# 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.

### 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