With both methods of adjustment it is the better bet, or more accurately, the least bad bet.
We can adjust these expected returns even further to exclude prize levels with odds that are worse than 1 in a million. However, the jackpots are smaller and less seductive.
. This gives a new set of adjusted expected returns:
Powerball: $0.1172 per $1Powerball w/ Power Play: $0.2027 per $1Mega Millions: $0.1202 per $1Mega Millions w/ Megaplier: $0.2323 per $1
With these calculations, the regular Powerball lottery has the worst expected return, while the Mega Millions with Megaplier has the best expected return.
Comparison to Hot Lotto: The smaller multi-state lottery game Hot Lotto has an adjusted expected return of $0.2656 per $1 bet, so it’s a better bet than either Powerball or Mega Millions, with or without the Megaplier and Power Play options. The Megaplier option expected return is calculated using an average multiplier value of 3.86667, while the Power Play option expected return is calculated using an average multiplier value of 2.59524. Most state lotteries offer a higher return than Powerball and Mega Millions. Statistically this is extraordinarily unlikely event that can safely be disregarded. P and M are divided by very large numbers that come from the odds and the price of a ticket. The regular Powerball ticket without the Power Play option has the lowest adjusted expected return on the dollar, while Mega Millions with Megaplier option has the highest adjusted expected return per dollar.
In the table, P stands for your share of the Powerball jackpot and M stands for your share of the Mega Millions jackpot. Since P and M vary and are unpredictable, one cannot know the precise unadjusted value of the expected return. Remember, jackpots can be split among two or more winning tickets.
Conclusion: To maximize the expected return per dollar, buy the $2 Mega Millions ticket with the Megaplier option. This excludes the second-tier prizes from the calculations, since you can consider the second-tier prizes to be somewhat outlier events. This gives us the adjusted expected returns
Powerball: $0.1599 per $1Powerball w/ Power Play: $0.2597 per $1Mega Millions: $0.1742 per $1Mega Millions w/ Megaplier: $0.3368 per $1
As you can see, the expected returns are all under $1, meaning you get back less than you “invest.” Equivalently, the expected profits are negative, i.e., a loss. But we can compare the adjusted expected returns of all four lottery options.
To adjust these returns, we ignore the outlier event of winning the jackpot