STATISTICSProbability TheoryStatistics Calculator
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Lottery Calculator

Lottery odds calculator. Powerball, Mega Millions, UK Lotto, EuroMillions. Pick-k-from-n odds, expec

Run CalculatorExplore data analysis and statistical calculations

Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

🎰
LOTTERY ODDSPick-k-from-n format with powerball

Lottery Calculator — Odds for Any Pick-k-from-n Format

Jackpot odds, match probabilities, expected value. Powerball, Mega Millions, UK Lotto, EuroMillions, and custom formats.

Roulette Payout →Expected Value →

Real-World Scenarios — Click to Load

Inputs

Set m=0 for no bonus ball. EuroMillions: use k=5, n=50, m=66 (C(12,2) for 2 lucky stars).

lottery_odds.sh
CALCULATED
$ lottery --k=6 --n=49 --m=0
1 in 13,983,816
Probability: 0.00000715%
Expected value
$-1.28
Ticket cost
$2
Jackpot
$10,000,000
Format
6/49
Share:
Lottery Calculator Result
1 in 13,983,816
0.00000715%
EV: $-1.28Format: 6/49
numbervibe.com/calculators/statistics/lottery-calculator

Match Probability Table

MatchProbabilityOdds (1 in X)
Match 60.0000%1.40e+7
Match 50.0018%54,200.837
Match 40.0969%1,032.397
Match 31.7650%56.656
Match 213.2378%7.554
Match 141.3019%2.421
Match 043.5965%2.294

Calculation Breakdown

COMPUTATION
Combinations C(n,k)
13,983,816
C(49,6)
COMPUTATION
Bonus factor
1
No bonus ball
RESULT
Jackpot odds
1 in 13,983,816
1 / (C(n,k) × m)
RESULT
Jackpot probability
0.00000715%
1 / ext{odds}
RESULT
Expected value
$-1.28
jackpot × P(jackpot) − ticket_cost

Match Probability Bar Chart

Probability Comparison (relative)

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • • Powerball odds are 1 in 292 million — you are ~4× more likely to be struck by lightning
  • • Expected value is almost always negative — lotteries are designed so the house wins
  • • Lottery is entertainment, not investment — play for fun, not profit
  • • Match probabilities follow the hypergeometric distribution
  • • Bonus balls multiply odds: Pick 5 from 69 + 1 from 26 → odds = C(69,5) × 26

Did You Know?

🎰Powerball changed to 5/69+1/26 in 2015, making jackpots harder to winSource: Powerball history
📊Expected value can briefly turn positive when jackpots roll over to hundreds of millionsSource: EV analysis
🌍EuroMillions uses 5/50 + 2/12 (lucky stars) — odds about 1 in 139 millionSource: EuroMillions
🎫UK Lotto 6/59 has better odds than Powerball — 1 in 45 millionSource: UK National Lottery
⚡Odds of being struck by lightning: ~1 in 1,000,000 per year in the USSource: NOAA
🃏Royal flush in poker: 1 in 649,740 — much more likely than any major lotterySource: Poker probability

Expert Tips

Treat as entertainment

Set a budget and never expect to win

EV is almost always negative

Only briefly positive during huge rollovers

Compare to other risks

Lightning, shark attacks — lottery is far less likely

Smaller lotteries

Pick 3, Fantasy 5 have much better odds (but smaller prizes)

Comparison Table

LotteryFormatJackpot Odds
Powerball5/69 + 1/261 in 292M
Mega Millions5/70 + 1/251 in 302M
UK Lotto6/591 in 45M
EuroMillions5/50 + 2/121 in 139M
6/49 Classic6/491 in 14M
Fantasy 55/361 in 377K

Frequently Asked Questions

Why is expected value almost always negative?

Lotteries keep ~50% of revenue for prizes and overhead. The rest funds programs. So on average, you get back less than you pay.

When can expected value be positive?

Rarely, when jackpots roll over to hundreds of millions. Even then, taxes and annuity reduce the effective value.

What are Powerball odds?

1 in 292,201,338. Pick 5 from 69 white balls + 1 from 26 red Powerballs.

How does the bonus ball affect odds?

Multiply base combinations by the bonus pool size. Powerball: C(69,5)×26. EuroMillions: C(50,5)×C(12,2).

What is the hypergeometric distribution?

Used for drawing without replacement. Match j of k: C(k,j)×C(n-k,k-j)/C(n,k).

Is the lottery a tax on hope?

Often said. It disproportionately affects lower-income players. Play responsibly.

What is EuroMillions format?

5/50 + 2/12 (lucky stars). Odds = C(50,5) × C(12,2) = 139,838,160.

How do I enter EuroMillions in this calculator?

Use k=5, n=50, m=66 (since C(12,2)=66).

By the Numbers

292M
Powerball odds
1 in 1M
Lightning strike
~50%
Lottery retention
C(n,k)
Combinations

Disclaimer: This calculator is for educational purposes. Lottery odds and expected value are approximate. Play responsibly. Gambling can be addictive.

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