French Loto Odds Calculator

French Loto on this page is FDJ's 5/49 plus numéro Chance 1 to 10. Default Ticket Price is 2.20 euros, default Jackpot 4,000,000. Draws are Monday, Wednesday and Saturday. Tickets is independent grids on one of those draws. Option 2nd tirage (a second draw on the same numbers, extra stake) is not a second ticket in this engine unless you explicitly model it as extra independent trials with their own jackpot rules — and 2nd tirage is not the same prize table. Super Loto specials are the same matrix with a larger advertised jackpot; put that larger figure in Jackpot, do not invent a new combination count.

Tickets: one line is five mains from 49 plus one Chance from 10. Ten lines are ten independent pairs. p = 1/C(49,5) × 1/10 = 1/19,068,840. The at-least-once chance is 1−(1−p)^n. A Monday three-line slip is n=3, not n=9 just because FDJ also draws Wednesday and Saturday; those are other p's on other nights. If you want a week of one line per draw, n=3 across the week as independent draws, still 1−(1−p)^3.

Ticket Price defaults to 2.20, the modern FDJ stake that replaced cheaper historical prices. If you add 2nd tirage, your real outlay rises; only increase Price if you are stuffing that extra euro into this EV without adding 2nd tirage's prize vector (which this calculator does not have). Super Loto price can differ; match Price to what you actually paid.

Jackpot is 4 million by default, FDJ's familiar starting-class advertised amount. Super Loto and jackpot-guarantee nights can sit far higher — type the advertised million. The engine treats it as unshared cash. French tax and FDJ's prize-fund statutes are outside the formula.

Main Matches 0–5 on the 49 grid. Bonus Matches is the numéro Chance: 1 hit, 0 miss. Rank 1 is 5+Chance. Five without Chance is Rank 2 in the usual FDJ table. 2nd tirage, if you play it, is a separate draw that may not even use the Chance the same way; this Bonus Matches field is the main tirage's 1-from-10 Chance. Joker+ and other FDJ add-ons are out.

Read Jackpot Odds 1 in 19,068,840, This Prize Odds, chances, EV, Expected Jackpot Return. At 4 million and 2.20, jackpot × p ≈ 0.210, EV ≈ −1.990 euros per line. That is a heavy jackpot-only loss per 2.20 euro stake, which is why FDJ's lower ranks and the 2nd tirage marketing exist: they sell extra hope next to a 19-million-to-one top prize that a 4 million euro bote cannot fairly cover.

Loto is Française des Jeux' flagship national lottery, launched in 1976, decades before FDJ's public listing. The current matrix is five from 49 plus a numéro Chance from 1 to 10, drawn Monday, Wednesday and Saturday. Earlier Loto history includes a 6/49 era; do not use those denominators on a 2020s slip. C(49,5)×10 = 19,068,840 jackpot combinations, about 1 in 19.07 million. That is the easiest top prize among the big Western European 5+bonus games on this site after Set For Life's 15.34 million, and it is still a lottery.

FDJ prices Loto at 2.20 euros, which is punchy next to German 1.20, Totoloto 1.00, or Bonoloto 0.50. The stake buys a dense prize table, a three-draw week, and periodic Super Loto specials where the advertised jackpot is inflated for a named event. Super Loto does not change C(49,5) or the Chance pool; it changes Jackpot and sometimes marketing noise. Option 2nd tirage lets you recycle the same five mains (Chance treatment depends on the product rules of the day) into a second draw for extra money. This calculator is the primary tirage 5+Chance jackpot model. Second draw is extra p only if you model it as extra independent tickets with a stated jackpot; it is not free coverage of the first draw.

1976 places French Loto in the same generation as modern state lotteries that professionalised television draws and retail terminals. FDJ is not SELAE and not Santa Casa: it is a listed company with a state-anchored monopoly narrative, responsible-gambling banners, and a product stack that includes EuroMillions, Keno, sports, and poker. None of that stack alters 1/19,068,840. Players who treat Loto as "the French EuroMillions" are category-wrong: EuroMillions is 5/50+2/12. Loto is domestic 5/49+1/10.

The numéro Chance is the bonus ball this engine expects: pool 10, drawn 1. It is closer to Set For Life's Life Ball than to EuroMillions stars. Matching five mains is 1/1,906,884; the Chance multiplies by ten for Rank 1. Lower FDJ ranks mix k mains with Chance hit or miss. Complementary-style extras in other countries are not Chance. Spiel 77 is not Chance. Joker+ is an add-on code, not the 1–10 ball.

Use this page to put 2.20 euros next to a 4 million euro bote and watch EV print almost minus two euros on jackpot-only terms. Then raise Jackpot to a Super Loto advertisement and watch EV improve (less negative) without ever crossing zero at realistic FDJ figures. Then set Main Matches to 2 and Bonus Matches to 1 to see why the table pays the Chance on sparse mains: hypergeometric mass sits in the low k's. Three draws a week means three independent EV hits if you subscribe; Tickets on this page is still per draw unless you say otherwise.

Française des Jeux does not sell a 6/49 Loto on a contemporary slip; the jackpot is five from forty-nine times a numéro Chance from 1 to 10. Historical Loto in 1976 lived in a six-from-forty-nine era. Current probability is 1/[C(49,5)×C(10,1)] = 1/1,906,884 × 1/10 = 1/19,068,840. Same main combination count as Totoloto; bonus pool ten instead of thirteen, so Totoloto's top prize is 30 percent harder purely from lucky-number size. Five mains without Chance: 9/19,068,840. Stake is 2.20 euros, punchy next to Totoloto's euro or Bonoloto's fifty cents. Super Loto specials inflate the advertised jackpot; they do not rewrite C(49,5) or the Chance pool.

Derivation of 1,906,884 is the five-factor falling product 49×48×47×46×45 / 120. Chance is an independent uniform digit from ten, combinatorially the same size as a Superzahl or a Life Ball, not two EuroMillions stars. Multiplying 1,906,884 by C(12,2)=66 invents a game FDJ does not sell as Loto. Monday, Wednesday and Saturday are three independent hypergeometric experiments, not a trinomial that “adds up” to a fair ticket.

Hypergeometric mains share Totoloto's 5/49 grid: C(5,k)×C(44,5−k)/1,906,884. Three mains with Chance: 9,460/19,068,840 ≈ 1 in 2,016. Four mains without Chance: (220/1,906,884)×(9/10) = 198/1,906,884 ≈ 1 in 9,631. Those ranks are cash rungs on the FDJ table, not a second annuity. Option 2nd tirage is a separately staked second draw; treating it as a square of the first probability is wrong. Model it as another independent trial only if its prize vector is stated; otherwise leave it out.

Independent grids on one tirage give chance 1−(1−p)^n with p = 1/19,068,840. Two lines on Super Loto night are still about 2p against that night's jackpot, not a new combination count. A week of one line per draw is three independent p's, still 1−(1−p)^3 across the week if you insist on aggregating.

Expected jackpot value is n×(J/19,068,840 − 2.20). Four million over 19.07 million is about 21.0 cents against 2.20 euros, so about −1.990 euros per line jackpot-only. Twenty million on a Super Loto advertisement: 20,000,000/19,068,840 − 2.20 ≈ 1.049 − 2.20 = −1.151, still negative. Non-negative jackpot-only EV would need J ≥ 2.20×19,068,840 ≈ 41.95 million euros unshared, which ordinary Mondays do not park. Lower ranks close some of the gap; they do not invert a 2.20 euro house game. Keep ten. Keep five. Keep FDJ Loto off the retired 6/49 denominator.