Expected Value Calculator

What's the mathematical value of a lottery ticket?

Calculate the expected value (EV) of any lottery game to understand the mathematical reality behind lottery tickets. Every game has a negative expected value, meaning you lose money over time. This calculator shows you exactly how much.

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Lottery Game Parameters

Cost of one ticket
Current jackpot prize
Total possible number combinations (C(n,k))
× winners
Optional: Second prize amount and number of winners

Expected Value Analysis

Popular Lottery Games

Understanding Expected Value

Expected Value (EV) is the average outcome of a random event if you repeated it many times. For lotteries, it's always negative because the probability of winning is extremely low.

EV = (Probability of Winning × Prize) + (Probability of Losing × Loss)

For a lottery ticket:

  • Probability of winning jackpot: 1 / total combinations
  • Prize if you win: Jackpot amount (minus taxes)
  • Probability of losing: 1 - (1 / total combinations)
  • Loss if you lose: Ticket price

Real Examples:

Powerball ($2 ticket, $100M jackpot)

EV: -$1.66 per ticket

Break-even jackpot: $584 million

Mega Millions ($2 ticket, $80M jackpot)

EV: -$1.68 per ticket

Break-even jackpot: $605 million

Pick 3 ($1 ticket, $500 prize)

EV: -$0.50 per ticket

Break-even odds: 1 in 2

Key Insights

  • All lotteries have negative EV: You always lose money over time
  • House edge: Lotteries keep 40-60% of ticket sales as profit
  • Break-even jackpot: The jackpot needed to make EV positive
  • Second prizes matter: They slightly improve EV but not enough
  • Entertainment value: Some play for fun, knowing they'll lose money
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