Lottery Math & Odds
Understanding the mathematics and probability behind lottery games. Knowledge is power (even if the odds aren't)!
🎓 How Powerball Works
Powerball requires players to choose 5 numbers from 1-69 (white balls) and 1 number from 1-26 (Powerball).
The Combinatorics Formula
White ball combinations: C(69, 5) = 69! ÷ (5! × 64!) = 11,238,513
Powerball choices: 26
Total possible combinations: 11,238,513 × 26 = 292,201,338
This means if you bought one ticket for every possible combination, you'd spend $584,402,676 to guarantee a jackpot win. The cash value would need to exceed this for it to be "worth it" mathematically!
🎯 Odds by Prize Tier
Your chances of winning each prize level
| Match | Prize | Odds | Probability |
|---|---|---|---|
| 5 + PB | JACKPOT | 1 in 292,201,338 | 0.000000342% |
| 5 | $1M | 1 in 11,688,053.52 | 0.000009% |
| 4 + PB | $50K | 1 in 913,129.18 | 0.00011% |
| 4 | $100 | 1 in 36,525.17 | 0.0027% |
| 3 + PB | $100 | 1 in 14,494.11 | 0.0069% |
| 3 | $7 | 1 in 579.76 | 0.17% |
| 2 + PB | $7 | 1 in 701.33 | 0.143% |
| 1 + PB | $4 | 1 in 91.98 | 1.09% |
| 0 + PB | $4 | 1 in 38.32 | 2.61% |
🧮 Lifetime Odds Calculator
What are your chances of winning if you play regularly over many years?
Your Lifetime Odds
Even after 50 years of playing 1 ticket(s) per week, your odds are still astronomically low. The lottery should be viewed as entertainment, not an investment strategy!
⚡ Odds Comparison
How does winning the Powerball jackpot compare to other unlikely events?
You're roughly 584 times more likely to be struck by lightning than to win the jackpot!
🎯 The Bottom Line
The odds are against you - by design. Lotteries are a form of entertainment, not a sound financial strategy.
Expected value is negative - On average, you'll lose money. For every $2 ticket, you can expect to get back about $0.90 in prizes.
It's okay to play for fun - Just set a budget you can afford to lose, like you would for a movie or concert ticket.
If you do win - Sign the ticket immediately, consult with a lawyer and financial advisor before claiming, and consider the annuity option for financial security.