Lottery Odds Calculator

Open the Lottery Odds Calculator and leave the defaults if you want a classic 6/49 matrix with a separate bonus pool: main pool 49, main drawn 6, main matches 6, bonus pool 10, bonus drawn 1, bonus matches 1. Those six fields are the entire model. Main pool is how many numbered balls sit in the first drum. Main drawn is how many of those balls the operator extracts. Main matches is the prize tier you are pricing — jackpot when it equals drawn, a lower tier when it is smaller. Bonus pool, bonus drawn, and bonus matches describe a second independent drum (Powerball-style), not a bonus ball drawn from the same 49.

Press calculate. The tool returns three numbers. This Prize Odds is 1 in N for the exact (main matches, bonus matches) pair you entered. Jackpot Odds is 1 in N for matching every main ball and every bonus ball. This Prize Probability restates the prize as a percentage so you can drop it into a spreadsheet. With the defaults, jackpot and this-prize coincide: you asked for 6 of 6 plus 1 of 1, so both read 1 in 139,838,160 (C(49,6)×C(10,1) = 13,983,816×10). The probability is about 0.000000715 percent.

To price a mid-tier instead of the jackpot, change only Main Matches. Set matches to 3 and leave the rest. Hypergeometric probability of exactly three of six from 49 is C(6,3)×C(43,3)/C(49,6) = 246,820 / 13,983,816, or roughly 1 in 56.66. If the bonus drum is still active, the tool multiplies by the bonus-match hypergeometric as well; set Bonus Pool to 0 when the game has no second drum so that factor stays 1.

Work a German-style 6/49 Superzahl by keeping pool 49, drawn 6, matches 6, bonus pool 10, bonus drawn 1. Work a Canadian 6/49 with no bonus by zeroing the three bonus fields: jackpot then collapses to 1 in 13,983,816. Work a 5/90 SuperEnalotto-like matrix with pool 90, drawn 6, matches 6, bonus 0: C(90,6) = 622,614,630. The calculator does not care about the brand printed on the slip; it only cares about n, k, m and the optional second pool.

Common mistakes: entering “matches 6” when you meant “I matched 3 last night”; treating a bonus ball drawn from the same urn as an independent bonus pool (that is not independent — leave bonus pool at 0 and drop matches to 5 if you want 5+bonus from one drum, which this simplified model does not encode); and reading 1:N as a prediction rather than a combinatorial identity. Recalculate whenever the operator changes matrix size. The fields accept integers only; fractions of a ball do not exist.

Lotteries are finite uniform draws without replacement. Every published jackpot table in a regulator’s brochure is a hypergeometric identity dressed up as marketing. The Lottery Odds Calculator exists so you can rebuild that table for any matrix — 6/49, 5/69+1/26, 5/50+2/12, 6/90 — without memorising a national brand. SorteCalc ships dedicated pages for named games; this tool is the generic engine underneath them.

The 6/49 format is the twentieth-century default. Lotto 6/49 launched in Canada in 1982; Germany’s 6aus49, Spain’s La Primitiva, Poland’s Lotto, and dozens of copycats use the same C(49,6) = 13,983,816 denominator. Adding a 0–9 Superzahl or a 1–10 bonus ball multiplies the jackpot denominator by ten and creates extra prize tiers (5+bonus, 4+bonus) that the operator can price with the same formula. Powerball and Mega Millions later split the bonus into its own urn so the operator can inflate jackpot odds without changing the white-ball count as aggressively.

Why a generic calculator still matters: matrices change. UK Lotto moved from 6/49 to 6/59. EuroMillions has altered Lucky Star counts. Australian Powerball redesigned the grid. A branded page goes stale; a parameterised hypergeometric does not. Journalists comparing “which lottery is hardest” routinely confuse 1-in-N jackpot odds with expected wait in years (which also depends on draw frequency) and with the odds of any prize (which is dominated by the 2-match and 3-match tiers). This tool isolates the combinatorial layer.

Use it as a sanity check on official “odds of winning” charts. If an operator lists 1 in 13,983,816 for 6/49 jackpot, they omitted the bonus drum or they do not have one. If they list 1 in 139,838,160, they included a 1-from-10 bonus. If they list something that is not an integer ratio of binomial coefficients, they are rounding, bundling multiplier add-ons, or describing a raffle overlay rather than the matrix.

The calculator is educational, not a prediction service. It assumes each ticket is an unordered k-subset (or k-subset plus independent bonus subset), uniform over the combinations, with no multiplier, no raffle, no double-play, and no guaranteed jackpot insurance. It does not model prize-fund rollovers, pari-mutuel leakage, or the chance someone else hits the same line. Pair it with the jackpot EV, wheeling, and multi-ticket tools when you want money or coverage rather than a single 1-in-N figure.

William Feller, in the combinatorics chapters of An Introduction to Probability Theory and Its Applications, treats a lottery as sampling without replacement from a finite urn. That is the correct classroom model for a numbered-ball drawing: every unordered k-subset of an n-pool is equally likely, and the ticket itself is such a subset. An independent bonus drum is a second urn. Because the machines do not share balls, the two probabilities multiply. Lottery combinatorics is therefore hypergeometric arithmetic dressed as a prize chart, not a sequence of coin tosses.

The default matrix on this page is a main pool of forty-nine with six balls drawn and a prize request of six main matches, together with a bonus pool of ten from which one ball is drawn and one bonus match is required. Matching every main number and every bonus number is the jackpot by definition. At those defaults the prize you are pricing is the jackpot, so the two 1-in-N readouts coincide. There is no hidden extra factor beyond the product of the two drums.

Hypergeometric counting answers a precise question. After the operator has marked k winning mains in a pool of n, you ask for exactly m hits on a k-number ticket. Favourable tickets choose m of the k winners and fill the leftover k minus m spots from the n minus k losers. The denominator is the number of equally likely k-subsets of n. Written with binomial coefficients, the main-match probability is C(k, m) times C(n minus k, k minus m), all divided by C(n, k), provided those binomial counts exist; otherwise the probability is identically zero. That mass function is the entire main-drum theory.

Jackpot on the main drum is the special case m equals k, which collapses the numerator to one, so the probability is simply one over C(n, k). For six-from-forty-nine the denominator is 13,983,816. The independent bonus jackpot factor is one over C(10, 1), namely one tenth. The product is therefore one over 139,838,160. Equivalently one may write C(6, 6) C(43, 0) / C(49, 6) times C(1, 1) / C(10, 1); both displays are the same identity. That is how to calculate the default prize and the default jackpot on this page.

Mid-tier prizes keep the same identity and drop m below k. Exactly three mains with no bonus is C(6, 3) C(43, 3) / C(49, 6) = 246,820 / 13,983,816, roughly one in 56.66. Exactly five mains is 258 / 13,983,816, about one in 54,201. A bonus ball taken from the same urn as the mains is not an independent second pool; zero the bonus fields when the game has a single drum. Combinations, not permutations: tickets are unordered sets, so the denominator is C(n, k) rather than the falling factorial P(n, k).

Assumptions are uniform combinations, no multiplier sticker, no raffle overlay, and no order of extraction. A 1-in-N figure is not a prediction of next Saturday and it is not a waiting time in weeks; waiting times need a draw calendar. Recalculate whenever the operator changes n or k. Feller would also insist that occupancy among many tickets is a separate problem from the chance that one given ticket matches m balls. This lecture prices one ticket against one drawing.