How Random is a Lottery?

Mohan Srivastava’s daughter is only eight years old, but she already knows how to pick winning lottery tickets up to 90 percent of the time. She’s not a prophetess, nor is she a genius—it’s a trick she was taught by her statistician father, who looks for hidden patterns among apparently random numbers for a living.

Mohan is a statistical sleuth based in Toronto, Canada, who consults to gold-mining companies. His job revolves around analyzing data from rock samples to help decide if it’s worth digging a mine there. Rocks don’t give up their secrets so easily. A geological statistician has to know about different types of rocks, the forces acting on them, and how metals in those rocks react to those forces.

Mining lottery cards for cash works pretty much the same way, as he discovered one day kind of by accident. Someone had given him two scratch-and-win cards, and the first was a loser and the second was a winner. That got him thinking: what made that second card a winner?

Perhaps it was experience, perhaps it was luck, or maybe a combination of the two, or even something else entirely. But the idea suddenly fell into his mind as he was walking by the gas station where he had cashed in his $3 tic-tac-toe prize ticket.

”That game can’t be random,” Mohan mused. “The lottery corporation just makes it look that way to make the buyer hopeful. There has to be some algorithm, some set of computer-coded logical rules, that stacks the odds in favor of the lottery while tantalizing the customer with a seemingly good chance of winning. If that is so, something about the numbers themselves should reveal that hidden code.”

Sure enough, it did. To understand the code you have to understand the card. On the right side is a mass of two-digit numbers between 01 and 39, arranged in many 3 × 3 grids like tic-tac-toe boards. Most of those numbers appear on the card two or three times. A few numbers appear only once. On the left side of the card is the latex surface with “your numbers” underneath. If any three of “your numbers” appear in sequence on any of the tic-tac-toe boards, you win.

The trick is this. The lottery corporation makes sure that of the many numbers that are hidden on the left, only a few match numbers revealed on the right. And those that do match appear only once. The bottom line is that if you find a card in the store with three “singletons” in a row, you can be almost sure it’s a winner.

In June 2003, the Ontario Lottery Corporation ignored Mohan Srivastava’s calls and e-mails claiming he had found a flaw in the game. What they did not ignore, however, was the packet of unscratched tickets that he couriered to the CEO along with his claim that 90% should be winners. They were, and the game was pulled from the shelves the next day.

The game may be gone, but the algorithm isn’t. There are hundreds of variations on this game in Canada, the US, and around the world, and they all can be hacked the same way—some with 60% accuracy, some 70, 80, 90 or more.

Mohan believes he is not the only one who has cracked the code. For example, there are many multimillionaires who made it not on one big game but on hundreds of smaller ones. Their pattern of wins is exactly what one would expect from an “exploited” game where the algorithm had been decoded.

Back to Eighth Grade

The Baal Shem Tov teaches that from everything a Jew sees or hears, he can learn a lesson in the service of his Creator. What can we learn from how to hack a lottery? I posed this question to my Grade 7 and 8 math students at Cheder Chabad, and here are some of their responses:

  • The numbers on a lottery card may seem meaningless and random, but if you know the code for interpreting them, you can find a hidden treasure. The same is true for Gematria. The number value of Hebrew words does not seem important, but our sages teach us how to find hidden treasures of meaning by analyzing the connection between different words that share one Gematria. —by Avi Kurtach
  • The statistician didn’t just take things at face value. He stopped to take a deeper look, thought about things and came up a winner. The same is with us in our struggle to improve ourselves. We have to outsmart the yetzer hara [evil inclination], by looking more deeply into why we react the way we do to certain things. Once we see what’s going on, instead of living randomly and making mistakes, we make wise choices and then . . . we win! —by Heshy Gitlin
  • Life is like a lottery. You win some, you lose some, and there are plenty of bumps along the way. If you are smart enough to learn from your experiences, you will make the right turn and get on the right road that takes you to your destination—success!
  • The man who figured out the lottery system was a special kind of a guy who wasn’t fooled by how things look. Because he understood things that others couldn’t, the miners could find the gold. We Jews also have a “consultant” who shows us how to hack olam ha-zeh [this world] and “get the gold” in olam haba [the next world]. And that consultant is, of course, the Rebbe. —by Moishie Rosenzweig
  • Lottery tickets may look random, but really they’re not. There’s a reason behind why the numbers are what they are, even though most people have no clue about that. You could say the same about life. It looks like things just happen, but it’s really according to a plan, the Torah. When you study the plan, then you too can play to win. —by Baruch Lipovenko

