German Lotto Odds Calculator

This calculator is locked to German Lotto 6aus49 as the Deutscher Lotto- und Totoblock actually sells the jackpot: six numbers from 49 plus a Superzahl from 0 to 9. Default Ticket Price is 1.20 euros, a typical field stake per normal line before Spiel 77 or Super 6. Default Jackpot is 10,000,000. Draws are Wednesday and Saturday. Tickets is your count of independent 6aus49 lines on one of those evenings, not a subscription and not a system slip unless you have already expanded the system into an equivalent number of singles.

Enter Tickets first. One ticket is one six-number combination; the Superzahl on a German slip is usually the last digit of the ticket number rather than a number you pick, but combinatorially it is still one digit from ten. Ten tickets are ten independent combinations. The at-least-once jackpot chance the page prints is 1−(1−p)^tickets with p = 1/139,838,160. Buying twenty lines on a Saturday does not give you a meaningful shot at Klasse 1. It gives you twenty times the expected count, which is still a fraction of a millionth.

Ticket Price defaults to 1.20. German prices are set by the sixteen state lottery companies inside the Totoblock, and the field stake has moved over the years; 1.20 euros per normal line is the usual figure this model uses. If you are costing a full slip that also has Spiel 77 (an extra seven-digit game) or Super 6 (six digits), do not dump those add-on euros into Price unless you are deliberately mixing products. This calculator does not include Spiel 77 or Super 6. Price exists to feed expected value: EV falls one-for-one with extra euros of stake.

Jackpot is the Klasse 1 pool you want to value. Ten million is a round working figure, not a promise. German jackpots rollover and are capped in ways that have changed; put the advertised Wednesday or Saturday figure here if you have it. The engine treats Jackpot as an unshared lump sum. If two winners appear, the real prize splits; this page's EV formula does not take a winners field.

Main Matches is how many of the six drawn mains you want odds for, from 0 through 6. Bonus Matches is the Superzahl: 1 if that digit hits, 0 if it misses. Klasse 1 in the real game is six mains plus Superzahl, so Main Matches 6 and Bonus Matches 1 is the jackpot probe. Six mains without Superzahl is a different prize class (still huge). The real 6aus49 table also uses a Zusatzzahl, a seventh ball drawn from the remaining 43, to define classes such as five-plus-Zusatzzahl. This calculator's bonus pool is the Superzahl 0–9, not the Zusatzzahl. If you want Zusatzzahl odds, this is the wrong model.

Outputs: Jackpot Odds (always the 6+Superzahl combination), This Prize Odds for the (mains, Superzahl) pair you set, multi-ticket chances, Jackpot EV, and Expected Jackpot Return. With a 10 million euro jackpot and a 1.20 euro line, jackpot-only EV is about −1.13 euros per ticket. Spiel 77 and Super 6 can only make the slip more negative if you add them without adding their own prize terms here.

Lotto 6aus49 is the backbone of German numbers gaming. The first draw under the modern 6-from-49 matrix ran on 9 October 1955; the Deutscher Lotto- und Totoblock is the interstate agreement that lets sixteen Landeslotteriegesellschaften sell the same Wednesday and Saturday draw. Nordrhein-Westfalen, Bayern, Berlin and the rest keep their own retail networks, sports betting brands, and social-mandate rhetoric, but the balls are common. Superzahl, a digit 0–9, was grafted onto the jackpot definition so that matching six mains is no longer enough for Klasse 1. You also need the Superzahl. Combinatorially that is a bonus pool of 10 with 1 drawn, which is how this calculator is wired.

The main grid is the classic European 6/49: C(49,6) = 13,983,816 combinations. Multiply by ten Superzahlen and Klasse 1 sits at 1 in 139,838,160. That is an order of magnitude harder than a 6/49 jackpot without a digit, and still easier than Eurojackpot or EuroMillions. Germans who want the transnational rollovers buy those; 6aus49 remains the domestic habit, the Wednesday night ritual, the Saturday slip next to the Zeitung. Typical line price around 1.20 euros keeps the game in grocery-ticket territory. Jackpots of several million euros are routine; nine-figure German-only jackpots are not the product's point.

