Should you buy all 175.2 million Powerball combinations?

Update 1: The Powerball annuity jackpot has been increased to $500 million, and the cash value is now $327 million. (Tuesday, Nov 27 3:31 PM)
 
With the Powerball jackpot now at $425 million, it is logical for players to wonder if they should buy tickets for all the possible combinations. At first glance, one might think this would be a winning strategy for picking up an easy $74.6 million. 

However, before one recklessly spends this much money, there are several factors that that must be considered.

1. In the 2012 Powerball game, each ticket costs $2. Since there are approximately 175.2 million combinations, one would have to spend $350.4 million to accomplish this.
2. The $425 million jackpot is the annuity value which is paid in 30 varying installments (29 years). This implies that the breakeven 0 profit financing rate is 1.144%. So, if one borrowed the $350.4 million, the borrowing rate must be less than this interest rate in order to make a profit. If the borrowing rate is more than 1.144%, you will lose money.
3. The cash value being offered today is $278.3 million. If you take the cash, you will immediately lose $72.1 million.
4. In order to guarantee yourself a winning ticket, you must buy all the 175.2 unique combinations. If you are lazy and buy 175.2 quick picks, then there is a 36.8% chance that you will not have the winning combination.
5. When the jackpot is this high, we can expect that approximately 120 million other tickets will be sold. Of these, there will be a 50% chance that one of these will be a winning ticket. This means that there is a 50% chance that you will have to share the jackpot prize with at least 1 other winner. If this happens, you might win only $212.5 million annuity or $139.2 million cash or less. Again, you will take a loss.

As you can quickly see, there is a very high probability that even if you buy all the unique combinations, you will end up losing millions of dollars if you purchase all the combinations. Thus, our advice is:

No, You should NOT but all the Powerball combinations.

But, what if no one wins the jackpot in the next drawing and the Powerball grows to $600 million. Should you buy the combinations then?
To help you answer this, we present the two graphs below. The first shows the chances of there being a losing Powerball as ticket sales grow to 500 million. As you can see, the chances decrease as sales increase. When 200 million tickets are sold. there is a 30% chance that nobody will win. When ticket sales hit 500 million, there is less than a 6% chance that there will be no winner.

The second graph shows the probabilities of having more than one winner. At sales of 200 million, there is a 40% chance of multiple winners. When sales reach 500 million, there is a 67% chance that there will be more than one winning ticket.

So, even as the temptation to purchase all combinations increases as the jackpot value grows, the likelihood that the prize will be shared by more than one winner also increases. So, even if the annuity jackpot reached $1 trillion, it would most likely be shared by 2 or more winners, which means that each winner would only receive a jackpot prize equal to or less than the $425 million currently offered.

Thus, we continue to recommend that you should:

NEVER buy all the Powerball combinations!

Why you should play the Pick 4 Lottery

The primary goal of a lottery player is to win money. However, the motive behind this goal varies from person to person. Some do this to win a large jackpot, and to be set for life. Others play to supplement their income by trying to continually win smaller prizes. And, a smaller group are addicted gamblers, hooked on the thrill of winning regardless of the prize.

This article is aimed at the second group of players, i.e. those who play to supplement their income. These are the people who treat the lottery expenditures as an investment. Their objective is to continually win smaller prizes and not to lose any of their own money. Their mindset is similar to those who invest in options. They know that they will:

• lose a little,
• lose a little,
• make a lot!

Play Pick 4
To accomplish a viable cash flow of winnings, we suggest that playing the Pick 4 lottery game in your individual states.

While there are slight variations in cost and payouts, the basic format of the game is identical in most states. To win, the player must select 4 numbers that range from 0 to 9 in each of the positions. This means that there are 10,000 possible combinations. In general, the cost of each ticket is $0.50 and the payout is $2,500. And, in most states, the Pick 4 drawings are held twice a day, seven days a week.

In some states, the cost of the ticket is double ($1.00), but the payout is also double ($5,000). Further, many states pay out a fixed prize, and others determine the winning prize on a pari-mutuel basis. In these instances, we can still assume that the average payout per $0.50 spent is $2,500.

