Polish Lotto Odds Calculator

This calculator is for Poland’s flagship Lotto, branded Lotto or Duży Lotek by Totalizator Sportowy: six numbers from 1 to 49. Set Tickets to how many 6/49 lines you are buying for one draw. If you play a system (pełny system) that expands eight or nine chosen numbers into many combinations, enter the expanded combination count, not “one coupon.” The probability engine assumes independent lines against a single draw.

Price defaults to 3 as a euro-tool stand-in for the usual 3 PLN stake. If you think in złoty, you can treat the unit as PLN and enter Jackpot in PLN as well; the math is currency-agnostic as long as Price and Jackpot share a unit. If you converted 3 PLN to euros for a travel comparison, keep Jackpot in euros too. Do not mix PLN price with a euro jackpot. Jackpot is the advertised Lotto jackpot (wygrana I stopnia). Paste the current figure from lotto.pl or the retail banner. EV uses only that top prize.

Main Matches defaults to 6 for the jackpot. Set it to 5, 4, or 3 to see hypergeometric odds of matching exactly that many of the six drawn numbers—the classic Duży Lotek lower degrees. There is no Bonus Matches field on this page. Polish Lotto’s main jackpot is a pure 6/49 hit; the Plus game and Mini Lotto (5/42) are different products. Do not enter Mini Lotto tickets here.

Outputs: Jackpot Odds for one 6/49 line, This Prize Odds for your Main Matches setting, Jackpot Chance across Tickets as 1 − (1 − p)^n, and Jackpot EV as n × (jackpot × p − price). Lotto in Poland has been drawn more often than the old Tuesday/Thursday/Saturday rhythm; the combination math does not care whether you play a daily-style draw or a classic weekend draw. Use Tickets for one drawing only unless you intentionally want a single-draw equivalent of a multi-draw strip, in which case you are approximating independent draws with the same p—acceptable for a back-of-envelope, not a substitute for multiplying separate draws in a dedicated multi-draw tool.

Polish Lotto, officially Lotto and widely called Duży Lotek, is Totalizator Sportowy’s 6-from-49 game. It has run since 1957, which makes it one of Europe’s long-running state lotteries, older than Vikinglotto, older than Austrian 6aus45, and in the same combinatorial family as Canada’s Lotto 6/49 and many other 6/49 brands. The stake is 3 PLN per line in the standard product, which is why this tool’s Price default is 3. Draws were historically Tuesday, Thursday, and Saturday; the modern schedule has added more drawings. Extra draw days do not shrink C(49,6). They only give you more independent chances per week if you buy more tickets.

Do not confuse Duży Lotek with Mini Lotto (5 from 42), Lotto Plus, Kaskada, or Multi Multi. Those are separate Totalizator Sportowy games with different matrices and prize structures. Eurojackpot is also sold in Poland; it is 5/50 plus two from 12, not 6/49. If a friend said “lotto odds in Poland” they might mean any of these. This page is strictly 6/49 jackpot math for Duży Lotek.

The jackpot is pari-mutuel and can roll. Headline millions of złoty still sit under a 1-in-13,983,816 wall. Sharing happens. Tax treatment of large wins is a legal question, not an input on this calculator. The EV line is pre-tax, jackpot-only, no split assumption.

Because 6/49 is the most copied lottery format on earth, people import myths from other countries: hot numbers, overdue numbers, and “the Polish 49 is easier than the Canadian 49.” Combinatorially they are identical: C(49,6) = 13,983,816. What differs is price (3 PLN versus C$3), jackpot distribution, draw frequency, and add-on games. Use this calculator to keep those differences in the Price and Jackpot fields and to keep the matrix honest. Main Matches is for inspecting lower degrees, not for turning this tool into Mini Lotto.

Duży Lotek has been Totalizator Sportowy's 6/49 since 1957, and the jackpot probability is exactly 1/C(49,6). That coefficient is 49×48×47×46×45×44 / 720 = 13,983,816, the same combination count as Spanish Bonoloto, Canadian 6/49, and many other European 6/49 brands. Same wall, different commercial object: stake 3 PLN, Polish prize fund, wygrana I stopnia, a calendar that was historically Tuesday/Thursday/Saturday and later grew extra drawings. Extra draw days do not shrink C(49,6); they only sell more independent trials per week. Mini Lotto is 5/42. Lotto Plus, Kaskada, Multi Multi, and Eurojackpot are other Totalizator products. This lecture is six from forty-nine only.

Pascal's coefficient is currency-agnostic. Three złoty versus fifty euro cents versus three Canadian dollars changes expected value, not the urn. People who claim “the Polish 49 is easier than the Canadian 49” are confusing price and jackpot distribution with combinatorics. C(49,6) is identical. Hot-number folklore imported from other 6/49 markets is equally empty here.

Hypergeometric exact m: C(6,m)×C(43,6−m)/13,983,816. Five mains: 6×43 = 258, about 1 in 54,201. Four mains: 15×903 = 13,545, about 1 in 1,032. Three mains: 20×12,341 = 246,820, about 1 in 56.66. Those fractions match Bonoloto's main-grid lecture because the urn is the same size; złoty amounts on each rung are not.

Independent lines give 1−(1−p)^n. Ten lines ≈ 7.15×10^−7. One hundred ≈ 7.15×10^−6. Covering 13,983,816 distinct combinations at 3 PLN is about 41.95 million PLN before split risk. A pełny system that expands eight chosen numbers into C(8,6) = 28 lines must be counted as twenty-eight trials, not as one coupon.

Expected jackpot value is n×(J/13,983,816 − 3) in a consistent unit. Two million over 13.98 million is about 14.3 cents, so 0.143 − 3 = −2.857 per line if stake and jackpot share a unit. Twenty lines at 3 PLN against an 8 million PLN headline: 20×(8,000,000/13,983,816 − 3) ≈ 20×(−2.428) ≈ −48.6 PLN. Mixing 3 PLN of stake with a euro jackpot fabricates a false hole or a false plus. Lower degrees add omitted złoty and still leave a negative game. Keep 1957, keep Totalizator Sportowy, keep 13,983,816, and keep Mini Lotto's 5/42 out of the denominator.