Lotto 6/49 Odds Calculator

Canada’s Lotto 6/49 is six numbers from 1 to 49, sold through OLG, BCLC, and the other Interprovincial Lottery Corporation partners. Set Tickets to the number of $3 lines (or whatever you actually paid per combination) for one Wednesday or Saturday draw. Gold Ball / Guaranteed Prize Draw extras and bundle promotions are not extra 6/49 combinations unless they literally add lines; do not inflate Tickets for a GPD envelope.

Price defaults to 3 Canadian dollars. Keep Jackpot in CAD. If you think in USD, convert both fields. Jackpot is the advertised 6/49 jackpot, not Lotto Max and not Daily Grand. Paste the current 6/49 figure. Guaranteed Prize Draw prizes are separate random-ticket prizes; they are not this jackpot field.

Main Matches defaults to 6. There is no Bonus Matches field: this model is pure 6/49. The bonus ball in the live 6/49 prize table affects some lower tiers (classic Match 5 + bonus stories). The jackpot is six of six. Use Main Matches to inspect exact-k on the six drawn numbers.

Read Jackpot Odds as 1 in 13,983,816, the same C(49,6) as Polish Lotto with a different currency and a different product stack. Jackpot Chance across Tickets, Jackpot EV with CAD price and CAD jackpot. If you are holding 6/49 because Max “feels too hard,” that instinct is combinatorially correct—Max is 7/50—but 6/49 is still 1 in 14 million, not a bargain because it is older.

Ontario versus B.C. does not change the boxes. Tickets is combination count on one Wednesday or Saturday 6/49 draw at OLG, BCLC, or another ILC partner. Price = 3 unless a promo printed a different line cost. Jackpot is the 6/49 advertised pot on that draw, never Max, never Daily Grand, never a Guaranteed Prize Draw headline. Main Matches = 6 for jackpot odds; 5 for exact-five combinatorics without inventing a bonus-ball field this instance lacks. If your group pool bought 25 lines, enter 25, not 1. If you also hold Max for Friday, that is a different calculator run on a different slug.

Lotto 6/49 launched in 1982 as Canada’s first truly national lottery, a joint product of the Interprovincial Lottery Corporation partners including what players now know as OLG in Ontario and BCLC in British Columbia. The format is the classic 6 from 49. Draws are Wednesday and Saturday. A standard line is $3 CAD in the current product, which is why Price defaults to 3. It is not Lotto Max (7/50, $5, Tuesday/Friday) and not Daily Grand (5/49 plus Grand Number).

The combination count C(49,6) = 13,983,816 is the same wall as Poland’s Duży Lotek and many European 6/49 games. What is Canadian is the retail wrapping: regional operators, often a bonus ball for lower prize tiers, and in some eras a Guaranteed Prize Draw attached to 6/49 tickets. GPD does not change jackpot odds. It is a separate prize mechanism. Putting a GPD headline into the Jackpot field would be a mistake.

6/49 jackpots can roll and are advertised in Canadian dollars. They are smaller than Lotto Max caps. Sharing happens. Tax treatment of lottery winnings in Canada is generally more favourable than in the United States, which is a legal/tax fact, not an EV input here. The calculator still reports jackpot-only EV before you start spending the money.

Use this page when the question is 6/49, especially when a group chat mixed Max, 6/49, and Daily Grand into one “Canadian lotto” blob. Three matrices, three prices, three draw calendars. This tool is the 1982 national 6/49 identity only.

1982 national-launch lore is branding, not a gentler matrix. Interprovincial 6/49 was Canada’s first coast-to-coast combination game; Max (2009) and Daily Grand (2016) were layered on later with other pools. Guaranteed Prize Draw marketing in some years attached extra random prizes to 6/49 purchases without rewriting C(49,6). Players who fold GPD “someone must win” language into jackpot probability are mixing two random experiments. This page stays on the six-from-forty-nine experiment. Provincial websites (OLG, BCLC, and peers) remain the source for the live advertised jackpot you paste into Jackpot.

The jackpot of Canada's Lotto 6/49 is calculated as a classical unordered combination, the same six-from-forty-nine template that European state lotteries popularised in the 1970s and that the Interprovincial Lottery Corporation took nationwide in 1982. Combinations, not permutations, are the right count because the Wednesday or Saturday barrel is a set: order of appearance on television does not create extra tickets. The binomial coefficient C(49,6) equals 49 factorial divided by 6 factorial times 43 factorial. Expanding the falling product 49 × 48 × 47 × 46 × 45 × 44 and dividing by 720 yields 13,983,816 equally likely six-number lines. A single ticket therefore wins the top prize with probability 1 / 13,983,816, about 7.15 × 10^−8, or one in 13,983,816. No second drum multiplies that identity; a live bonus ball that splits some lower Canadian tiers is irrelevant to six-of-six.

Partial scores on the six main numbers are read from the hypergeometric distribution. After the draw, six balls are hits and forty-three are misses. A six-spot ticket then matches exactly m of the six with probability C(6,m) × C(43, 6−m) / 13,983,816. Matching five is 6 × 43 / 13,983,816 = 258 / 13,983,816, about one in 54,201. Matching four is 15 × 903 / 13,983,816 = 13,545 / 13,983,816, about one in 1,032. Matching three is 20 × 12,341 / 13,983,816 = 246,820 / 13,983,816, about one in 57. Those cells are exact-m events, not “at least m,” and they are not the official Match-5-plus-bonus split used in some prize tables.

Several independent lines convert a single-trial probability p into an at-least-once chance 1 − (1 − p)^n. Ten distinct combinations therefore sit near 7.15 × 10^−7. Linear n times p is an excellent approximation until n is enormous. Covering the whole matrix would still cost 13,983,816 × $3 ≈ $41.95 million before anyone else hits the same six numbers and splits the pot. A Guaranteed Prize Draw envelope, when one exists, is a separate random experiment and does not appear in this formula.

Expectation is ticket count times (advertised jackpot times p minus stake). With the default three-dollar line and a five-million jackpot, one combination contributes 5,000,000 / 13,983,816 − 3 ≈ 0.358 − 3 = −$2.642. Ten lines scale that hole to about −$26.42. Jackpot-only breakeven, ignoring splits and lower prizes, is 3 × 13,983,816 = $41,951,448 advertised. A worked walk-through with fifteen three-dollar lines against a twelve-million pot gives chance ≈ 1.07 × 10^−6 and expected value 15 × (12,000,000 / 13,983,816 − 3) ≈ −$32.13.

Assumptions worth stating in the lecture hall: uniform random six-subsets of forty-nine, independent tickets, one jackpot winner, no lower-tier cash credited to the expectation, Canadian dollars throughout, and no Gold Ball or Guaranteed Prize Draw mixed into the jackpot term. Lotto Max is seven from fifty at five dollars. Daily Grand is five from forty-nine plus a Grand Number from seven. Neither identity belongs in this six-from-forty-nine calculation. Provincial logos on the slip — Ontario, British Columbia, and the other partners — do not change C(49,6).