Decoding the Grand Lottery

The month of Adar is upon us, and the holiday of Purim is around the corner. The word Purim means lottery. The wicked Haman made a lottery to choose a random date to destroy the Jews—and the date fell out on a month that worked to our benefit, the month in which Moses was born. Unbeknownst to Haman, the dice were loaded—by the Master Lotto Maker of the Universe Himself.

Which means that the story of Purim is much like Mohan Srivastava’s discovery: that behind apparently random, haphazard events lies a hidden, deliberate scheme. The same applies to our own daily lives: once we enter the times of Moshiach, we will finally see that all this apparent chaos was orchestrated by a hidden plan, and that plan works according to the will of the Hidden of all hidden—G‑d Himself.

In the state of the world as it is now, it’s often very hard to see purpose or meaning. But hey—if an eight-year-old girl or a Grade 8 boy can see through the facade to the reality behind it, then maybe we can too.The line between creator and creation has gotten blurrier lately, thanks to sophisticated robots that are smart enough to invent technologies of their own. These are not simplistic gadgets the likes of which you might concoct while daydreaming at a red light or doodling on a napkin. We are speaking about innovative pharmaceutical formulations and genetic fixes that might normally take dozens of scientists many years and millions of dollars to develop.

The robot itself has become the scientist’s scientistThis new breed of robot has taken information technology to a whole new level. What once was called the science of automation has been overturned to become the automation of science. Yes, the robot itself has become the scientist’s scientist.

Divine Providence is often credited with providing the remedy before the affliction. The modern affliction is complexity. For example, the problems that scientists face today in biotechnology involve thousands of variables, each having various states and interactions with other variables and environmental elements, resulting in millions of possible outcomes that all have to be evaluated before you even get to the stage of making an experiment to physically test anything. Whew!

The cure is processing power. Today’s robots can identify problems, review existing options, design new alternatives, test them all theoretically, and determine the most effective and robust solutions. Amazing.

But the new cures generate their own set of afflictions, one of which is legal. Who has the right to patent these cybersolutions, the inventor of the robot, or the robot itself? Believe it or not, according to the journal, SCIENCE, it depends on where you (or the robot) lives. In the USA, only inventions by humans can be protected by patents. In Europe, it seems, the laws governing intellectual property extend to any legal entity, possibly even robots.

What can we learn from all this? First let’s look at things from the robot’s perspective. Left to its own devices, such a smartbot could look at himself proudly and proclaim, “Wow, I’m amazing! I’ve studied everything out there and there’s nothing that can analyze problems and create solutions like I can.”

Well hang on there, Mr. Bot. You are yourself a mere creation, the product of analysis and design by a creative intelligence greater than yours. True, you too can invent, and brilliantly at that, but your scope is limited, your intelligence artificial, your personality vacuous, your circuitry simplistic. And besides, the very tasks you have been hardwired from the outset to perform are the very tasks you falsely pride yourself in. If anyone deserves the credit, it is the creative genius that made you the creative genius you are.

And the same may be said of us.

Man, the inventor, is the invention of an inventive mind like his, but infinitely greater still. True, his analytic and creative prowess is incomparable in all the world, but man would do well to heed the Torah’s admonition in Deuteronomy 7:12-11:25: “And you think, ‘My strength and the power of my hand acquired this wealth for me.'”

Is it any more ludicrous for our techno-babies to take exclusive credit for their inventions than it is for us to boast of ours? Honesty demands that we too look upstream to acknowledge our source and recognize who owns what.

There’s another lesson to learn from robots. As sophisticated as they get, they only appear to be conscious, sentient and free-willed. To equate robots with humans is not only a false vaunting of their qualities, it is an abdication and gross neglect of ours. And if that happens, G‑d forbid, then indeed they would deserve their patent rights – at least more than we would.

Vive la difference.

Previous ArticleNext Article

Share this Post