental questions regarding govt-run gambling matters such as easily hackable arrangements such as the ability for an observant “analyst” to crack a tic-tac-toe scratch & win game, and apparently many others, is:

Why aren’t the govt-administrators of such gambling on the constant alert for exploitable weaknesses?

and,

Why do so many of us as a society, seeing such examples of lousy management from our government (gambling being but one of a multitude of examples), still want to put govt in charge of so much that matters so so much???

“This streak caused the bushy appurtenances perched atop certain supraorbital foramens”

Of course it’s deliberate but NO!:

If you must, say,

“This streak caused bushy appurtenances perched atop certain orbital foramen”

OR

“This streak caused bushy appurtenances perched atop certain supra-orbital areas”

The foramen is called the Orbit.

There are tiny foramen for blood vessels or nerves here and there but I don’t think that’s what you meant. They tend to be called by special names in the cranium. Such as the external acoustic meatus. (ear hole).

Or there’s the external occipital protuberance which as we all learned in first year anatomy that either from phrenology or myth, was directly proportional to something not physical. Guaranteed to make everyone check theirs and that of their neighbour in class.

To Dear bugs,

“going back on the carrots…”

https://www.youtube.com/watch?time_continue=25&v=GJ8T8Uoc3P4

Digby only eats baby carrots. He’s no trouble at all.

https://www.youtube.com/watch?v=2NaE4h-Ti1c

Where I live scratch-offs come on a reel. You get the next N in line and don’t get to choose. Knowing how to recognize a winner isn’t much help but since you wouldn’t need to actually scratch off anything it could save time.

In any case, the woman with a Russian sounding name in Pennsylvania obviously proves the nefarious Russians rigged the last election.

209 tickets over 12 years? How many did she purchase?

Years ago, I worked with a guy who bought 50 $1 Lotto tickets every payday (twice a month). He once won $250,000. Yes, I get it that Lotto is different than Treasure Hunt–but my point is some people spend a LOT of money on lottery games.