Positive Expected Value Lottery Math Porn

Remember this post I wrote last year about Massachusetts Lottery Arbitrage?  Well, the Inspector General’s Report on the subject is out, serving as an in-depth post mortem tale of the story from start to finish, including interviews with some of the syndicates who profited from the payout structure.   The report is awesome – porn for expected value geeks – and answers many of the questions that any prudent inquisitor would be asking.  In all of the following answers, the emphasis is mine:

how on Earth did they manage to physically buy so many tickets?

“Another constraint was locating stores that would handle large volume purchases. Many retail outlets balked at processing tickets on the scale that the MIT group and other high-volume bettors were seeking. Handling 10,000 tickets, including scanning in the slip with the requested numbers, could easily take several hours. Many store managers objected to having a staff member monopolized for long stretches. Although retail stores make a 5 percent commission on Lottery sales, tying up a clerk for hours at the lottery terminal could interfere with other store operations.

In addition, the MIT group, like other high-volume bettors, invariably had thousands of “free bets” to redeem from prior drawings. The store clerk is required to do twice as much work to process a free bet. First, the agent must scan the earlier ticket to redeem the free bet and then scan the betting slip. In addition, the store only gets a 1 percent commission – 2 cents – on a free bet redemption because it is considered a claimed prize, not a new sale. In Mr. Harvey’s words, “it was really a grind.”

Over time, Mr. Harvey said the group found a handful of retail Lottery agents – a Texaco station and a White Hen Pantry in Belmont, a convenience store in Back Bay across the Charles River from MIT, and a Mobil station in Amesbury – that would process the group’s large orders accurately. The MIT group used these four locations over and over again.

Did they pay in cash? (IG’s report suggests cashier’s check)

How long does it take to print out all of these tickets?

“They did a risk analysis and determined that $1.7 million was the tipping point. In order to increase the jackpot from $1.7 million to $2 million, a player would have to buy $1 million worth of tickets. Assuming that player was using Quic Pics, he could spend $10 for five bets in three seconds or $200 a minute. That would require a minimum of 83 hours to buy 500,000 tickets and spend the $1 million needed to force a roll-down. The IT department concluded that that couldn’t be done.

The MIT group did the same analysis regarding the time, effort and operational logistics of forcing a roll-down. They concluded that it could be done, and that the potential reward was worth the risk of trying.”

That’s definitely the best part of the entire Report.  It can’t be done?  Bullshit.  Watch us.

Did they have to manually fill out all the different combinations – or did they just go with random quick-picks?

“Even when the MIT group had enough money to purchase 300,000 tickets for a drawing, its ticket buying was limited by other factors. One constraint was simply getting enough ticket slips filled out. Mr. Harvey developed a computer program that would generate sets of numbers that would provide an optimal distribution across the range of possible drawing results. Under Lottery rules, betting slips can’t be computer generated so the group had to fill out betting slips by hand – oval by oval – to match each set of numbers generated by Mr. Harvey’s computer program. Simply filling out the betting slips was time-consuming. However, the betting slips could be reused so that once the slips had been created, Mr. Harvey and his friends did not have to repeat that part of the operation…”

Note that the “optimal distribution” refers to minimizing variance – not altering expected value.

“Unlike the MIT group and other high-volume bettors, Mr. Selbee’s Michigan group relied on Quic Pics, a system that allows the Lottery’s computer to randomly choose the numbers on each betting slip.

Mr. Selbee said using Quic Pics saved time by allowing him to skip two steps – filling out each bet slip and scanning each one through the machine. In exchange for speed, Mr. Selbee’s system had two weaknesses: he wasn’t sure of a broad distribution across the range of possible combinations and he invariably played duplicates.”

What about the logistics of sorting through your tickets to find the winners?

“While Mr. Selbee’s use of Quic Pics saved some time, he did not have shortcuts when it came to collecting his group’s winnings. Mr. Selbee said he and his wife sorted the tickets by hand into winners and losers. This process – visually inspecting approximately 60,000 paper betting slips, each with five panels of six-number bets printed on them – took days. Mr. Selbee said he and his wife would cull the winning tickets while still in Massachusetts and then drive the losing tickets back to Michigan where they would sort through the losing tickets again because they invariably missed some winners. He said he and his wife spent 10 hours per day for 10 days examining the losing tickets a second time.”

Do you save all of the losing tickets?

“Like Mr. Harvey and Mr. Selbee, Dr. Zhang said he has held onto his losing tickets, which number in the millions. He had first stored them in boxes in his attic. But when his ceiling started to crack under the weight of his growing ticket collection, he promptly moved the ticket boxes to the garage.”

 

Interested readers will want to go straight to the Inspector General’s Report, which explains everything in detail, and answers many of the deeper questions (see footnotes).  Here’s another teaser tidbit from the IG’s report:

“The rewards of his participation in Cash WinFall have not dramatically changed Mr. Harvey’s lifestyle. Mr. Harvey said that when he began playing Cash WinFall, his car was a 1995 Chevrolet Corsica which he had purchased for $500 at a government auction. As the MIT group became successful at Cash WinFall, he upgraded his ride to a high-mileage 1999 Nissan Altima.”

Must read: Inspector General’s Report

There is a phenomenal story on page 14 of the report about how the MIT Syndicate singlehandedly triggered the rolldown in the prize pool, and ended up owning 7 of every 8 outstanding tickets for that drawing.

The IG’s conclusion echoes what I wrote in my initial post:

“Cash WinFall was designed to attract a huge influx of betting by distributing a windfall to bettors whenever the jackpot reached $2 million. The emergence of individuals and groups buying large volumes of tickets was legal and financially advantageous to the Lottery. As long as the Lottery announced to the public an impending $2 million jackpot that would likely trigger a roll-down, an ordinary bettor buying a single ticket or any number of tickets was not disadvantaged by high-volume betting. In short, no one’s odds of having a winning ticket were affected by high-volume betting. Small bettors enjoyed the same odds as high-volume bettors. When the jackpot hit the roll-down threshold, Cash WinFall became a good bet for everyone, not just the big-time bettors. However, the unique structure of the game created unprecedented enforcement challenges for the Lottery.”

-KD

ps – My favorite thing about this story is that a buddy of mine, Lou, knew about the +EV when it was happening – but he didn’t form a syndicate, or tell me & Big Show, or anything.  Now, every time I send an email to my friends about new information on the subject, Big Show writes back “F*CK YOU, Lou!”

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