Lottery: Mega Millions

Introduction

The calculator will calculate the odds for the Mega Millions, or any similar game such as Powerball, based on the same formal of five regular balls and one extra ball.

The defaults shown are the fixed prizes for all wins except the jackpot. The win for the jackpot shown is roughly the current jackpot amount.

The return column shows the ratio of the expected win to the amount bet for each event. In other words, the relative value of that prize to the amount bet. The total return in the lower right cell is the overall expected return of the, before considering taxes, the time value of annuity payments, and jackpot sharing.

Rules

The following rules are based on the last known set of rules changes in October, 2017.
 

1. The cost of a ticket is $2.
2. The player will choose 5 White Balls from 1 to 70, and one Mega Ball from 1 to 25.
3. Twice a week, the Lottery will randomly choose the same number of balls from the same ranges.
4. The pay table is shown in the default values of the calculator below.
5. The jackpot starts at $40 million and grows by a percentage of sales with every drawing that nobody wins the jackpot.
6. For an extra $1, the player may also bet the Megaplier.
7. If the Megaplier is invoked, any win will be multiplied by a random multiplier, except the top prize.
8. The Megaplier is determined electronically. However, it equates to choosing one of 15 outcomes, with the following distribution per multiplier: 2x: 5, 3x: 6, 4x: 3, 5x: 1. This equates to an average multiplier of 71/15=4.7333.
9. California has funky rules, where the fixed prizes also grow and there is no Megaplier option.

 

Calculator

The default values are currents wins (as of October 27, 2017). The wins should be before applying the Megaplier.

Largest White Ball
Largest Power Ball
Cost of ticket
Cost of Megaplier
Average Megaplier

Check if betting the Megaplier:


 

Event	Pays	Combinations	Probability	Return
5 + PB
5
4 + PB
4
3 + PB
3
2 + PB
2
1 + PB
1
0 + PB
0
Total

 

Disclaimer: The values in the return column do not reflect taxes, the time value of annuity payments, and jackpot sharing. These all play a significant effect of lowering the overall value. I find there the relationship between jackpot size and ticket sales is exponential, causing the value of a ticket to be significantly reduced due to jackpot sharing. In short, the Mega Millions is never remotely close to a good bet.

Internal Links

• Powerball calculator.
• Powerball analysis.
• Pick Six calculator.
• Probabilities in the Lottery.
• Former Ask the Wizard questions about the lottery.
• Are Lottery Players Smart?
• Lottery Jackpot Ticket Sales Calculator — Estimate ticket sales and probability of a winner for any jackpot size for the Power Ball and MegaMillions.

External Links

• Maryland — page.
• Wikipedia — page.

Written by:Michael Shackleford