Lottery EV Calculator

Calculate the expected value of any lottery ticket

Formula:EV = (Jackpot × (1-Tax) / Odds) + Other Prizes - Cost

Lottery Parameters

Enter lottery details to calculate EV

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Expected Value Analysis

Very Poor Value

Expected Value Per Ticket
-$1
Average loss per ticket

Return Rate

26.8%

House Edge

73.2%

Jackpot EV

$0

After-Tax Jackpot

$63,000,000

Break-Even Analysis

The jackpot would need to reach $779,203,568 for this ticket to have zero expected value (break even), assuming no other winners.

EV Breakdown

Jackpot EV Component:$0
Other Prizes EV:$0
Ticket Cost:-$2
Total Expected Value:-$1
Note: This calculation assumes you're the only winner. Large jackpots attract more players, increasing split probability and reducing actual EV. The true EV is likely even lower than calculated.

Example Scenarios

Quick-start with common scenarios

Quick Answer

Lottery EV = (Jackpot × (1 - Tax Rate) / Odds) + (Other Prizes EV) - Ticket Cost. For a $100M Powerball: EV ≈ ($100M × 0.63 / 292M) + $0.32 - $2 = -$1.46 per ticket. Most lotteries have -40% to -50% EV, meaning you lose $0.80-$1.00 for every $2 spent on average.

Key Facts

  • Most lottery tickets have -40% to -50% expected value
  • Break-even jackpot for Powerball is ~$600M+ (varies with sales/splits)
  • Non-jackpot prizes add about $0.32 to Powerball EV
  • Federal tax (24% withholding, 37% top bracket) significantly reduces EV
  • State taxes range from 0% (California) to 13%+ (New York City)
  • Multiple winners split the jackpot, reducing your EV
  • Higher jackpots attract more players, increasing split probability
  • Lottery is worse EV than most casino games (slots: -5% to -15%)

FAQ

What is expected value (EV) in lottery?

Expected value is the average amount you can expect to win (or lose) per ticket over many purchases. It's calculated by multiplying each prize by its probability and summing the results, then subtracting the ticket cost. A negative EV means you lose money on average.

Why is lottery EV always negative?

Lotteries must fund prizes, operations, and state revenue from ticket sales. Typically only 50-60% of revenue goes to prizes. Combined with taxes on winnings, the mathematical return is significantly less than what you pay.

When does the lottery become positive EV?

Theoretically, when jackpots get extremely large (Powerball ~$600M+), the EV can turn positive before taxes. However, higher jackpots attract more players, increasing the probability of splitting the prize, which reduces actual EV. Practically, lottery is almost never +EV.

How do taxes affect lottery EV?

Taxes dramatically reduce EV. Federal withholding is 24%, with a top bracket of 37%. State taxes vary from 0% to 13%+. A $100M jackpot might net only $35-40M after all taxes, cutting the EV component by more than half.

Should I consider non-jackpot prizes in EV?

Yes. Non-jackpot prizes (Match 5, Match 4, etc.) add meaningful value. In Powerball, these prizes contribute about $0.32 to the EV per ticket. However, this still doesn't overcome the overall negative EV.