Two add-ons dominate the till and are deliberately absent from this model. Spiel 77 is a seven-digit evaluation against the ticket number, launched in the mid-1970s. Super 6 is a six-digit add-on from 1991. Both are extra stakes and extra prize tables. If you load a 1.20 euro 6aus49 line plus both add-ons, your outlay is no longer 1.20 and your probability object is no longer 6aus49 plus Superzahl. Keep Price at the 6aus49 line if you want this page to tell the truth. The Zusatzzahl, drawn after the six mains from the remaining 43 balls, also sits outside the bonus field. It creates mid-table classes (5+Z, 4+Z, and so on). Superzahl is the jackpot digit. Do not confuse them.

History is unusually long for a still-running matrix. 1955 puts 6aus49 among the oldest large-pool lotteries in Europe that a contemporary player would still recognise. The Totoblock structure is political: lottery is a Land competence, so a national game exists only as a cartel of state companies. That is why you see Toto-Lotto Niedersachsen, Lotto Bayern, Lotto Hamburg on receipts while the combination is the same. Odds do not depend on which Land printed the ticket. Expected value depends on the jackpot you type and the price you type, not on the logo.

Use the calculator when you want Klasse 1 and the Superzahl-conditioned lower classes as pure combinations, without Spiel 77 noise. Set Main Matches to 3 and Bonus Matches to 0 to see the dense middle of the hypergeometric. Set Tickets to the size of a small system expansion. Remember that German prize funds pay many classes, so jackpot-only EV understates the ticket's return and still will not make it a fair game at 1.20 euros times 139 million to one.

German Lotto 6aus49 has used the same main drum since 9 October 1955, then multiplied the top class by a Superzahl digit from zero to nine. The Deutscher Lotto- und Totoblock lets sixteen state companies sell one Wednesday and Saturday draw. Klasse 1 requires six mains and the Superzahl. Combinatorics: 1 / [C(49,6)×C(10,1)] = 1/139,838,160. A typical field stake is about 1.20 euros before Spiel 77 or Super 6. The working jackpot here is ten million euros. That 139,838,160 denominator equals current EuroMillions, but the route is C(49,6)×10 rather than C(50,5)×66, and the operator is not FDJ or Santa Casa.

Six-from-forty-nine: C(49,6) = 49×48×47×46×45×44 / 720 = 13,983,816. Without the digit, six-correct would be one in 13.98 million, the classic European 6/49 jackpot. Superzahl is an independent ten-way factor, so multiply: 13,983,816×10 = 139,838,160. Covering every main combination still leaves a nine-in-ten chance of missing Klasse 1 if the digit is wrong. The Superzahl on a German slip is often the last digit of the ticket number rather than a picked ball; combinatorially it remains one from ten.

Hypergeometric six: C(6,k)×C(43,6−k)/C(49,6). Superzahl: one tenth or nine tenths. Three mains regardless of digit: C(6,3)×C(43,3)/13,983,816 with C(43,3) = 12,341, so 20×12,341 = 246,820, about one in 56.7, the familiar Dreier. Times nine tenths if the digit misses: about one in 63. Six mains without Superzahl: 9/139,838,160. Five mains plus Superzahl: C(6,5)×C(43,1)/13,983,816 × 1/10 = 258/139,838,160, about one in 542,008. The Zusatzzahl, a seventh ball from the remaining forty-three, defines 5+Z classes and is not the Superzahl. Spiel 77 and Super 6 are separate numbered add-ons.

One hundred lines: expected Klasse 1 count 100/139,838,160. Expected jackpot euros at ten million are 10,000,000/139,838,160 ≈ 0.072 against 1.20, so jackpot-only expectation is about minus 1.13 a line. Lower classes add omitted return; the Totoblock is not a 100 percent prize charity. A system slip must be expanded to C(m,6) singles before you count trials.

La Primitiva uses the same C(49,6)×10 skeleton with a Reintegro and a 1985 SELAE reconstruction, not a 1955 Totoblock. Keep 6aus49 since 1955, Superzahl 0–9, 1.20 euros, Klasse 1 at 139,838,160. Identical denominators are not identical histories.