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.
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.