Australia Powerball Odds Calculator

This is Australian Powerball, Thursday night, The Lott — not the US 5/69+1/26 game and not Saturday Lotto. Defaults: Tickets 1, Ticket Price AU$1.20, Jackpot 20,000,000, Main Matches 7, Bonus Matches 1. The matrix is seven numbers from 1–35 plus one Powerball from 1–20. Calculate and read Jackpot Odds: 1 in 134,490,400, which is C(35,7)×C(20,1)=6,724,520×20. That is the only way Division 1 pays. Jackpot Chance on one ticket is about 7.44×10^−9 as a percentage, and Jackpot EV at a $20 million headline is about −AU$1.05 because you still spend $1.20 on an expected jackpot return near 15 cents.

Leave Main Matches at 7 and set Bonus Matches to 0. You are now asking for seven correct mains and a missed Powerball: This Prize Odds become 1 in 7,078,442, twenty times easier than the jackpot because 19 of 20 Powerballs fail. That division exists in the real prize table; this calculator will show the probability even though it will not name the division. Put Bonus Matches back to 1 and drop Main Matches to 6 to price six mains plus the Powerball (about 1 in 686,176). Six mains without the Powerball is Main Matches 6 and Bonus Matches 0, near 1 in 36,115.

Tickets scales the at-least-once chance as 1−(1−p)^n with p the jackpot probability, not the prize you are inspecting. A Thursday office syndicate with 100 games should enter 100. Chance stays microscopic; EV goes to about −AU$105 at the $20 million default. If you bought a System entry that expands into 8 or 28 standard games, count the standard games, not the playslip rows. Price stays AU$1.20 per game unless you are modelling a promotional discount, which is rare.

Jackpot is the advertised Division 1 pool in Australian dollars. Paste the Thursday figure. Australia has printed Powerball headlines above AU$200 million, including the April 2024 region around $200 million that still gets quoted in newsagents. At $200 million and one ticket, EV=200,000,000/134,490,400−1.20≈1.487−1.20=+0.29 dollars before splits — one of the few default-matrix lotteries where a record roll can push jackpot-only EV through zero. That still ignores sharing, tax treatment, and every lower division.

Do not confuse this form with Saturday Lotto (6/45, 80 cents, Saturday, no Powerball) or Oz Lotto (7/47, $2.50, Tuesday, no Powerball). The Bonus Matches field exists here because there is a 1–20 Powerball. It does not exist on those two pages. If Bonus Matches is blank in your head, you are pricing the wrong Australian game.

Australian Powerball launched in 1996 as the Thursday national jackpot and was rebuilt on 26 April 2018 into the current 7-from-35 plus Powerball 1-from-20 matrix. Before that change the game was 6/40+1/20 with far softer Division 1 odds. The 2018 rebuild was explicitly about larger advertised jackpots: C(35,7)×20=134,490,400 possible tickets, in the same harsh neighbourhood as Oz Lotto’s 7/47 but with a separate Powerball drum. The Lottery Corporation sells it through The Lott, Tatts, and the state shop brands. It is not a franchise of US Powerball; the name is a generic product label that Australia used decades ago.

Thursday is the draw night. Saturday remains TattsLotto/Saturday Lotto, Tuesday remains Oz Lotto. Mixing those three is how people quote the wrong odds in a beer garden. Powerball tickets are AU$1.20 per game, cheaper than Oz Lotto’s $2.50, which is why a $150 million Powerball headline feels “cheap to chase” even though the combination count is more than double Oz Lotto’s. Cheap per line is not cheap per unit of probability.

The record zone around AU$200 million, including the April 2024-scale jackpots, is the cultural memory that sends newsagents queues around the block. Pari-mutuel Division 1 means the pool is a share of sales plus previous rolls. A single winner takes it; a syndicate or two independent tickets sharing the numbers split it. This calculator’s EV assumes one winner. When the whole country buys the same QuickPick patterns on a $200 million week, the sharing risk is not theoretical.

System entries are the other Australian habit. A System 8 on 7/35 is C(8,7)=8 games; you still need the Powerball correct for Division 1. Enter 8 in Tickets at $1.20, or compute EV on the $9.60 outlay as one bundle. The engine does not expand systems for you. Powerball Plus-style add-ons from other countries are not this product; do not paste South African or US rules into Thursday’s form.

Use the page to separate “we matched six and the Powerball” from “we matched seven and missed the Powerball,” to watch EV flip sign only at absurd advertised pools, and to stop treating Australian Powerball as a rebadged Mega Millions. It is a 7/35+1/20 Thursday game with a $1.20 line and a 134 million combination space.

The Division 1 prize of Australian Powerball is calculated from two independent drums, and it is not the United States Powerball matrix. Seven unordered mains are drawn from thirty-five; a Powerball is drawn from twenty. The main count is C(35,7) = 35 × 34 × 33 × 32 × 31 × 30 × 29 / 5,040 = 6,724,520. Multiply by twenty Powerballs to reach 134,490,400 tickets. Jackpot probability is 1 / 134,490,400, about 7.44 × 10^−9, or one in 134,490,400. United States Powerball is five from sixty-nine plus one from twenty-six (292,201,338). South African PowerBall is five from fifty plus one from twenty (42,375,200). Thursday night in Australia is this 7/35 plus 1/20 game only. Before April 2018 the Australian product was 6/40 plus 1/20; that historical ticket does not belong in this count.

Hypergeometric scores on the thirty-five-ball drum are P(exactly m mains) = C(7,m) × C(28, 7−m) / 6,724,520, then multiplied by 1/20 or 19/20 according to the Powerball. Seven mains and the Powerball is the jackpot, one in 134,490,400. Seven mains and a missed Powerball is 19 / 134,490,400, about one in 7,078,442. Six mains plus the Powerball is 196 / 134,490,400, about one in 686,176. Six mains without the Powerball is about one in 36,115. Those products are exact combinatorial cells, not Monte Carlo.

Independent Thursday games give at-least-once chance 1 − (1 − p)^n with the jackpot p. Ten games sit near 7.44 × 10^−8. One hundred games sit near 7.44 × 10^−7. Linear scaling holds until n approaches the hundred-million combination wall.

Expectation is ticket count times (jackpot times p minus stake). Default stake is AU$1.20 and default advertised jackpot is $20 million, so one game contributes 20,000,000 / 134,490,400 − 1.20 ≈ 0.149 − 1.20 = −$1.051. Ten games: about −$10.51. Jackpot-only breakeven with one winner is 1.20 × 134,490,400 = AU$161,388,480. A record-scale $200 million headline can push jackpot-only expected value through zero (200,000,000 / 134,490,400 − 1.20 ≈ +$0.29) before sharing, tax treatment, and every lower division. Sharing risk rises with sales in those weeks, so the sign flip is fragile.

Assumptions: uniform independent drums, independent games, one Division 1 winner, Australian dollars, $1.20 stake, 2018 matrix, and no confusion with Oz Lotto's 7/47 Tuesday game or Saturday Lotto's 6/45. Cheap per line is not cheap per unit of probability: $1.20 times 134 million combinations is still a harsh purchase at ordinary pools.