## Powerball Power Play Analysis

The Powerball has 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 multiplied by either 2, 3, 4 or 5. The multiplier will be selected from a pool of 16 numbers just prior to the Powerball draw. The pool contains (4) 2's,(4) 3's, (4) 4's, and (4) 5's.

The average PowerPlay multiplier is 3.5, which is used for calculation purposes. This is determined by taking the probability weighted average of the four possible multipliers: 0.25 * ( 2 + 3 + 4 + 5 ) = 3.5

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.L%

For this analysis, LotteryPowerPicks calculated and compared the the payout return values of buying 1 Powerball Ticket against buying 1 ticket with the Power Play Option for \$2. The higher the return, the better for players.

 Table PB-PP1 Powerball Summary Money Returned to Players per \$1 Spent Jackpot \$0 \$15,000,000 \$43,200,045 \$90,000,000 1 Ticket \$0.197 \$0.300 \$0.493 \$0.813 w/ Power Play \$0.345 \$0.396 \$0.493 \$0.653 Breakeven
As Table PB-PP1 illustrates, the Power Play Option returns more money to players when theJackpot is less than \$43,200,045. When the Jackpot is greater than this amount, more money is returned to players who buy tickets without the Power Play Option.

### J = O*(m-2)*c

J = Breakeven Jackpot Amount - Calculated
O = Odds of Winning Jackpot - 146,107,962 given
m = multiplier - 3.50 Calculated (see above)
c = constant ( sum( p(i)*prize(i) where i=2,n ) - 0.197 from Table PB-PP3a

### How These are Calculated

Probability     \$0 Jackpot
Constant Variable 'c'
\$15 Million Jackpot     \$43,200,045 Million
Jackpot Breakeven
\$90 Million Jackpot
 Table PB-PP2 Powerball Probability Matrix One Ticket Won Probability 5+mb 0.000001% 5 0.000028% 4+mb 0.000171% 4 0.007015% 3+mb 0.008384% 3 0.343753% 2+mb 0.134147% 2 5.500042% 1+mb 0.788116% 1 32.312750% 0+mb 1.450133% 0 59.455459%

 Table PB-PP3a Powerball \$1 Single Ticket No Power Play Won Prize Prob Wtd 5+mb 0 \$0.000 5 200,000 \$0.056 4+mb 10,000 \$0.017 4 100 \$0.007 3+mb 100 \$0.008 3 7 \$0.024 2+mb 7 \$0.009 2 \$0.000 1+mb 4 \$0.032 1 \$0.000 0+mb 3 \$0.044 0 \$0.000 Per \$ \$0.197
Constant Variable 'c'

 Table PB-PP3b Powerball \$1 Single Ticket No Power Play Won Prize Prob Wtd 5+mb 15,000,000 \$0.103 5 200,000 \$0.056 4+mb 10,000 \$0.017 4 100 \$0.007 3+mb 100 \$0.008 3 7 \$0.024 2+mb 7 \$0.009 2 \$0.000 1+mb 4 \$0.032 1 \$0.000 0+mb 3 \$0.044 0 \$0.000 Per \$ \$0.300

 Table PB-PP3c Powerball \$1 Single Ticket No Power Play Won Prize Prob Wtd 5+mb 43,200,045 \$0.296 5 200,000 \$0.056 4+mb 10,000 \$0.017 4 100 \$0.007 3+mb 100 \$0.008 3 7 \$0.024 2+mb 7 \$0.009 2 \$0.000 1+mb 4 \$0.032 1 \$0.000 0+mb 3 \$0.044 0 \$0.000 Per \$ \$0.493
Jackpot Breakeven

 Table PB-PP3d Powerball \$1 Single Ticket No Power Play Won Prize Prob Wtd 5+mb 90,000,000 \$0.616 5 200,000 \$0.056 4+mb 10,000 \$0.017 4 100 \$0.007 3+mb 100 \$0.008 3 7 \$0.024 2+mb 7 \$0.009 2 \$0.000 1+mb 4 \$0.032 1 \$0.000 0+mb 3 \$0.044 0 \$0.000 Per \$ \$0.813
With Power Play Option
 Table PB-PP4a Powerball \$2 Single Ticket With 3.5x Power Play Won Prize Prob Wtd 5+mb 0 \$0.000 5 700,000 \$0.196 4+mb 35,000 \$0.060 4 350 \$0.025 3+mb 350 \$0.029 3 24.50 \$0.084 2+mb 24.50 \$0.033 2 \$0.000 1+mb 14 \$0.110 1 \$0.000 0+mb 10.5 \$0.152 0 \$0.000 Sum \$0.690 Per \$ \$0.345
Constant Variable 'c'

 Table PB-PP4b Powerball \$2 Single Ticket With 3.5x Power Play Won Prize Prob Wtd 5+mb 15,000,000 \$0.103 5 700,000 \$0.196 4+mb 35,000 \$0.060 4 350 \$0.025 3+mb 350 \$0.029 3 24.50 \$0.084 2+mb 24.50 \$0.033 2 \$0.000 1+mb 14 \$0.110 1 \$0.000 0+mb 10.5 \$0.152 0 \$0.000 Sum \$0.793 Per \$ \$0.396

 Table PB-PP4c Powerball \$2 Single Ticket With 3.5x Power Play Won Prize Prob Wtd 5+mb 43,200,045 \$0.296 5 700,000 \$0.196 4+mb 35,000 \$0.060 4 350 \$0.025 3+mb 350 \$0.029 3 24.50 \$0.084 2+mb 24.50 \$0.033 2 \$0.000 1+mb 14 \$0.110 1 \$0.000 0+mb 10.5 \$0.152 0 \$0.000 Sum \$0.986 Per \$ \$0.493
Jackpot Breakeven

 Table PB-PP4d Powerball \$2 Single Ticket With 3.5x Power Play Won Prize Prob Wtd 5+mb 90,000,000 \$0.616 5 700,000 \$0.196 4+mb 35,000 \$0.060 4 350 \$0.025 3+mb 350 \$0.029 3 24.50 \$0.084 2+mb 24.50 \$0.033 2 \$0.000 1+mb 14 \$0.110 1 \$0.000 0+mb 10.5 \$0.152 0 \$0.000 Sum \$1.306 Per \$ \$0.653