Should You Buy the Power Play, Sizzler, or Megaplier?

Introduction
Very often, someone asks me whether they should buy the Powerball Power Play Option. Not knowing the mathematical answer, my gut feeling was to tell them No. However, since one popular website encourages players to sign a petition to add a Megaplier Option to the Mega Millions lottery, I had my doubts. At present, the State of Texas offers this option. More recently, I read that Hot Lotto would be adding a Sizzler Option beginning in January 2008.

Realizing the importance of this topic, it was time to conduct research on this topic. What I learned is that for each of these three lottery options, the answer to the question:

Should I Buy the Power Play, Sizzler, or Megaplier?

The correct answer is both Yes and No!
It depends on the size of the Jackpot.

How do you know when to buy it?
You should always buy the multiplier option whenever the current jackpot value is below its Jackpot Breakeven level.

• For Powerball, Breakeven is $43.2 million: Buy the Power Play Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
• For Hot Lotto, Breakeven is $2.59 million: Buy the Sizzler Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
• For Mega Millions, Breakeven is $47.2 million: Buy the Megaplier Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.

Why is that?
The reason is that the Jackpot prizes in each of these lotteries are not multiplied. So, as the Jackpot increases above its minimum, only the probability weighted amount of jackpot money returned to players increases. At some point, which we call Jackpot Breakeven, the jackpot returns outweigh the sum of the payouts of all the other prizes. Once this is reached, buying the multiplier option is not a good investment. Remember, because the multiplier option costs $1 more, it is necessary to divide these probability weighted returns by 2 before comparing them to single $1 tickets. When the jackpot is above the breakeven level, the per dollar return of multiplier tickets becomes less and less valuable compared to that of a regular ticket.

As lottery players, we want to play the option that returns the most money back to us, the players. As you will see below, your option changes depending on the jackpot level.

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Powerball Power Play
When a player buys the Power Play option, any prize that the player wins, except the Jackpot, will be multiplied by either 2, 3, 4 or 5. The odds that any one of these multipliers will occur is (typically) a constant 25%, which means that a player can expect an average 3.5 times multiplier on average.

Based on this assumption, the graph below illustrates both the expected Power Play return (in blue) against the expected return of a single Ticket without the Power Play (in red).

When the jackpot is set to the minimum $15 million, Power Play returns $0.396 of each dollar received, compared to $0.300 for those without the option.

When the jackpot level reaches $43.2 million, both tickets with and without the Power Play returns $0.493 for each dollar received. We refer to this $43.2 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Power Play return more to the players. When the jackpot grows to $90 million, $0.813 is returned to straight ticket holders compared to only $0.653 to those who bought the Power Play.


Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Powerball jackpot is below $43.2 million, the Power Play should be purchased. When the jackpot is above this level, never purchase the Power Play. Go for the Jackpot instead.

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Hot Lotto Sizzler
When a player buys the Sizzler option, any prize that the player wins, except the Jackpot, will be multiplied by a fixed 3 times.

Given this, the graph below illustrates both the expected Sizzler return (in blue) against the expected return of a single Ticket without the Sizzler (in red).

When the jackpot is set to the minimum $1 million, Sizzler returns $0.401 of each dollar received, compared to $0.329 for those without the option.

When the jackpot level reaches $2.59 million, both tickets with and without Sizzler returns $0.474 of each dollar received. We refer to this $2.59 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Sizzler return more to the players. When the jackpot grows to $5 million, $0.694 is returned to straight ticket holders compared to only $0.584 to those who bought the Sizzler.


Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Hot Lotto jackpot is below $2.59 million, the Sizzler should be purchased. When the jackpot is above this level, never purchase the Sizzler. Go for the Jackpot instead.

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Mega Millions Megaplier (available only in Texas)
When a player buys the Megaplier option, any prize that the player wins, except the Jackpot, will be multiplied by either 2, 3, or 4. The odds that any one of these multipliers will occur is not constant, but on the average, a player can expect an average 3.476 times multiplier.

Based on this assumption, the graph below illustrates both the expected Megaplier return (in blue) against the expected return of a single Ticket without the Megaplier (in red).

When the jackpot is set to the minimum $12 million, Megaplier returns $0.350 of each dollar received, compared to $0.250 for those without the option.

When the jackpot level reaches $47.2 million, both tickets with and without Megaplier returns $0.451 of each dollar received. We refer to this $47.2 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Megaplier return more to the players. When the jackpot grows to $90 million, $0.694 is returned to straight ticket holders compared to only $0.523 to those who bought the Megaplier.



Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Mega Millions jackpot is below $47.2 million, the Megaplier should be purchased. When the jackpot is above this level, never purchase the Megaplier. Go for the Jackpot instead.

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Conclusion
As you can see, the decision to buy the Power Play, Sizzler, or Megaplier multiplier option is dependent upon the jackpot size. When the jackpot is below its breakeven level, players are encouraged to buy the multiplier option. But, when the jackpot is above its breakeven level, players should forego this option, and buy 2 straight tickets instead.


Learn More
To learn more about this subject, visit our in-depth pages that provide the detailed numbers behind each of these options.

• Powerball Power Play Analysis
• Hot Lotto Sizzler Analysis
• Mega Millions Megaplier Analysis

Focus for February: The Canadian Territories

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