South Africa Lotto Odds Calculator

South Africa’s National Lottery Lotto is a 6-from-52 game operated by Ithuba. Defaults: Tickets 1, Ticket Price 2.50 (rand), Jackpot 3,000,000, Main Matches 6. There is no Bonus Matches field on this page even though the live prize table uses a bonus ball for divisions below the jackpot. This model is 6/52 Division 1 only. Calculate: Jackpot Odds 1 in 20,358,520, which is 1/C(52,6). Jackpot EV at R3 million is about −R2.35, because 3,000,000/20,358,520≈R0.15 of expected jackpot against a R2.50 ticket.

Set Main Matches to 5 for exactly five of the six main numbers: about 1 in 73,763. That is not the official “5+bonus” division; the real draw pulls a bonus ball from the remaining 46, and 5+bonus is a different cell. This calculator will not take a bonus match count because bonusPool is not wired for ZA Lotto here. Use Main Matches as overlap with the six mains only.

Tickets should equal how many independent 6-number boards you hold for that Wednesday or Saturday draw. A township syndicate with 20 boards enters 20. Chance becomes 1−(1−p)^20≈9.82×10^−7. EV≈−R47.05 at the R3 million default. Price is R2.50 per standard board. Lotto Plus 1 / Plus 2, when you add them, are separate draws with their own prize funds; do not fold those extra rands into this Jackpot field unless you are doing a private what-if.

Jackpot is the advertised Lotto Division 1 in rand. Paste Ithuba’s figure. Rollovers are common; a rolled pool still faces the same 20.36 million combinations. Main Matches=6 is the jackpot. Dropping to 4 shows about 1 in 1,311 for exactly four mains — a pub conversation number, not a substitute for Ithuba’s published division odds that include the bonus ball.

Confirm you are not on South African PowerBall (5/50+1/20, R5, Tuesday/Friday). Lotto is 6/52, R2.50, Wednesday and Saturday, since 2000. Read Jackpot Odds as C(52,6), Chance as 1−(1−p)^n, EV as n·(J·p−price) in rand, jackpot-only.

South Africa’s National Lottery opened on 2 March 2000, first under Uthingo, later Gidani, and since 2015 under Ithuba. Lotto is the original 6-from-52 midweek-and-Saturday jackpot, sold in spaza shops, retailers, and digital channels with the familiar rainbow branding. A bonus ball is drawn for the lower divisions; Division 1 remains six main numbers. This calculator refuses to pretend it is a full prize-table clone: it prices the 6/52 jackpot and hypergeometric main-number overlaps, not 5+bonus.

Wednesday and Saturday are the Lotto nights. Tuesday and Friday belong to PowerBall. Mixing those calendars is how people quote 42 million PowerBall odds on a Lotto ticket. R2.50 is the classic Lotto stake, cheaper than PowerBall’s R5, with a softer combination count (20.36 million versus 42.38 million). Cheap is not fair: EV at a R3 million advertised jackpot is still about −R2.35 per board.

Lotto Plus add-on draws recycle your numbers against extra barrels for extra rands. They do not change C(52,6) on the main draw. If you paid for Plus, your total outlay is higher than the R2.50 this Price field defaults to; raise Price only if you insist on stuffing add-on cost into a main-draw EV, which is methodologically messy. Cleaner: model the main Lotto ticket here and treat Plus as another product.

Sharing, rollovers, and pari-mutuel Division 1 are the usual lottery politics. A long roll produces queues and identical QuickPicks. This EV assumes one winner. National Lottery proceeds fund good causes under the licence; that social story does not alter p. Born in 2000, Lotto is younger than Australian Saturday Lotto (1972) and in the same 6-from-N family as many world games, with N=52 sitting between Saturday Lotto’s 45 and Mega-Sena’s 60.

Use the page when you want Ithuba Lotto’s jackpot combinatorics in rand, not when you want the official bonus-ball division chart. For 5/50+PowerBall, switch calculators.

The Division 1 prize of South African Lotto is calculated as six unordered numbers from fifty-two, Ithuba's Wednesday and Saturday game, and the fifty-two is a useful mnemonic because it matches a card deck even though the balls are not suits. Combinations: C(52,6) = 52 × 51 × 50 × 49 × 48 × 47 / 720. The falling product is 14,658,134,400; divide by 720 to obtain 20,358,520. Jackpot probability is 1 / 20,358,520, about 4.91 × 10^−8, or one in 20,358,520. A bonus ball drawn from the remaining forty-six numbers splits some lower official divisions; six-of-six does not use it. National Lottery Lotto opened in 2000 (Uthingo, then Gidani, Ithuba since 2015). This lecture is 6/52, not 6/49 and not PowerBall.

Hypergeometric overlap for a six-spot board is P(exactly m) = C(6,m) × C(46, 6−m) / 20,358,520. Matching five is 6 × 46 / 20,358,520 = 276 / 20,358,520, about one in 73,763. Matching four is 15 × 1,035 / 20,358,520 = 15,525 / 20,358,520, about one in 1,311. Matching three is about one in 67. Official five-plus-bonus odds would multiply the five-match cell by 1/46, about one in 3.39 million; that product is a different row and is omitted here because this jackpot path has no second drum.

Independent boards give at-least-once chance 1 − (1 − p)^n. Ten boards sit near 4.91 × 10^−7. Twenty syndicate boards sit near 9.82 × 10^−7. Covering the matrix at R2.50 would cost about R50.9 million before splits. Lotto Plus add-on draws recycle numbers against extra barrels; they do not divide C(52,6) on the main draw.

Expectation uses the default R2.50 (modelled as $2.50) stake and a $3 million advertised jackpot: 3,000,000 / 20,358,520 − 2.50 ≈ 0.147 − 2.50 = −$2.353 per board. Ten boards: about −$23.53. Jackpot-only breakeven with one winner is 2.50 × 20,358,520 = $50,896,300. Raising the advertised jackpot to $10 million still leaves 10,000,000 / 20,358,520 − 2.50 ≈ −$2.01. A twelve-board syndicate costs $30, has chance ≈ 5.89 × 10^−7, and expected value about −$28.23 at the $3 million default.

Assumptions: uniform six-subsets of fifty-two, independent boards, one Division 1 winner, bonus-ball divisions out of scope, $2.50 stake, and no confusion with Ithuba PowerBall (5/50 plus 1/20, Tuesday and Friday, $5). Saturday Lotto's C(45,6) = 8,145,060 is softer; Mega-Sena's 50 million is harsher. Licence history does not change the binomial coefficient.