## Superceded - See Revised Mega Millions Megaplier Analysis (February 2011)

The Mega Millions Megaplier is a special feature that gives players the opportunity to increase the size of their winnings. By purchasing the Megaplier option for \$1 more, all prizes except the Jackpot will be multiplied by either 2, 3, or 4 depending what is drawn. The multiplier will be selected from a pool of 21 numbers. The pool contains (2) 2's,(7) 3's, and (12) 4's.

The average Megaplier multiplier is 3.47619, which is used for calculation purposes. This is determined by taking the probability weighted average of the four possible multipliers: ( ( 2 * 2 ) + ( 7 * 3 ) + ( 12 * 4 ) ) / 21 = 3.47619

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 1 Mega Millions Ticket against buying 1 ticket with the Megaplier Option for \$2. The higher the return, the better for players.

 Table MM-MP1 Mega Millions Summary Money Returned to Players per \$1 Spent Jackpot \$0 \$12,000,000 \$47,207,272 \$90,000,000 1 Ticket \$0.182 \$0.250 \$0.451 \$0.694 w/ Megaplier \$0.316 \$0.350 \$0.451 \$0.523 Breakeven

As Table MM-MP1 illustrates, the Megaplier Option returns more money to players when the Jackpot is less than \$47,207,272. When the Jackpot is greater than this amount, more money is returned to players who buy tickets without the Megaplier Option. Thus, we recommend the following rule:

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

J = Breakeven Jackpot Amount - Calculated
O = Odds of Winning Jackpot - 175,711,536 given
m = multiplier - 3.47619 Calculated (see above)
c = constant ( sum( p(i)*prize(i) where i=2,n ) - 0.182 from Table MM-MP3a

### How These are Calculated

Probability     \$0 Jackpot
Constant Variable 'c'
\$12 Million Jackpot     \$47,207,272 Million
Jackpot Breakeven
\$90 Million Jackpot
 Table MM-MP2 Mega Millions Probability Matrix One Ticket Won Probability 5+mb 0.000001% 5 0.000026% 4+mb 0.000145% 4 0.006531% 3+mb 0.007256% 3 0.326530% 2+mb 0.118518% 2 5.333315% 1+mb 0.711109% 1 31.999891% 0+mb 1.336884% 0 60.159795%

 Table MM-MP3a Mega Millions \$1 Single Ticket No Megaplier Won Prize Prob Wtd 5+mb 0 \$0.000 5 250,000 \$0.064 4+mb 10,000 \$0.015 4 150 \$0.010 3+mb 150 \$0.011 3 7 \$0.023 2+mb 10 \$0.012 2 \$0.000 1+mb 3 \$0.021 1 \$0.000 0+mb 2 \$0.027 0 \$0.000 Per \$ \$0.182
Constant Variable 'c'

 Table MM-MP3b Mega Millions \$1 Single Ticket No Megaplier Won Prize Prob Wtd 5+mb 12,000,000 \$0.068 5 250,000 \$0.064 4+mb 10,000 \$0.015 4 150 \$0.010 3+mb 150 \$0.011 3 7 \$0.023 2+mb 10 \$0.012 2 \$0.000 1+mb 3 \$0.021 1 \$0.000 0+mb 2 \$0.027 0 \$0.000 Per \$ \$0.250

 Table MM-MP3c Mega Millions \$1 Single Ticket No Megaplier Won Prize Prob Wtd 5+mb 47,207,272 \$0.269 5 250,000 \$0.064 4+mb 10,000 \$0.015 4 150 \$0.010 3+mb 150 \$0.011 3 7 \$0.023 2+mb 10 \$0.012 2 \$0.000 1+mb 3 \$0.021 1 \$0.000 0+mb 2 \$0.027 0 \$0.000 Per \$ \$0.451
Jackpot Breakeven

 Table MM-MP3d Mega Millions \$1 Single Ticket No Megaplier Won Prize Prob Wtd 5+mb 90,000,000 \$0.512 5 250,000 \$0.064 4+mb 10,000 \$0.015 4 150 \$0.010 3+mb 150 \$0.011 3 7 \$0.023 2+mb 10 \$0.012 2 \$0.000 1+mb 3 \$0.021 1 \$0.000 0+mb 2 \$0.027 0 \$0.000 Per \$ \$0.694
With Megaplier Option
 Table MM-MP4a Mega Millions \$2 Single Ticket With 3.47619x Megaplier Won Prize Prob Wtd 5+mb 0 \$0.000 5 869,047.6 \$0.223 4+mb 34,761.9 \$0.050 4 521.4 \$0.034 3+mb 521.4 \$0.038 3 24.3 \$0.079 2+mb 34.8 \$0.041 2 \$0.000 1+mb 10.4 \$0.074 1 \$0.000 0+mb 7.0 \$0.093 0 \$0.000 Sum \$0.633 Per \$ \$0.316
Constant Variable 'c'

 Table MM-MP4b Mega Millions \$2 Single Ticket With 3.47619x Megaplier Won Prize Prob Wtd 5+mb 12,000,000 \$0.068 5 869,047.6 \$0.223 4+mb 34,761.9 \$0.050 4 521.4 \$0.034 3+mb 521.4 \$0.038 3 24.3 \$0.079 2+mb 34.8 \$0.041 2 \$0.000 1+mb 10.4 \$0.074 1 \$0.000 0+mb 7.0 \$0.093 0 \$0.000 Sum \$0.701 Per \$ \$0.350

 Table MM-MP4c Mega Millions \$2 Single Ticket With 3.47619x Megaplier Won Prize Prob Wtd 5+mb 47,207,272 \$0.269 5 869,047.6 \$0.223 4+mb 34,761.9 \$0.050 4 521.4 \$0.034 3+mb 521.4 \$0.038 3 24.3 \$0.079 2+mb 34.8 \$0.041 2 \$0.000 1+mb 10.4 \$0.074 1 \$0.000 0+mb 7.0 \$0.093 0 \$0.000 Sum \$0.901 Per \$ \$0.451
Jackpot Breakeven

 Table MM-MP4d Mega Millions \$2 Single Ticket With 3.47619x Megaplier Won Prize Prob Wtd 5+mb 90,000,000 \$0.512 5 869,047.6 \$0.223 4+mb 34,761.9 \$0.050 4 521.4 \$0.034 3+mb 521.4 \$0.038 3 24.3 \$0.079 2+mb 34.8 \$0.041 2 \$0.000 1+mb 10.4 \$0.074 1 \$0.000 0+mb 7.0 \$0.093 0 \$0.000 Sum \$1.145 Per \$ \$0.572