The powerball lottery suspects fraud, but its the Fortune Cookies

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Who needs Giacomo? Bet on the fortune cookie
New York Times, May 11, 2005, National desk; Pg 1
Jennifer Lee

This article reports unexpected winnings in the Powerball lottery of March 30, 2006, which the lottery officials thought, might be fraudulent but which had a much simpler explanation.

For the Powerball lottery, a player chooses 5 distinct numbers from 1 to 53, which we call the "basic numbers." In addition, the player chooses another number between 1 and 42 which we call the "bonus number." The lottery randomly chooses 5 basic numbers and one bonus number. If your 6 numbers agree with those chosen by the lottery you win the jackpot (a huge amount). If there is more than one jackpot winner, you share the jackpot with the other winners. There are 8 additional prizes that you do not have to share with other winners. For example, if you buy a $1 ticket and your 5 basic numbers match those of the lottery, but your bonus number does not, you win $100,000.

When you buy a $1 lottery ticket, the lottery offers another bet called the "Power Play" for an addition $1. For the Power Play the lottery choose random, called "the multiplier", from the numbers 2,3,4,5,5. If you make this bet, and you win any prize other than the Jackpot, this prize is multiplid by the multiplier.

On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and 40 as their bonus number. The lottery chose the same five basic numbers but chose 42 for their bonus number. They chose 5 for the multiplier. 89 of these players did not choose the Power Play and so they each won $100,000. 21 players did choose the Power Play and, since the lottery chose 5 for the multiplier, they each won $500,000 dollars. Thus the lottery paid out to these winners 19.4 million dollars. They actually didn't have to pay out this much since we read on the back of a ticket:

In unusual circumstances, the set prize amount may be paid on a pari-mutuel basis, which will be lower than the published prize amounts.

Evidently the Lottery officials decided not to use this option in this case. In addition the article states that the Lottery keeps a $25 million reserve for odd situations

Power ball officials stated that, considering the number of tickets sold in the 29 states, they expected 4 or 5 winners.

The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:

Panic began at 11:30 pm. March 30 when he got a call from a worried staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?

They tried a number of theories about the way people choose their numbers. For example many players pick their numbers following a geometric designs on the ticket. Nothing worked, but then the first three winners said they had obtained the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. They found that many different brands of fortune cookies come from the same Long Island City factory owned by Wonton Food. This company turns out four million a day, which are used by dealers over the entire country. When shown the numbers Derrick Wong, of Wonton Food, verified that they had used these numbers. The numbers were chosen from a bowl but the company plans to switch to having them chosen by a computer and Derrick plans to play the lottery.


(1) The articles says:

Of course, it could have been worse. The 110 had picked the wrong sixth number -- 40, not 42 -- and would have been first-place winners if they did.

Worst for whom?

(1) How do you calculate the probability of getting the 5 basic numbers but not the bonus number correct?

(2) How many tickets would you have to sell to expect about 110 people to get the five basic numbers but not the bonus number correct?

(3) Do you think that the sales of fortune cookies will increase?