All you need is a dollar and a dream.

Prepared by Gary Simon, Stern School of Business, September 2006

Annie Donnelly had a dream. . .

And she had a dollar.

2.3 million of them, in fact.

Lots of dollars.

Annie worked as a bookkeeper for Great South Bay Surgical Associates in Babylon, Long Island. (It’s now in West Islip.)

Over a period of three years, she took 2.3 million dollars out of the firm.

The word “took” could be replaced by “misappropriated” or “embezzled.”

She used the embezzled money to buy New York State Lottery tickets.

She had hoped that a big prize would allow her to replace the misappropriated funds and still have a big money pile left over.

It didn’t happen.

Here are some details from Newsday, 24 AUG 2006. The report is by staff writer Susana Enriquez.

After more than three years of stealing from her employer to gamble up to $6,000 a day on lottery tickets, a 38-year-old mother of three from Farmingville finally gambled away her freedom. …

Annie Donnelly pleaded guilty to second-degree grand larceny and faces a maximum of 4 to 12 years in prison for stealing $2,323,919 from Great South Bay Surgical Associates in Babylon, where she worked as a bookkeeper.

“We didn’t find anything significant where this money could be going, except she did have quite a Lotto habit,” said Assistant District Attorney Donna Planty.

Is the claim “up to $6,000 per day” believable?

Yes it is. Note that $2.3 million over three years is

or about $2,100 per day, on average.

$2,300,0003 365

Maybe there was a day off now and then. Occasional winnings were returned to the game.

Annie did a good bit of her betting at MK Cards and Gifts.

This small store is in a nondescript strip shopping mall on Portion Road in Ronkonkoma, New York.

It’s between a self-defense instructor and a pizza shop. It’s two doors down from a nail salon.

Shawn, who ran MK Cards, noted that by herself, she brought the store more income than any single line of goods, including cellphones, beverages, and magazines.

How did she move that much money around without attracting attention?According to the Newsday account…

Between June 30, 2002, and Nov. 17, 2005, Donnelly wrote company checks to cash, petty cash or to herself, then listed the name of a vendor in the QuickBooks computer accounting program.

She started off by taking small amounts of money and worked her way up, [assistant DA] Planty said. She wrote a “significant” number of checks, of which the average amount was about $3,000, Planty said.

In the last half of 2002, Donnelly took $41,261, Planty said. Last year, from January until she was arrested in November, she took $1,381,927.

Donnelly was caught when the paycheck of one of the doctors bounced, Planty said. When he went to the bank to check on the problem, he discovered that she had been fixing the books to cover up her scheme.

Commentary on the Web and in print has not been kind to Annie.

She had $2.3 million. Wasn’t that good enough?

Why play it away with the lottery?

The kindest summary of her situation ….

“She obviously had a gambling problem and seemed to be caught up on the high of winning.”

Assistant DA Planty, from Newsday account.

“She has a sickness.”

Husband Scott Donnelly, 42, of Farmingville.

Perhaps she just didn’t understand the mathematics of the lottery.

Let’s reject that argument.

She was a talented bookkeeper and an even more talented embezzler.

Let’s assume that she did not want to just walk away with the embezzled money. She would have been caught eventually.

Is it realistic to believe that she had a decent chance of winning enough lottery money to replace the embezzled money and still have a big pile left over?

Betting on big-money games is critical to this strategy. Annie may not have realized this.

Why? Small-money games should be evaluated on an expected-value basis. Since the lottery take is about 50%, the small-money games have no chance of moving to a positive position.

Shawn, the counter person at MK Cards, said that she once won $25,000.

… but what’s $25,000 when you are trying to cover $2,300,000?

The WIN4 game has a maximum payout of $5,000 for a $1 bet.

TakeFive notes that “Prizes are paid on a pari-mutuel basis.” The odds suggest that a maximum prize would be around $250,000.

New York Numbers has a maximum payout of $500 for a $1 bet.

Shawn at MK Cards said that Ms. Donnelly played quite a few of those low-payout games.

“The irony is the total amount of money she stole is more than she would have won if she hit the lottery. When I first got the case, I said, ‘You’ve got to be kidding.’ ”

Assistant DA Donna M. Planty, from

New York Times account.

Some games, such as Lotto, have the statement “Prizes are paid on a pari-mutuel basis and must be claimed within one year of the draw date.” Still, a big win at Lotto could have been $7,000,000.

The MegaMillions game has a second prize of $250,000 for a $1 bet, but there is the disclaimer “In some cases, the fixed prizes may be paid on a pari-mutuel basis and will be lower than the published amounts.”

The first prize is described as JACKPOT with the prize divided equally among all winners. There are no projected figures, but the odds suggest that a $10,000,000 would be possible. This might work for Annie Donnelly’s purposes.

MegaMillions had possibilities. So did LOTTO.

With LOTTO, The chance of winning the big prize with $1 is 1 out of 22,528,737. (You get two bets with $1.)

To play LOTTO, you choose six numbers from 1 through 59. The Lottery draws six numbers.You need to match six-of-six to get the big win.

The probability comes right from the hypergeometric distribution:

6 536 0

596

The probability is printed right on the game card, too.

Suppose that Annie played 2,300,000 times. What is the probability that she’d win at least once?

This is 1 – P(all losers)

This math cannot be done on an ordinary calculator. The value is about 10.71%.

2,300,00022,528,736122,528,737

This seems like a small number… but 10.71% is hardly invisible.

If you were in a deep financial hole, possibly facing jail time, might you consider such a strategy?

Would you steal lots of money for a 10.71% chance of coming out OK?

Annie Donnelly played this game. She did not play it as wisely as she might have. And she lost.

On Tuesday, 26 SEP 2006, Annie Donnelly was sentenced to 4-to-12 years in prison.

She caused quite a scene at the sentencing. “Tell me how you’re helping me!” she screamed. The tirade lasted for several minutes.

Newsday account by staff writer Alfonso Castillo, 27 SEP 2006.

Let’s examine the damage…

Annie Donnelly will do jail time.

Her husband and three children will be without her.

The family home was sold as part of the settlement.

Actually, this asset was divided. Half the proceeds went to Scott and the children.

Great South Bay Surgical Associates lost $2.3 million, less what they recovered from the house sale.

With a dollar and no dream…

at least you get to keep the dollar.

THE END