Lottery Odds Calculator & Number Analyzer
Calculate exact odds for any lottery game, analyze expected value per ticket, simulate draws to debunk hot-number myths, and generate quick picks.
Select a Lottery Game
Jackpot Odds
Your chance of winning:1 in 292,201,338
3.4223e-9 probability
Prize Tiers
| Match | Odds (1 in X) | Prize | EV Contribution |
|---|---|---|---|
| 5 + PB | 292,201,338 | $200,000,000 | $0.6845 |
| 5 | 11,688,054 | $1,000,000 | $0.0856 |
| 4 + PB | 913,129 | $50,000 | $0.0548 |
| 4 | 36,525 | $100 | $0.0027 |
| 3 + PB | 14,494 | $100 | $0.0069 |
| 3 | 580 | $7 | $0.0121 |
| 2 + PB | 701 | $7 | $0.0100 |
| 1 + PB | 92 | $4 | $0.0435 |
| 0 + PB | 38 | $4 | $0.1044 |
Expected Value Analysis
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Advertised jackpots are 30-year annuity values; the lump-sum cash option is typically 45-55% of the headline. EV uses the number you enter, so enter the cash value for the honest version.
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Total EV per Ticket$-0.9957-EV (Unfavorable)
Return on Investment-49.78%
+EV Jackpot Threshold$490,936,628Jackpot must exceed this for +EV
Expected Loss per 1,000 Tickets$996
Break-Even Jackpot $846.4M Jackpot needed for this ticket to become +EV Current jackpot is 24% of break-even
Tax-Adjusted EV$-1.2831Federal 37% + State 5% = 42% on jackpot
Jackpot Split Chance40.2%Expected share: 78.2% of prize
100-Ticket StrategySame numbers vs random
Same numbers P(win) = 3.422e-7 EV = $-167.33
Random (100 tickets) P(at least 1 win) = 3.422e-5 EV = $-99.57
Identical tickets split the jackpot with each other, so copies add lower-tier value only. Distinct random picks keep the full jackpot chance on every ticket. Neither escapes the negative EV.
Quick Pick Generator
Number Frequency Simulator
Simulate thousands of draws to see how number frequency converges. This demonstrates that no numbers are truly "hot" or "cold", every number has equal probability over time.
Lottery Odds Comparison
| Game | Format | Jackpot Odds | Any Prize Odds | Ticket Cost | EV Loss (typical jackpot, pre-tax) |
|---|---|---|---|---|---|
| Powerball | 5/69 + 1/26 | 1 in 292,201,338 | 1 in 25 | $2.00 | -$1.00 |
| Mega Millions | 5/70 + 1/24 | 1 in 290,472,336 | 1 in 23 | $5.00 | -$3.71 |
| Pick 3 | 3 digits 0-9 | 1 in 1,000 | 1 in 143 | $1.00 | -$0.02 |
| Pick 4 | 4 digits 0-9 | 1 in 10,000 | 1 in 400 | $1.00 | -$0.02 |
| Pick 6 (6/49) | 6/49 | 1 in 13,983,816 | 1 in 54 | $2.00 | -$1.41 |
You're More Likely To...
Putting Powerball's 1 in 292,201,338 odds into perspective:
⚡Be struck by lightning this year1 in 1,222,000239x more likely
🦈Be attacked by a shark1 in 3,748,06778x more likely
☄️Be hit by a meteorite1 in 1,600,000183x more likely
🎬Become a movie star1 in 1,505,000194x more likely
🏆Win an Olympic gold medal1 in 662,000441x more likely
♠️Get a royal flush in poker1 in 649,740450x more likely
🧢Find a four-leaf clover on first try1 in 10,00029,220x more likely
🎲Roll a six 5 times in a row1 in 7,77637,577x more likely
Understanding Lottery Mathematics
How Lottery Odds Work
Lottery odds are calculated using combinatorics. For a game where you pick k numbers from a pool of n, the total combinations are C(n,k) = n! / (k!(n-k)!). For Powerball, that's C(69,5) x 26 = 292,201,338 possible outcomes. Each ticket has exactly one chance per outcome, so the odds are truly astronomical.
The Expected Value Trap
A $2 Powerball ticket returns about $1.00 in raw expected value at a $200M advertised jackpot, and that is the generous version: the advertised figure is a 30-year annuity (cash value roughly half), the jackpot is taxed, and big draws get split. Adjust for all three and the real return is closer to $0.60, a 60-70% house take. Even record jackpots barely reach break-even on paper.
Why Hot/Cold Numbers Don't Work
Each lottery draw is an independent event. Past results have zero influence on future outcomes. The "law of large numbers" means frequencies converge over millions of draws, not that overdue numbers become more likely. Use our simulator above to see this principle in action with your own eyes.
Lottery Pools & Syndicates
Pooling tickets with others increases your coverage but splits winnings proportionally. A pool of 100 people buying 100 tickets improves jackpot odds from 1-in-292M to about 1-in-2.92M, but each share is only 1% of the prize. Mathematically, EV per dollar spent remains identical whether playing solo or in a pool.
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