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Powerball 2012 continues to have a special feature that gives players the opportunity to increase the size of their winnings. By purchasing the Power Play option for $1 more, all prizes except the Jackpot will be increased by a fixed amount. Beginning January 2012, the old multiplier will be retired but all other prizes except the jackpot will be increased by a factor of 2, 3, 4 and 5 times.
For example, the lower tier prize for matching the Powerball and 0 or 1 white ball will increase by 3 times to $12. Those matching 2 white + PB, 3 white (with or without the PB), or 4 white balls only will receive double the standard prizes. If you match 4 white and the Powerball, the prize is increased 4 times to $40,000. And lastly, those matching all 5 white balls but not the Powerball will earn an even $2 million.
Is this a good value for players? Should the player buy this option? Lottery Power Picks believes that the answers are both Yes and No , depending on the Jackpot size.
For this analysis, LotteryPowerPicks calculated and compared the the payout return values of buying one $2 Powerball Ticket against buying a single ticket with the Power Play Option for $3. The higher the return, the better for players.
As shown below, we now calculate the Powerball Powerplay Jackpot Breakeven point to be $112,513,144.
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Table PB-PP1 Powerball Summary
Money Returned to Players per $1 Spent
| | Jackpot | $0 | $40,000,000 | $112,513,144 | $180,000,000
| | 1 Ticket | $0.180 | $0.294 | $0.501 | $0.694
| w/ Power Play | $0.287 | $0.363 | $0.501 | $0.629
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| Breakeven
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As Table PB-PP1 illustrates, the Power Play Option returns more money to players when theJackpot is less than $112,513,144.
When the Jackpot is greater than this amount, more money is returned to players who buy tickets without the Power Play Option.
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Powerball Power Play Rule
Jackpot < $112,513,144: Buy Power Play
Jackpot > $112,513,144: Do NOT Buy Power Play
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How This is Calculated
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| Probability
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| $0 Jackpot
Constant Variable 'c'
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| $40 Million Jackpot
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| $112,513,144 Million
Jackpot Breakeven
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| $180 Million Jackpot
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Table PB-PP2 Powerball
Probability Matrix
One Ticket
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| Won | Probability
| | 5+mb | 0.000001%
| | 5 | 0.000019%
| | 4+mb | 0.000154%
| | 4 | 0.005239%
| | 3+mb | 0.008167%
| | 3 | 0.277668%
| | 2+mb | 0.141556%
| | 2 | 4.812916%
| | 1+mb | 0.902422%
| | 1 | 30.682338%
| | 0+mb | 1.804843%
| | 0 | 61.364676%
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Table PB-PP3a Powerball
$2 Single Ticket
No Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 0 | $0.000
| | 5 | 1,000,000 | $0.194
| | 4+mb | 10,000 | $0.015
| | 4 | 100 | $0.005
| | 3+mb | 100 | $0.008
| | 3 | 7 | $0.019
| | 2+mb | 7 | $0.010
| | 2 | | $0.000
| | 1+mb | 4 | $0.036
| | 1 | | $0.000
| | 0+mb | 4 | $0.072
| | 0 | | $0.000
| | Sum | $0.360
| | Per $ | $0.180
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Constant Variable 'c'
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Table PB-PP3b Powerball
$2 Single Ticket
No Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 40,000,000 | $0.228
| | 5 | 1,000,000 | $0.194
| | 4+mb | 10,000 | $0.015
| | 4 | 100 | $0.005
| | 3+mb | 100 | $0.008
| | 3 | 7 | $0.019
| | 2+mb | 7 | $0.010
| | 2 | | $0.000
| | 1+mb | 4 | $0.036
| | 1 | | $0.000
| | 0+mb | 4 | $0.072
| | 0 | | $0.000
| | Sum | $0.589
| | Per $ | $0.294
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Table PB-PP3c Powerball
$2 Single Ticket
No Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 112,513,144 | $0.642
| | 5 | 1,000,000 | $0.194
| | 4+mb | 10,000 | $0.015
| | 4 | 100 | $0.005
| | 3+mb | 100 | $0.008
| | 3 | 7 | $0.019
| | 2+mb | 7 | $0.010
| | 2 | | $0.000
| | 1+mb | 4 | $0.036
| | 1 | | $0.000
| | 0+mb | 4 | $0.072
| | 0 | | $0.000
| | Sum | 1.003
| | Per $ | $0.501
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Jackpot Breakeven
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Table PB-PP3d Powerball
$2 Single Ticket
No Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 180,000,000 | $1.027
| | 5 | 1,000,000 | $0.194
| | 4+mb | 10,000 | $0.015
| | 4 | 100 | $0.005
| | 3+mb | 100 | $0.008
| | 3 | 7 | $0.019
| | 2+mb | 7 | $0.010
| | 2 | | $0.000
| | 1+mb | 4 | $0.036
| | 1 | | $0.000
| | 0+mb | 4 | $0.072
| | 0 | | $0.000
| | Sum | $1.388
| | Per $ | $0.694
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| With Power Play Option
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Table PB-PP4a Powerball
$3 Single Ticket
with Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 0 | $0.000
| | 5 | 2,000,000 | $0.388
| | 4+mb | 40,000 | $0.062
| | 4 | 200 | $0.010
| | 3+mb | 200 | $0.016
| | 3 | 14 | $0.039
| | 2+mb | 14 | $0.020
| | 2 | | $0.000
| | 1+mb | 12 | $0.108
| | 1 | | $0.000
| | 0+mb | 12 | $0.217
| | 0 | | $0.000
| | Sum | $0.860
| | Per $ | $0.287
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Table PB-PP4b Powerball
$3 Single Ticket
with Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 40,000,000 | $0.228
| | 5 | 2,000,000 | $0.388
| | 4+mb | 40,000 | $0.062
| | 4 | 200 | $0.010
| | 3+mb | 200 | $0.016
| | 3 | 14 | $0.039
| | 2+mb | 14 | $0.020
| | 2 | | $0.000
| | 1+mb | 12 | $0.108
| | 1 | | $0.000
| | 0+mb | 12 | $0.217
| | 0 | | $0.000
| | Sum | $1.088
| | Per $ | $0.363
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Table PB-PP4c Powerball
$3 Single Ticket
with Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 112,513,144 | $0.642
| | 5 | 2,000,000 | $0.388
| | 4+mb | 40,000 | $0.062
| | 4 | 200 | $0.010
| | 3+mb | 200 | $0.016
| | 3 | 14 | $0.039
| | 2+mb | 14 | $0.020
| | 2 | | $0.000
| | 1+mb | 12 | $0.108
| | 1 | | $0.000
| | 0+mb | 12 | $0.217
| | 0 | | $0.000
| | Sum | $1.502
| | Per $ | $0.501
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Jackpot Breakeven
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Table PB-PP4d Powerball
$3 Single Ticket
with Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 180,000,000 | $1.027
| | 5 | 2,000,000 | $0.388
| | 4+mb | 40,000 | $0.062
| | 4 | 200 | $0.010
| | 3+mb | 200 | $0.016
| | 3 | 14 | $0.039
| | 2+mb | 14 | $0.020
| | 2 | | $0.000
| | 1+mb | 12 | $0.108
| | 1 | | $0.000
| | 0+mb | 12 | $0.217
| | 0 | | $0.000
| | Sum | $1.887
| | Per $ | $0.629
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