Last Updated: September 10, 2014

# 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 is never remotely close to a good bet.

Powerball \$ 160000000
Euro Millions 89000000
SuperEnalotto 51000000
Mega Millions \$ 45000000
SuperLotto Plus \$ 33000000
Lotto Max CA\$ 30000000
FDJ Loto 20000000
Lotto 19000000
Lotto 6/49 CA\$ 17000000
Vikinglotto 11800000
Eurojackpot 10000000
Mega Sena R\$ 59000000
Lotto Texas \$ 9000000
Melate MXN 160800000
Lotto \$ 7300000
Swiss Lotto CHF 5700000
El Gordo 5400000
Powerball AU\$ 8000000
Megabucks \$ 5500000
Powerball R 77000000
Saturday Lotto AU\$ 5000000
La Primitiva 3100000
Powerball NZ\$ 5000000
Lotto \$ 3000000
Lotto £ 2000000
Pick 6 \$ 2500000
Lotto 6aus49 2000000
Ontario 49 CA\$ 2000000
Oz Lotto AU\$ 2000000
Hoosier Lotto \$ 1200000
Daily Million 9PM 1000000
Daily Million 2PM 1000000
Monday & Wednesday Lotto AU\$ 1000000
Thunderball £ 500000
Fantasy 5 \$ 286000
Jersey Cash 5 \$ 258000
Two Step \$ 200000

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