Oz Lotto Odds Calculator

Open the Oz Lotto odds calculator with Tickets at 1, Ticket Price at AU$2.50, Jackpot at 3,000,000, and Main Matches at 7. That is one standard Tuesday game under The Lott / Tatts matrix: seven numbers from 1–47, no Powerball field. Press calculate and read Jackpot Odds first. For a single line the engine returns 1 in 62,891,499, which is exactly 1/C(47,7). Jackpot Chance is the at-least-once probability for the ticket count you entered, and Jackpot EV is tickets times (jackpot times that tiny p minus price). With the defaults you should see an EV around −AU$2.45: you spend $2.50 to buy a $3 million shot whose mathematical expectation is only a few cents.

Change Tickets to 10 and leave price and jackpot alone. Chance becomes 1−(1−p)^10, which is still about 1.59×10^−7, not ten times a round percentage you can feel. EV scales linearly to about −AU$24.52. That is the whole point of the Tickets field: it does not invent luck, it compounds independent trials. A Tuesday syndicate that splits 50 lines should type 50, not 1, so the EV and the chance both describe the book, not one member’s share of the cost.

Ticket Price defaults to AU$2.50 because that is the standard Oz Lotto game cost. If you bought a System 8 (C(8,7)=8 games) type 8 in Tickets and keep $2.50, or type 1 ticket at $20 if you want EV on the bundle as a lump. Do not mix the two conventions. Jackpot is the Division 1 advertised pool in Australian dollars. Paste the current Tuesday figure from The Lott rather than leaving three million if the pool has rolled; EV is extremely sensitive to that input because p is fixed by the 7/47 barrel.

Main Matches defaults to 7, so This Prize Odds equals Jackpot Odds. Drop Main Matches to 6 to see the hypergeometric chance of exactly six of the seven drawn numbers: about 1 in 224,613. Five matches sit near 1 in 3,840, four near 1 in 182. There is no Bonus Matches field on this page because the calculator models Division 1 as 7/47 only. Real Oz Lotto also draws two supplementary numbers from the remaining forty balls to pay Divisions 2–7 (7+1 supp, 6+supp, and so on). Those extra balls do not change C(47,7) and they are not an input here.

Read the six result rows together. Jackpot Odds never moves with tickets; Jackpot Chance and EV do. This Prize Odds and This Prize Chance follow Main Matches. Expected Jackpot Return is tickets × jackpot × p, a few cents on a $3 million headline. If two syndicates hit on the same Tuesday, the published jackpot is split and this EV, which assumes one winner, is too optimistic. Treat the tool as a 7/47 jackpot microscope, not a substitute for The Lott prize table.

Oz Lotto is Australia’s midweek national lottery, launched on 26 February 1994 so the country would have a Tuesday jackpot distinct from Saturday TattsLotto. It is operated under The Lottery Corporation brands — The Lott, Tatts, Gold Lotto, X Lotto, depending on the state — but the barrel is one national 7-from-47 draw. Early Oz Lotto used 45 balls; the field was later widened to 47 to slow Division 1 hits and let advertised jackpots climb. The two supplementary numbers that Australians quote in the pub are real, and they decide almost every prize below the top division. This calculator ignores that second layer on purpose: it prices the jackpot as a pure 7/47 combination, which is the only number that belongs in an EV discussion of Division 1.

Tuesday night is the ritual. Newsagents print playslips with seven crosses, system entries, and QuickPicks; television and the apps read the seven winning numbers plus two supplementary. A Division 1 winner must match all seven main numbers. Matching six plus a supplementary is a different, much more common division and is not what Main Matches=7 computes. If you came here from a US Powerball page, reset your instincts: Oz Lotto has no Powerball, costs AU$2.50 not USD$2, and lives on Tuesday not Saturday. Saturday Lotto is the 6/45 cousin; Australian Powerball is the Thursday 7/35+1/20 cousin. Mixing those three matrices is the most common error this page exists to prevent.

The Lott’s prize fund is a pari-mutuel slice of ticket sales, so the advertised jackpot is a pool, not a fixed annuity. Guaranteed minimums apply on some draws; rollovers stack when nobody matches seven. Headline Division 1 figures in the tens of millions appear after long droughts, which is exactly when people overrate a $2.50 ticket. Combinatorics do not care that the pool looks “due.” C(47,7) stays 62,891,499 every Tuesday until the operator changes the barrel again.

Syndicates, office clubs, and pub tabs are culturally normal in Australia because the 7/47 jackpot is harsh on a single line. Pooling fifty tickets multiplies chance almost linearly at this probability and multiplies expected loss the same way. The calculator’s Tickets field is how you model that book. It will not tell you whether your syndicate’s numbers are “hot”; it will tell you that fifty independent 7/47 lines still miss Division 1 with probability (1−1/62,891,499)^50, which is indistinguishable from 1 for any practical evening.

Use this page when you want the honest Tuesday jackpot probability, a hypergeometric look at six-or-five matches, and a jackpot-only expected value in Australian dollars. Do not use it as a full prize-table replica, a tax engine, or a prediction tool. Supplementary divisions, prize splitting, and state-by-state claiming rules live on The Lott, not in these six output rows.

The Division 1 prize of Oz Lotto is calculated as seven unordered numbers from forty-seven, a Tuesday national barrel under The Lott, with no Powerball field at all. Combinations: C(47,7) = 47 × 46 × 45 × 44 × 43 × 42 × 41 / 5,040. The falling product is 317,073,154,960; divide by 5,040 to obtain 62,891,499 equally likely tickets. Single-line jackpot probability is therefore 1 / 62,891,499, about 1.590 × 10^−8, or one in 62,891,499. Early Oz Lotto used forty-five balls; the later widening to forty-seven is already inside this count. Two supplementary numbers drawn from the remaining forty balls pay lower Australian divisions and never change C(47,7).

Hypergeometric overlap for a seven-spot ticket against seven draws from forty-seven is P(exactly m) = C(7,m) × C(40, 7−m) / 62,891,499. Matching six is 7 × 40 / 62,891,499 = 280 / 62,891,499, about one in 224,613. Matching five is 21 × 780 / 62,891,499 = 16,380 / 62,891,499, about one in 3,840. Matching four is 35 × 9,880 / 62,891,499 = 345,800 / 62,891,499, about one in 182. Those figures are exact-m on the seven mains, not “six plus a supplementary,” which is a different official division.

Independent Tuesday lines give at-least-once chance 1 − (1 − p)^n. Ten games sit near 1.59 × 10^−7. Fifty syndicate lines still miss Division 1 with probability indistinguishable from one for any practical evening. A full wheel of the matrix at the default AU$2.50 game cost would be about $157.2 million before sharing.

Expectation uses ticket count times (jackpot times p minus price). Defaults are a $2.50 game and a $3 million advertised Division 1, so one line contributes 3,000,000 / 62,891,499 − 2.50 ≈ 0.0477 − 2.50 = −$2.452. Ten games: about −$24.52. Jackpot-only breakeven with one winner is 2.50 × 62,891,499 = AU$157,228,747.50. Ordinary Tuesday pools do not live there. Expected jackpot return on the $3 million headline is only about five cents, which is why a rolled “due” pool is not a bargain.

Assumptions: uniform seven-subsets of forty-seven, independent games, one Division 1 winner, Australian dollars, $2.50 stake, supplementary balls omitted from the jackpot term, and no Saturday 6/45 or Thursday Powerball mixed in. Australian Powerball is seven from thirty-five plus one from twenty. Saturday Lotto is six from forty-five. Both are different lectures.