Lottery Odds Calculator · Hypergeometric Probability + EV — Vectobox
Free hypergeometric lottery odds + expected value calculator for Powerball, Mega Millions, EuroMillions, UK Lotto, 双色球 and 大乐透. Every prize tier verified against the issuing commission's official chart. Pure browser, zero tracking.
Pure browser. Zero upload. Your picks never leave this tab.
5 from 1-69 + 1 from 1-26 · USD 2 · revised 2017-08-23
| Match | Prize | Odds | Formula |
|---|---|---|---|
| 5 main + 1 bonus | Jackpot (variable) | 1 / 292,201,338 | (i)C(5,5)·C(64,0)·C(1,1)·C(25,0) / [C(69,5)·26]Source: www.powerball.com |
| 5 main | $1,000,000 | 1 / 11,688,053.52 | (i)C(5,5)·C(64,0)·C(1,0)·C(25,1) / [C(69,5)·26]Source: www.powerball.com |
| 4 main + 1 bonus | $50,000 | 1 / 913,129.18 | (i)C(5,4)·C(64,1)·C(1,1)·C(25,0) / [C(69,5)·26]Source: www.powerball.com |
| 4 main | $100 | 1 / 36,525.17 | (i)C(5,4)·C(64,1)·C(1,0)·C(25,1) / [C(69,5)·26]Source: www.powerball.com |
| 3 main + 1 bonus | $100 | 1 / 14,494.11 | (i)C(5,3)·C(64,2)·C(1,1)·C(25,0) / [C(69,5)·26]Source: www.powerball.com |
| 3 main | $7 | 1 / 579.76 | (i)C(5,3)·C(64,2)·C(1,0)·C(25,1) / [C(69,5)·26]Source: www.powerball.com |
| 2 main + 1 bonus | $7 | 1 / 701.33 | (i)C(5,2)·C(64,3)·C(1,1)·C(25,0) / [C(69,5)·26]Source: www.powerball.com |
| 1 main + 1 bonus | $4 | 1 / 91.98 | (i)C(5,1)·C(64,4)·C(1,1)·C(25,0) / [C(69,5)·26]Source: www.powerball.com |
| 0 main + 1 bonus | $4 | 1 / 38.32 | (i)C(5,0)·C(64,5)·C(1,1)·C(25,0) / [C(69,5)·26]Source: www.powerball.com |
| Any prize | — | 1 / 24.87 | Σ tier probs |
How are these odds computed?
Every tier probability is the hypergeometric formula `C(K, k)·C(M−K, K−k) / C(M, K)` for the main pool, multiplied by the analogous term for the independent bonus pool when one exists. C(n, k) is the binomial coefficient (number of n-choose-k subsets). For Powerball the jackpot is `C(5,5)·C(64,0) / C(69,5) × 1/26 = 1 / 292,201,338` — matching the figure printed on every ticket. UK Lotto's 7th ball is drawn from the same 53 remaining balls, so its 5+bonus tier uses `C(6,5)·C(53,1) / [C(59,6)·53] = 1 / 7,509,579` instead of the generic two-pool form.
Lifetime probability is not (1/N) × tickets
A common error is treating odds linearly: "1 in 292M jackpot × 4,160 tickets in 80 years = 1 in 70,240". The correct formulation is `1 − (1 − 1/N)^n`, evaluated as `−expm1(n · log1p(−1/N))` to stay numerically stable at tiny probabilities. For weekly Powerball over 80 years this gives ~1.42×10⁻⁵ jackpot probability, not 1.42×10⁻⁵ × any naïve scaling.
Expected value vs jackpot size
Gross EV is the sum over every tier of `prize × probability`. Powerball at a $40 M jackpot gives a gross EV well below the $2 ticket price; you need a roughly $600 M jackpot before the gross EV crosses $2 (and that's still before tax, annuity discount, and split-jackpot risk). The EV here is GROSS — UI subtracts the ticket price for the (net gain) / (net loss) label.
Lottery odds & disclaimers
All prize structures and 1-in-N values are copied from the issuing lottery commission's official chart, with the source URL embedded in each tier's formula popover. This calculator does not solicit, sell, or facilitate lottery participation; it is an educational probability tool. Past draws have no predictive value (every draw is independent). If gambling is harming you or someone you know, US: 1-800-GAMBLER · UK: 0808 8020 133 · CN: 12320.
FAQ
- Why does the calculator's odds differ slightly from a published 1-in-N value?
- Lottery commissions usually round 1-in-N values to two decimals for display (e.g. Powerball 0+1 → 1 in 38.32). This calculator computes the hypergeometric value directly and may display 1 / 38.33 because the underlying probability is closer to 0.02609. Both are correct — ours just doesn't round.
- Why is UK Lotto special?
- UK Lotto draws 6 main balls then a 7th "bonus" ball from the same remaining 53 balls — it does NOT have an independent bonus pool. The generic two-pool hypergeometric formula doesn't apply to the 5+bonus tier, so this calculator uses the canonical 1 / 7,509,579 from the National Lottery game procedures document.
- Why is the expected value negative?
- Lotteries are designed so that the expected value per ticket is below the ticket price; otherwise the operator could not fund prizes, retailer commissions, and good-causes contributions. EV crosses break-even only at exceptionally large advertised jackpots — and even then, taxation, lump-sum discounting, and the probability of sharing the jackpot with other winners typically push the true EV back below ticket price.
- Is anything I enter sent to a server?
- No. Every probability, combination, and lifetime calculation runs in your browser. There are no network requests, no analytics on your picks, and no third-party scripts on the math.
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