Break-Even Calculator

When does a lottery ticket become a 'fair' bet?

Find out how big the jackpot needs to be for your ticket to have positive expected value. Spoiler: It's a lot bigger than you think, and even then, you probably won't win.

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$ million

Calculation Options

Understanding Lottery Expected Value

The Simple Formula

EV = (Prize × Probability) − Ticket Cost

If EV is negative, you lose money on average. If positive, you "profit" on average (though you'll almost certainly never see that profit).

Reality Checks

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Cash vs Annuity

The advertised jackpot is the annuity value paid over 30 years. The cash option is typically 50-60% less. This dramatically affects EV.

🏛️

Taxes Take a Bite

Federal tax is 37% on winnings over ~$500K. Many states add another 5-13%. A $1B jackpot might become $300M after taxes.

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Splitting the Prize

Big jackpots attract more players. A $2B jackpot might have 3-5 winners splitting it. This effect is hard to predict but very real.

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Secondary Prizes

We ignore them in break-even calculations, but they add small value back. Still not enough to make lotteries good investments.

🎯 The Bottom Line

Even when the theoretical EV goes positive, it's still a terrible "investment" because:

  • Variance is astronomical. You need to buy millions of tickets to "realize" that positive EV.
  • One ticket = almost certain loss. Your ticket will almost certainly be worth $0.
  • Risk of ruin is 99.9999997%. That's your chance of NOT winning the jackpot.
  • Opportunity cost matters. $2 invested in the S&P 500 has actual expected gains.

Play for entertainment, not profit. If $2 of fun is worth it to you, go ahead. Just don't call it an investment strategy.

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