What is the Expected Value (EV) of a lottery ticket?

The Expected Value (EV) represents the average amount you can expect to win or lose on a lottery ticket if you were to play an infinite number of times. A negative EV, which is common for lotteries, indicates an average statistical loss over the long term. For example, an EV of -$1.50 on a $2.00 ticket means you're expected to lose an average of $1.50 for every ticket purchased.

How do I use this calculator?

To use the calculator, first enter the cost of a single ticket. Then, click 'Add Prize Tier' for each prize level. For each tier, input the prize amount and the odds of winning (e.g., for '1 in 100,000' odds, enter 100000). Once all prize tiers are added, click 'Calculate' to see the Expected Value (EV) and Return on Investment (ROI).

Is a positive EV possible for a lottery?

A positive Expected Value (EV) is extremely rare for standard lotteries but can theoretically occur if a jackpot grows to an exceptionally large size, making the potential payout statistically profitable. However, this does not guarantee a win, and the overall odds of winning the jackpot remain incredibly low.

Lottery Expected Award Value Calculator

What's Your Lottery Ticket Really Worth? Use this Expected Award Value calculator to see the average financial loss or gain per ticket.

Calculator

Cost per Ticket ($)

Prize Tiers

How to Use This Calculator

This tool calculates the Expected Value (EV) of a lottery ticket. EV is the average amount you can expect to win or lose per ticket if you played the lottery an infinite number of times.

Step-by-Step Guide:

Enter Ticket Cost: Input the price of a single lottery ticket in the "Cost per Ticket" field.
Add Prize Tiers:
- Click the "Add Prize Tier" button to create a new line for each prize level.
- For each tier, enter the prize amount and the odds of winning that prize.
- The odds are usually presented as "1 in X". You only need to enter the 'X' value. For example, if the odds are 1 in 302,575,350, enter `302575350`.
Find Lottery Data:
- You can find prize and odds information on official lottery websites such as MegaMillions.com or trusted sources like LotteryUSA.com.
- For example, to find the data for Mega Millions, you would navigate to their specific page.
Handle Jackpots: The jackpot prize is often variable. You can enter the current advertised jackpot amount for your calculation. Note that this is often an annuity value; the cash value will be lower.
Calculate: Once all prize tiers are entered, click the "Calculate" button to see the results.
Remove Tiers: You can remove any prize tier by clicking the 'Remove' button next to it.

Understanding the Results:

Expected Value (EV):
- A negative EV indicates a statistical loss over time. For example, an EV of -$1.50 means you're expected to lose an average of $1.50 for every ticket purchased.
- A positive EV indicates a statistical profit over time. This is extremely rare for standard lotteries.
Return on Investment (ROI): This shows your expected return (or loss) as a percentage of the ticket cost.

For comparison purposes, many Las Vegas, Nevada casinos have expected payout rates of 60% to 99.5% per Las Vegas Casino Games Odds (updated January 30, 2025). In other words, playing casino games, including slot machines, are designed for players to lose money in the long-run.

Disclaimer: This calculator is for informational and entertainment purposes only. Playing the lottery is a game of chance and should be done responsibly.