A Winning Strategy
To limit one's costs, we recommend that a player select only number that they wish to play. Then, we suggest that they play that number in every drawing until it wins.

By doing this, a player will be spending only $0.50 to win $2,500. Thay is a return of 5,000 to 1.

However, we recognize that the players number may not be drawn immediately. This means that the player will be spending $1.00 per day until it wins. This represents $365 per year and 700 drawings. If the number is not drawn for a while, the player has approximately 6.9 years (6 years 10 months) until he reaches the breakeven level (which is 5,000) drawings.

Comparison
To help understand this strategy, we have prepared the table and graphs below comparing the Pick 4 lottery game to Powerball (PB), Powerball with Powerplay (X PB), Mega Millions, Mega Millions with Megaplier (X MM), Lotto 649 (L6), Lotto Max (LM), and Pick 3. The charts only consider prizes in those games where the player matches 4 balls.  

	Cost per Ticket	Prize	Odds	Winnings per $	Return	Dwgs per Week	Weeks to Prize	Years to Prize	Cost per Year
Pick 4	$0.50	$2,500	10,000	$5,000	$0.25	14	357.1	6.9	364.0
PB 4/5+	$2.00	$10,000	648,976	$5,000	$0.02	2	2,500.0	48.1	208.0
PB 4/5	$2.00	$100	19,088	$50	$0.01	2	25.0	0.5	208.0
PB 3/5+	$2.00	$100	12,245	$50	$0.01	2	25.0	0.5	208.0
X PB 4/5+	$3.00	$40,000	648,976	$13,333	$0.06	2	6,666.7	128.2	312.0
X PB 4/5	$3.00	$200	19,088	$67	$0.01	2	33.3	0.6	312.0
X PB 3/5+	$3.00	$200	12,245	$67	$0.02	2	33.3	0.6	312.0
MM 4/5+	$1.00	$10,000	689,065	$10,000	$0.01	2	5,000.0	96.2	104.0
MM 4/5	$1.00	$150	15,313	$150	$0.01	2	75.0	1.4	104.0
MM 3/5+	$1.00	$150	13,781	$150	$0.01	2	75.0	1.4	104.0
X MM 4/5+	$2.00	$40,000	648,976	$20,000	$0.06	2	10,000.0	192.3	208.0
X MM 4/5	$2.00	$400	19,088	$200	$0.02	2	100.0	1.9	208.0
X MM 3/5+	$2.00	$400	12,245	$200	$0.03	2	100.0	1.9	208.0
L6 5/6	$2.00	$2,478	55,491	$1,239	$0.04	2	619.5	11.9	208.0
L6 4/6	$2.00	$87	1,033	$44	$0.08	2	21.8	0.4	208.0
LM 6/7	$1.67	$6,973	299,305	$4,184	$0.02	1	4,183.8	80.5	86.7
LM 5/7	$1.67	$138	4,751	$83	$0.03	1	82.8	1.6	86.7
LM 4/7	$1.67	$20	214	$12	$0.09	1	12.0	0.2	86.7
LM 3/7+	$1.67	$20	230	$12	$0.09	1	12.0	0.2	86.7
Pick 3	$0.50	$250	1,000	$500	$0.25	14	35.7	0.7	364.0

As you can see, the games with the highest return to the players are both the Pick 4 and Pick 3 games.



Next, we examine the Per Dollar Prize amounts. Here, we see that only 4 prize levels return as much money per dollar spent as that of Pick 4. These are the Powerball and Mega Millions payouts for matching 4 white balls and the Power or Mega ball.



Now lets consider the amount of time we have before we reach the $0 (zero dollar) profit level. Of the 6 prizes that exceed the 6.9 year level, total amount spent is substantially higher than the Pick 4 total of $2,500.



Lastly, we illustrate the yearly cost of purchasing one single ticket for each of the games. Here, we see that the Pick 4 and Pick 3 cost is highest. However, this is primarily a function of there being 14 drawings held in a week verses 2 for most games (and 1 for Lotto Max).



Summary
In summary, we believe that playing 1 Pick 4 combination continually in each drawing is a viable strategy for those lottery players looking to earn investment income at a relatively low and affordable cost!

JL ..............