Powerball

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The following is about the multi-state lottery game in the United States; Powerball is also a lottery operated in Australia. There is also a Powerball gyroscopic toy.

Powerball is an American lottery operated by the Multi-State Lottery Association (MUSL), a consortium of lottery commissions in 29 states, the District of Columbia, and the U.S. Virgin Islands. Powerball is licensed as the monopoly provider of multistate lotteries in these jurisdictions.

Official Logo (USA)

Started in 1988 as Lotto America, the name was officially changed to Powerball on June 8, 1996. The matrix has been changed periodically. On November 2, 1997, the matrix was changed from 5 out of 45 numbers to 5 out of 49, and the PowerBall changed from 1 in 45 to 1 in 42. Also on that date, the annuity period was changed from 20 to 25 years.

On October 9, 2002, the matrix was expanded from 49 numbers to 53. The most recent change came on August 28, 2005, when the matrix went from 53 to 55 numbers, though the Powerball matrix remained at 42 numbers. This is the current format.

1 Playing the game
2 Powerplay Payoff Analysis
3 Odds decrease, payouts increase
4 Largest payoff
5 Fortune cookie payout
6 Participating states
7 Licensed Products
8 References
9 External links

[edit] Playing the game

To play the game, a player pays one dollar and picks five distinct numbers from 1 to 55 and one number from 1 to 42, (the Powerball number). The player wins according to the following:

Matches	Payoff	Odds of winning^[1]
powerball only	$ 3	1 in 69 [1]
1 number and powerball	$ 4	1 in 127
2 numbers and powerball	$ 7	1 in 745
3 numbers but no powerball	$ 7	1 in 291
3 numbers and powerball	$ 100	1 in 11,927
4 numbers but no powerball	$ 100	1 in 14,254
4 numbers and powerball	$ 10,000	1 in 584,432
all 5 numbers but no powerball	$ 200,000	1 in 3,563,609
all 5 numbers and powerball	Jackpot	1 in 146,107,962

The player also has the option to pay an additional dollar in order to have any prize winnings (other than the jackpot) multiplied up to 5 times the normal prize. This is known as PowerPlay. The multiplier is chosen randomly at the same time as the numbers.

Overall odds of winning a prize are 1 in 36.61.

Jackpot winners have the option of receiving an annuity prize or a single lump sum cash payment. The minimum jackpot prize is a $15 million annuity disbursed in 30 payments over 29 years. The lump sum payment is typically approximately half the annuity value. The 30 annuity payments are not equal but based on an increasing rate schedule. For example, the first annual gross annuity payment on the base US$15 million jackpot would be approximately $267,000 while the final annual payment would be approximately $834,000.

Powerball drawings are held every Wednesday and Saturday at MUSL's headquarters in Urbandale, Iowa, normally at 10:59 p.m. Eastern Time. Drawings are occasionally scheduled at remote locations; when this occurs, the time may be adjusted, but the day remains the same.

[edit] Powerplay Payoff Analysis

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Please check for any inaccuracies, and modify and cite sources as needed.

Not counting Jackpot payoff and Match 5 bonus payoff, the expected payout per ticket without powerplay is: $E [X] = $3 / 68.96 + $4 / 126.88 + ... + $200,000 / 3,563,608.83 = 0.197115144.$ The powerplay ball gives a multiplier of 2,3,4 or 5 with equal probablity for each. The expected payout per ticket with powerplay is 3.5 times the expected payoff for a non powerplay ticket. $E [X] = 3.5 * 0.197115144 = 0.689903006.$ The net gain is 0.492787861. Since it costs $1 to play the powerplay option, you are expected to lose 1-0.493 = 51 cents every time you choose the powerplay option.

Having said that, losing 51 cents for every powerplay dollar is not as bad as losing 80 cents for every non-powerplay ticket. In the long run, for every 1000 dollars spent on standard tickets, you will lose 803 of it. For every 1000 dollars spent on 500 tickets with the powerplay option, you will only lose 655.

The lottery is probably counting on the average person spending more money with the powerplay option, not the same amount. Considering that the payout-adjusted odds are better, one might be inclined to raise their standard 5 tickets per drawing to 5 powerplay tickets. Then, instead of losing 8 dollars a week, they lose about 13. In short, even though your odds are better, you're playing a virtually guaranteed loser, and if you put more in, you are just guaranteed to lose more.

