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Rule Changes to Mega Millions Lottery
Logic Puzzle
Before we get to this week’s topic of changes to the Mega Millions lottery, here is our weekly logic puzzle. There are ten coins in groups of 1, 2, 3 and 4, going from left to right. The colors are not relevant. How can you change the direction of the groups, going 4 to 1 from left to right, by moving one coin only? The answer is at the bottom of the newsletter.
Mega Millions Rule Changes
Effective April 5, 2025, the Mega Millions made the following changes to their lottery.
- Cost of a ticket increased from $2 to $5.
- A Megaplier is included, as opposed to an option the player had to pay an extra $1 for.
- The Megaplier now goes as high as 10x, with an average of 3x.
- The number of gold (Mega) balls reduced from 25 to 24.
- Win for matching one white ball and the Mega ball increased from $4 to $7.
- Win for matching zero white balls and the Mega ball increased from $2 to $5.
- Reseed jackpot increased to $50 million.
The following table shows the weighting and probability of each Megaplier. As a reminder, the Megaplier is a multiplier that applies to all wins except the jackpot. The lower right cell shows an average Megaplier of 3x.
| MEGAPLIER | WEIGHT | PROBABILITY | RETURN |
|---|---|---|---|
| 10 | 1 | 0.031250 | 0.312500 |
| 5 | 2 | 0.062500 | 0.312500 |
| 4 | 4 | 0.125000 | 0.500000 |
| 3 | 10 | 0.312500 | 0.937500 |
| 2 | 15 | 0.468750 | 0.937500 |
| TOTAL | 32 | 1.000000 | 3.000000 |
The following table shows the probability and contribution to the return for all fixed wins. The return is the ratio of the expected win to the bet amount, assuming a 3x Megaplier. The lower right cell shows fix wins contribute 22.37% to the total return. By way of comparison, the previous rules contributed 24.70%.
| WHITEBALLS | GOLD BALL | COMBINATIONS | PROBABILITY | PAYS | RETURN |
|---|---|---|---|---|---|
| 5 | 1 | 1 | 0.0000000034 | Jackpot | ? |
| 5 | 0 | 23 | 0.0000000792 | 1000000 | 0.047509 |
| 4 | 1 | 325 | 0.0000011189 | 10000 | 0.006713 |
| 4 | 0 | 7475 | 0.0000257339 | 500 | 0.007720 |
| 3 | 1 | 20800 | 0.0000716075 | 200 | 0.008593 |
| 3 | 0 | 478400 | 0.0016469727 | 10 | 0.009882 |
| 2 | 1 | 436800 | 0.0015037577 | 10 | 0.009023 |
| 1 | 1 | 3385200 | 0.0116541219 | 7 | 0.048947 |
| 0 | 1 | 8259888 | 0.0284360573 | 5 | 0.085308 |
| 2 ot less | 0 | 277883424 | 0.9566605475 | 0 | 0.000000 |
| TOTAL | 290472336 | 1.0000000000 | 0.223695 |
For each $100 million in the jackpot the return increases by 6.89%, before considering the annuity, taxes or jackpot sharing.
Assuming the jackpot is cut in half if invoking the lump sum option and the highest marginal tax rate of 37%, I show the breakeven jackpot is $3,579,287,810. When factoring in jackpot sharing, the game never goes positive, due to positive correlation between jackpot size and ticket sales.
The bottom line is the Mega Millions is still about an equally terrible bet as it was before. You should only play if you get an entertainment value of about 50% the cost of a ticket, even if you lose. If you must play the lottery, the best value is in scratch off tickets. The return of those goes up with the cost. For example, the expected return is better to buy one $20 ticket than 20 $1 tickets. That return is still only about 77%.
Following are some links to my new material on Mega Millions at Wizard of Odds.
Mega Millions page: https://wizardofodds.com/games/lottery/mega-millions
Mega Millions calculator (2025 rules): https://wizardofodds.com/games/mega-millions- calculator-2025-rulescalculator
Solution to logic puzzle
Move the second blue coin from the right to the space between the red and green coins.
