14,003,318
14,003,318
0.000007
%
0.000007
%
0.07
currency
0.000007
%
14,003,318
14,003,318
0.000007
%
0.000007
%
0.07
currency
0.000007
%
The Lottery Number Generator creates pseudo-random lottery numbers from a configurable pool size using a seed-based algorithm. Whether you play 6/49 (Canada, Germany), Powerball (1-69), EuroMillions (1-50), or any other format, this tool generates numbers and calculates the exact odds of matching all numbers. Understanding lottery mathematics reveals just how astronomical the odds truly are.
Lotteries are the ultimate exercise in combinatorial probability. The number of possible combinations grows factorially with pool size, quickly reaching into the millions or hundreds of millions. Despite the near-zero probability of winning, lotteries remain immensely popular worldwide, generating over $300 billion annually in ticket sales.
Each lottery number is generated using a sinusoidal hash function mapped to the pool range:
$$n_i = \lfloor h_i \times N \rfloor + 1$$
where $$N$$ is the pool size and $$h_i$$ is the pseudo-random value for position $$i$$. The total number of possible combinations (unordered selections without replacement) is given by the binomial coefficient:
$$\binom{N}{k} = \frac{N!}{k!(N-k)!}$$
For the classic 6/49 lottery:
$$\binom{49}{6} = \frac{49!}{6! \times 43!} = 13{,}983{,}816$$
This means the probability of matching all 6 numbers is:
$$P(\text{jackpot}) = \frac{1}{13{,}983{,}816} \approx 7.15 \times 10^{-8}$$
For Powerball (5/69 + 1/26):
$$\binom{69}{5} \times 26 = 292{,}201{,}338$$
The expected value of a lottery ticket is typically negative: a $2 ticket for a $100 million jackpot with 1/292M odds has an expected value of about $0.34, a 83% loss.
The generated numbers are your lottery picks for the configured format. Numbers showing 0 are beyond your selected pick count. Total Combinations shows how many unique number sets are possible. Odds (1 in X) expresses the probability of matching all numbers with a single ticket. Note that duplicate numbers may appear since each is generated independently; in real lotteries, numbers are drawn without replacement.
For perspective: if you bought 1,000 tickets per week, it would take an average of 13,984 weeks (~269 years) to hit the 6/49 jackpot, and 292,201 weeks (~5,619 years) for Powerball.
Inputs
Results
Generated numbers 25, 15, 38, 21, 8, 44 for a 6/49 lottery. The odds of matching all 6 are 1 in 13,983,816 — roughly 1 in 14 million.
Inputs
Results
For the main Powerball draw (5 numbers from 69), the odds of matching all 5 white balls are 1 in 11,238,513. The full Powerball jackpot odds of 1 in 292M include the separate Powerball number from a pool of 26.
6/49 (Canada, Germany): 1 in 13,983,816. Powerball (5/69 + 1/26): 1 in 292,201,338. Mega Millions (5/70 + 1/25): 1 in 302,575,350. EuroMillions (5/50 + 2/12): 1 in 139,838,160. UK Lotto (6/59): 1 in 45,057,474.
In this generator, yes, because each number is generated independently. Real lottery draws are without replacement (each ball is removed after drawn). If you get duplicates, simply change the seed. For small picks from large pools, duplicate probability is low due to the birthday paradox threshold.
Rarely. When jackpots roll over to extreme amounts (e.g., Powerball > $600 million), the expected value can theoretically exceed the ticket price. However, after taxes, multiple winner probability, and lump sum discount, the expected value almost never truly exceeds the ticket price.
No. In a fair lottery, every number has exactly the same probability of being drawn. However, choosing less popular numbers (higher numbers, avoiding patterns like 1-2-3-4-5-6) can reduce the chance of splitting a jackpot with other winners, improving the conditional expected payout.
The binomial coefficient $$\binom{N}{k}$$ counts the number of ways to choose $$k$$ items from $$N$$ without regard to order. The formula $$N!/(k!(N-k)!)$$ divides the total ordered arrangements ($$N!/(N-k)!$$) by the number of ways to reorder $$k$$ items ($$k!$$), since lottery order does not matter.
Any seed produces valid numbers. For entertainment, try your birthday, current date, or any meaningful number. Remember that no seed is luckier than another — lottery outcomes are determined by physical ball draws, completely independent of your number selection method. Every combination has equal probability.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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