Lottery Odds Calculator

How to Use This Calculator

1. Enter numbers to pick and pool size (e.g. 6 and 49 for 6/49).
2. Enter a bonus ball pool for Powerball/Mega-style games, or 0 for standard.
3. Enter the jackpot amount and ticket cost for EV.
4. Use the Known Lotteries tab to look up Powerball, Mega Millions, etc.
5. Use Professional for after-tax EV and syndicate analysis.

Formula

Example

Frequently Asked Questions

• What are the odds of winning Powerball? ▼
  Powerball jackpot odds are 1 in 292,201,338 (pick 5 from 69, then 1 Powerball from 26). Mega Millions: 1 in 302,575,350. EuroMillions: 1 in 139,838,160. UK National Lottery: 1 in 45,057,474.
• How are lottery odds calculated? ▼
  Using combinations: C(n,k) = n! / (k! × (n−k)!). For 6/49: C(49,6) = 13,983,816. For Powerball: C(69,5) × 26 = 11,238,513 × 26 = 292,201,338.
• Is a lottery ticket ever positive EV? ▼
  Rarely. A $2 Powerball ticket needs a jackpot of ~$585M pre-tax (or ~$928M at 37% tax) to break even. In practice, jackpots are split, taxes take 37%+, and the lump sum is ~60% of advertised prize — making most tickets deeply negative EV.
• Does buying more tickets improve odds significantly? ▼
  Buying 100 tickets (a 100× improvement) at 1 in 292 million still gives odds of 1 in 2.9 million — still astronomically unlikely. A syndicate of 100 costs 100× more but wins 1/100th the payout per member.
• What is the expected value of a lottery ticket? ▼
  EV = (jackpot × win probability) + (prize tier values × their probabilities) − ticket cost. At typical jackpot sizes ($100M), EV is strongly negative (−$1.40 on a $2 ticket). Break-even jackpots require hundreds of millions.

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