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Beginning with the January 22 2014 drawing, Powerball 2014 reinstituted the variable multiplier option 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 factor of 2, 3, 4 and 5 times. This multiplier will be determined by a seperate Powerplay drawing, in which 1 number will be drawn from a set of 30.
For example, the lower tier Powerplay prize when matching the Powerball and 0 or 1 white balls will range from $8 to $20. Those matching 2 white + PB, or 3 white will receive $14 to $35; and winners matching 3 white + PB or 4 white balls receive $200 to $500. Lastly, anyone who matches 4 white + PB will win $20,000 to $50,000. However, the match 5 white balls Powerplay prize is fixed at $2 million.
The distribution of Powerplay multiplier numbers includes: 15 2s, 9 3s, 3 4s, and 3 5s. This means that the there will be a 50% probability of a 2x multiplier, 30% probability of a 3x multiplier, a 10% probability of a 4x multiplier, and a a 10% probability of a 5x multiplier.
Thus, the weighted average multiplier is 2.8x, which will be used for this analysis.
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, Lottery Power Picks compared the the payout return values of buying a single $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 $109,831,912.
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Table PB-PP1 Powerball Summary
Money Returned to Players per $1 Spent
| | Jackpot | $0 | $40,000,000 | $109,831,912 | $180,000,000
| | 1 Ticket | $0.180 | $0.294 | $0.494 | $0.694
| w/ Power Play | $0.285 | $0.361 | $0.494 | $0.627
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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 $109,831,912.
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 < $109,831,912: Buy Power Play
Jackpot > $109,831,912: 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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| $109,831,912 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 | 109,831,912 | $0.627
| | 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 | 0.987
| | Per $ | $0.494
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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 | 28,000 | $0.043
| | 4 | 280 | $0.015
| | 3+mb | 280 | $0.023
| | 3 | 19.6 | $0.054
| | 2+mb | 19.6 | $0.028
| | 2 | | $0.000
| | 1+mb | 11.2 | $0.101
| | 1 | | $0.000/
| | 0+mb | 11.2 | $0.202
| | 0 | | $0.000
| | Sum | $0.854
| | Per $ | $0.285
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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 | 28,000 | $0.043
| | 4 | 280 | $0.015
| | 3+mb | 280 | $0.023
| | 3 | 19.6 | $0.054
| | 2+mb | 19.6 | $0.028
| | 2 | | $0.000
| | 1+mb | 11.2 | $0.101
| | 1 | | $0.000
| | 0+mb | 11.2 | $0.202
| | 0 | | $0.000
| | Sum | $1.082
| | Per $ | $0.361
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Table PB-PP4c Powerball
$3 Single Ticket
with Power Play
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| Won | Prize | Prob
Wtd
| | 5+mb | 109,831,912 | $0.627
| | 5 | 2,000,000 | $0.388
| | 4+mb | 28,000 | $0.043
| | 4 | 280 | $0.015
| | 3+mb | 280 | $0.023
| | 3 | 19.6 | $0.054
| | 2+mb | 19.6 | $0.028
| | 2 | | $0.000
| | 1+mb | 11.2 | $0.101
| | 1 | | $0.000
| | 0+mb | 11.2 | $0.202
| | 0 | | $0.000
| | Sum | $1.502
| | Per $ | $0.494
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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 | 28,000 | $0.043
| | 4 | 280 | $0.015
| | 3+mb | 280 | $0.023
| | 3 | 19.6 | $0.054
| | 2+mb | 19.6 | $0.028
| | 2 | | $0.000
| | 1+mb | 11.2 | $0.101
| | 1 | | $0.000
| | 0+mb | 11.2 | $0.202
| | 0 | | $0.000
| | Sum | $1.881
| | Per $ | $0.627
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