2014 Powerball Lottery

Power Play Recommendation Analysis

Effective January 19, 2014


Recommendation:
Buy xxx?
answer
Here's Why:
blah blah

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.



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
  Breakeven  
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.

Powerball Power Play Rule

Jackpot < $109,831,912: Buy Power Play

Jackpot > $109,831,912: Do NOT Buy Power Play





How This is Calculated

Probability     $0 Jackpot
Constant Variable 'c'
    $40 Million Jackpot     $109,831,912 Million
Jackpot Breakeven
    $180 Million Jackpot
Table PB-PP2 Powerball
Probability Matrix
One Ticket
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%
   
Table PB-PP3a Powerball
$2 Single Ticket
No Power Play
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
Constant Variable 'c'

   
Table PB-PP3b Powerball
$2 Single Ticket
No Power Play
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
   
Table PB-PP3c Powerball
$2 Single Ticket
No Power Play
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
Jackpot Breakeven

   
Table PB-PP3d Powerball
$2 Single Ticket
No Power Play
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
With Power Play Option    
Table PB-PP4a Powerball
$3 Single Ticket
with Power Play
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


   
Table PB-PP4b Powerball
$3 Single Ticket
with Power Play
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
   
Table PB-PP4c Powerball
$3 Single Ticket
with Power Play
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
Jackpot Breakeven

   
Table PB-PP4d Powerball
$3 Single Ticket
with Power Play
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