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%.