Beating the Lottery: When Math (Not Gambling) Pays Off

April 21st, 2013 by 
Picture of a casino floor in Las Vegas, NV

Today we're going to tell a story about something you've always wanted to do - beat the lottery

Subtitle it: Massachusetts Oddsmakers Meet High Volume Betting and Lose.

Lottery Tickets as a Form of Investing?

  • Have you ever walked into a gas station or a convenience store and, on a whim, purchased a few scratch tickets? 
  • Do you play scratch tickets during the holidays? 
  • Do you have a weekly, monthly, or perhaps even daily 'numbers' habit? 

Odds are you're just tossing money away, hopefully for a few minutes of entertainment. Presumably, indulging your habit you're not thinking you can beat the lottery by figuring out a flaw in the game.

Truth is, for the vast majority of us, scratch and lottery tickets are just dollars risked for a shot at a faraway dream. Maybe we're just practicing escapism before getting back inside our refueled car

I didn't beat the lottery.
I didn't beat the lottery: there are not winners.

But... what if you had an edge? 

What if a dollar of lottery tickets was worth more than a dollar in expected returns? How would you behave if, dare I say it... you could actually beat the lottery with an exploitable edge?

Well, in that case, the lottery goes from a few dollars of entertainment or, at worst, a painful addiction to a legitimate investment.

Beating the Scratch Ticket System

Over the last few years, there have been more and more examples of people, literally, beating the lottery system. 

The first person to come to prominence was probably Mohan Srivastava, a Canadian statistician and the subject of an awesome Wired article

Mr. Srivastava recognized that a false constraint made lottery tickets beatable. Srivastava realized the tic-tac-toe game printed on the front of the ticket was exploitable – it gave clues to the game's numbers.

Even though he realized the game was beatable, Srivastava did some quick math and realized it wasn't worth his time. He got in touch with the Lottery Commission's Security Team. Once they realized he was the real deal, they pulled the game from shelves almost immediately.

Srivastava cracked a type of game with a so-called "baited hook". 

Games of this type reveal some public, teaser information. Combining the teaser information with the concealed information reveals whether a ticket is a winner.

Baited hook games are designed to extend the entertainment value of a scratch ticket. Matching numbers and looking up information in tables is a more interesting hook than simple boolean win/loss games. 

The problem? Many early baited hook games suffered from a fatal flaw. Just like with card counting in blackjack, public information was enough to nudge to odds of winning into the player's side.

Beat the Lottery and Gain The Key to a Larger Kingdom!

At the point the Wired article was written, very few lone wolves had gone public with their lottery 'prowess'. Srivastava was one of them, Joan Ginther (also mentioned in the article) another. Ginther was later revealed (or at least rumored) to have a Math PhD. 

Still, if two lottery beaters are known, how big is the iceberg?

Further, what if the majority of lottery-beaters isn't made up of lone wolves but, perhaps a seedier mix of individuals. Think: everything from organized crime to  betting syndicates... 

Wired published that article in January of 2011. At that point in time, although there was some evidence that some states had exploitable scratch ticket lotteries audited evidence wasn't available (although the Whitey Bulger reference was a nice touch).

Now, there are a few potential flaws in game design where a lone wolf might have a harder time competing. 

One - when flaws are only evident on a large scale, perhaps across a store's ticket sales, or even a state's complete ticket sales. 

Consider the fact that lottery commissions often guarantee a certain prize amount per issuance. If you had (possibly inside) access to sale and prize information, you could estimate prize payouts. If prizes were running above or below predicted returns, it'd be easy to change your behavior. 

Two - as we'll see later, you might discover a small but definite edge with only a small expected value. With that sort of edge, you'd need a massive bankroll and good organization to beat a lottery.

Massachusetts and WinFall's Not-Surprise Windfalls

WinFall was a game in Massachusetts which started in 2004. It had an interesting structure: it was a single state lottery system where a player would pick 6 numbers between 1 and 46 for twice a week shots at a prize. 

This particular lottery was designed to pay out 60 cents of every incoming dollar in prizes, but it also had an innovative twist - it had a memory, and therein lied the problem.

There was one feature which made WinFall stand out from a normal lottery. The odds of matching 6/6 numbers 1-46 is 1 in 9,366,819. However, WinFall had a prize cap, which kicked in at $2,000,000

When the prize built to that amount and there was no winner, the lottery would "roll down" the prize amongst the lower tier winners:

  • 26% to all those holding 5/6 numbers.
  • 47% for all those holding 4/6 numbers .
  • And so on (in addition to the standard prizes).

So, what's the issue? Well, nothing, at least not for the lottery commission. 

For smaller prizes, the lottery would pay out its standard amounts for lesser wins, and continue to build the pot for an eventual "rolldown". However, when a rolldown happened there would be $1.15 in the pot for every $1.00 in tickets bought. Even after Massachusetts took their cut, sophisticated players could play the lottery with Other People's Money.

How was the WinFall rolldown exploited?

Of course, once sophisticated players realized the odds, chaos ensued. 

The official Inspector General's report is an unintentionally hilarious look at a cat and mouse game between gambling groups and lottery officials. Officials took (mostly ineffective) pains to prevent high volume ticket buyers from bulk purchases during rolldowns.

How many groups were in the field? 

At least three major ones:

  1. An MIT Group (of Bringing Down the House fame)
  2. A competing group from Boston University
  3. A betting syndicate from Michigan

They matched up with a few more college and university affiliated groups. Oh, and I've got a bridge to sell you if you think those are the only ones.

Anyway, amongst the shenanigans they pulled? 

The Massachusetts lottery IT department would forecast ticket sales and predict when rolldowns would occur. Of course, the groups were watching the site, which led to predictable shenanigans. –

Did any group force a rolldown by buying hundreds of thousands more in tickets than the IT Department predicted? That almost certainly happened (at least once). 

Did any groups computerize entries to buy more tickets? Yep. 

Did any groups ally with stores and cut them in on the action? It certainly appears so.

By leaving previous tickets in the pot and through its determination of prizes, WinFall wasa 'flawed' game. 

Unlike games like Powerball or Mega Millions, there was an actual positive EV for the game after the rolldown. That's an absurd position for a lottery.

Exploitable Lottery Edge Stories Don't Excuse Gambling Habits

That said, just because we just shined a light on the real life Ocean's Eleven doesn't justify your weekly ticket purchase.

It's not that this is hard math. With a little creativity, some 101-level statistics, and luck, you too can find a hitch in the system. However, I doubt that most of us who buy scratch and lottery tickets have ever calculated an expected value.

If you are buying a lottery ticket, there are exactly three options:

  1. It's entertainment.
  2. You've done some math.
  3. You're a sucker.

Now, I love you readers. However, admittedly, most of the people we know who buy tickets fall right in the middle of #3. The vast majority of buyers don't have the edge necessary to beat the lottery.

That in mind - do you think you can beat the lottery?



PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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