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Revised February 1, 2011 to account that the second level Megaplier prize of matching 5 white balls but not the Megaball will automatically be fixed at $1 million.
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.
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Table MM-MP1 Mega Millions Summary
Money Returned to Players per $1 Spent
| | Jackpot | $0 | $12,000,000 | $53,100,120 | $90,000,000
| | 1 Ticket | $0.182 | $0.250 | $0.484 | $0.694
| w/ Megaplier | $0.333 | $0.367 | $0.484 | $0.589
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| Breakeven
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As Table MM-MP1 illustrates, the Megaplier Option returns more money to players when the Jackpot is less than $53,100,120. 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:
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Mega Millions Megaplier Rule
If Jackpot < $53,100,120: Buy Megaplier
If Jackpot > $53,100,120: Do NOT Buy Megaplier
Introducing the Multiplier Jackpot Breakeven Formula
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
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How These are Calculated
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| Probability
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| $0 Jackpot
Constant Variable 'c'
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| $12 Million Jackpot
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| $53,100,120 Million
Jackpot Breakeven
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| $90 Million Jackpot
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Table MM-MP2 Mega Millions
Probability Matrix
One Ticket
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| 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%
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Table MM-MP3a Mega Millions
$1 Single Ticket
No Megaplier
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| 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
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Constant Variable 'c'
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Table MM-MP3b Mega Millions
$1 Single Ticket
No Megaplier
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| 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
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Table MM-MP3c Mega Millions
$1 Single Ticket
No Megaplier
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| Won | Prize | Prob
Wtd
| | 5+mb | 53,100,120 | $0.302
| | 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 $ | $0.0.484
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Jackpot Breakeven
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Table MM-MP3d Mega Millions
$1 Single Ticket
No Megaplier
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| 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
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| With Megaplier Option
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Table MM-MP4a Mega Millions
$2 Single Ticket
With 3.47619x Megaplier
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| Won | Prize | Prob
Wtd
| | 5+mb | 0 | $0.000
| | 5 | 1,000,000.0 | $0.256
| | 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 | $0.666
| | Per $ | $0.333
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Constant Variable 'c'
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Table MM-MP4b Mega Millions
$2 Single Ticket
With 3.47619x Megaplier
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| Won | Prize | Prob
Wtd
| | 5+mb | 12,000,000 | $0.068
| | 5 | 1,000,000.0 | $0.256
| | 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 | $0.734
| | Per $ | $0.367
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Table MM-MP4c Mega Millions
$2 Single Ticket
With 3.47619x Megaplier
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| Won | Prize | Prob
Wtd
| | 5+mb | 53,100,120 | $0.302
| | 5 | 1,000,000.0 | $0.256
| | 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 | $0.968
| | Per $ | $0.484
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Jackpot Breakeven
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Table MM-MP4d Mega Millions
$2 Single Ticket
With 3.47619x Megaplier
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| Won | Prize | Prob
Wtd
| | 5+mb | 90,000,000 | $0.512
| | 5 | 1,000,000.0 | $0.256
| | 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 | $1.178
| | Per $ | $0.589
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Calculating the Mega Millions Breakeven Jackpot
J = O*(m-2)*c
J = 175,711,536*(3.47619-1.66046219)*0.182
J = $53,100,120
References
A Revised Look at the Mega Millions Megaplier Option
Superceded Mega Millions Megaplier Analysis (Original - Pre Febuary 2011)
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