Finally, one might argue that the only sensible reason to play the lottery is for a chance at the jackpot. If you were to live forever, a winning strategy would be only to buy tickets when the cash-payout after taxes is better than 146 million dollars, giving at least a one dollar average payout on a one dollar ticket purchase, assuming no Powerplay option was used. However, such a strategy requires that the immortal player plays only when the payout, after taxes, and after accounting for the likelihood of other winners, is more than 146 million dollars. Assuming a Federal and state tax burden totaling 40%, even the largest Powerball drawing to date would only give you a return of approximately 75 cents on your one dollar investment. A jackpot of over 500 million would be required to break even, even if you assume that the number of players for the drawing stayed the same. Given that the number of tickets sold for each drawing, and thus the likelihood of your splitting the jackpot, goes up as the value of the jackpot increases, a "break-even" jackpot would likely have to be even more.

An immortal player playing this "winning" strategy would therefore likely find himself playing Powerball very rarely, as he would not have played once during the game's entire history to date. If he were, at that time, to invest one dollar for every drawing he had not previously entered in the intervening time since his last bet, in order to increase his chances of winning in a "reasonable" time, he would still, at two Powerball drawings per week, average about 1.4 million years between jackpots, though he has an even chance of getting a winning jackpot at less than 930,000 years. However this assumes that the odds stay the same for millions of years, and, since the rules have changed three times in ten years, each time reducing the jackpot odds, the immortal player can expect to go much longer between jackpots.

[edit] Odds decrease, payouts increase

On August 28, 2005, the game was modified to provide larger jackpots and faster jackpot pool growth. The main pool of numbers was increased from 53 to 55 and jackpots now begins at US$15 million rather than US$10 million. The Powerball number pool remains 42.

Odds of picking the jackpot winning numbers decreased to 1:146.1 million. Overall odds of winning a prize increased slightly to 1:36.61.

Some lower tier prizes also increased. The second tier prize increased from US$100,000 to $200,000 and the third tier prize doubled to US$10,000.

[edit] Largest payoff

The drawing held on Saturday February 18, 2006, worth $365,000,000, was won by a single ticket sold in Lincoln, Nebraska. That single ticket was shared by eight meat plant workers. Prior to this, a drawing held Wednesday, October 19, 2005 was the largest in the history of Powerball: worth an estimated $340,000,000, sold to the West family in Jacksonville, Oregon. The family won less than two months after the rules were changed to promote larger payouts. Steve West, who purchased the ticket, (Rumors after the record drawing circulated that his 17 year old son bought the ticket, which is illegal in Oregon) put in $20 for tickets, along with another $20 from his in-laws. The family plans to split the prize among themselves.

February's cash payout is worth approximately $177,300,000. The October payout had a lump sum value of $164.4 million, slightly below the $170 million payout from an December 25, 2002 drawing.

One of the secondary winners to the largest payout was New Hampshire U.S. Senator Judd Gregg, who won $850,000 after buying 20 tickets, one of which matched all the numbers but the Powerball.

Prior to the $340 million winner, Jack Whittaker was the claimant to the biggest jackpot.

[edit] Fortune cookie payout

The Powerball drawing of the March 30, 2005 game produced an unprecedented 110 second-place winners, all of whom picked five numbers correctly with no powerball number. The total came out to $19.4 million in unexpected payouts. 89 tickets won $100,000, but 21 additional tickets won $500,000 due to the Power Play multiplier option.

Powerball officials initially suspected fraud, but it turned out that all the winners received their numbers from fortune cookies made by Wonton Food Inc., a fortune cookie factory in Long Island City, Queens, New York. Apparently, number combinations printed on fortunes are reused in thousands of cookies per day. The five winning numbers were 22, 28, 32, 33, and 39. The sixth number in the fortune, 40, did not match the powerball number, 42. None of the employees of Wonton Food played those numbers.

[edit] Participating states

Also available in:

Powerball winnings are exempt from state income taxes in Delaware, North Dakota, New Hampshire, Pennsylvania, and Tennessee. South Dakota has no state income tax.

Georgia left Powerball in 1996 to join Mega Millions, another multi-state lottery.