Last Updated: January 5, 2016

# Powerball Calculator

## Introduction

The calculator that follows will calculate the odds for the Powerball lottery, or any lottery, such as Powerball, based on the same formula 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 return to the amount bet. The total return in the lower right cell is the overall expected return, before considering taxes and jackpot sharing.

## Rules

The following rules are based on the last known set of rules changes in January, 2014.

1. The cost of a Powerball ticket is \$2.
2. The player will choose 5 White Balls from 1 to 69 and one Powerball from 1 to 26.
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 Power Play.
7. If the Power Play is invoked, any win will be multiplied by a random multiplier, except the top two prizes. The exceptions are that the jackpot is never multiplied and the multiplier for catching all five White Balls, but not the Power Ball, is always 2.
8. To determine the Power Play multiplier, one ball is selected from 42 or 43 with the following multipliers: 24 balls at 2x, 13 balls at 3x, 3 balls at 4x, 2 balls at 5x. There is also one ball at 10x added to the pool of the jackpot is under \$150 million. This equates to an average multiplier of 2.595 without the 10x ball and 2.767 with it.
9. California has funky rules, where the fixed prizes also grow and there is no Power Play option.

## Calculator

The default values are current wins as of the latest rule change on October 7, 2015. The wins should be before applying the Power Play multiplier.

 Largest White Ball Largest Power Ball Cost of ticket Cost of Power Play Average Power Play multiplier

Check if betting the Power Play:

 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 have a significant effect in lowering the overall value. I find the relationship between jackpot size and ticket sales is exponential. Given the hysteria, and subsequent enormous ticket sales, that always accompanies large jackpots, I find that the Powerball is never a good value. Based on the Oct. 7, 2015 rule changes, I find that the optimal time to play is with a jackpot of \$557 million, but even then the expected return, all things considered, is 81.3%.

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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