Lottery Odds Calculator

The number of ways to choose $$k$$ numbers from a pool of $$n$$ is given by the combination formula:

$$C(n, k) = \binom{n}{k} = \frac{n!}{k!(n-k)!}$$

Jackpot Odds (main draw only):

$$\text{Odds} = C(n, k)$$

Since there is exactly 1 winning combination, the probability is $$\frac{1}{C(n,k)}$$.

With Bonus Ball:

If the lottery also draws bonus balls from a separate pool of size $$b$$, the total odds become:

$$\text{Odds} = C(n, k) \times C(b, d)$$

where $$d$$ is the number of bonus balls you must match (typically 0 or 1).

Match One Fewer Number:

The number of ways to match exactly $$k-1$$ of the $$k$$ drawn numbers is:

$$\text{Ways} = C(k, k-1) \times C(n-k, 1) = k \times (n-k)$$

You choose which $$k-1$$ of the $$k$$ winning numbers to match ($$k$$ ways), and then which 1 of the $$n-k$$ non-winning numbers fills the remaining spot ($$n-k$$ ways). The odds are total combinations divided by these ways.

The calculator uses logarithms internally to handle the very large numbers involved in combinatorial calculations without overflow.

The Jackpot Odds show "1 in X" — this is the total number of possible ticket combinations. For a 6/49 lottery, X = 13,983,816.

The Match One Less odds are typically much better but still very long. For 6/49, matching 5 of 6 has odds of about 1 in 54,201.

To put lottery odds in perspective: you are more likely to be struck by lightning (~1 in 500,000 per year) than to win a 6/49 jackpot with a single ticket. Buying 100 tickets changes your odds from 1 in 14 million to 100 in 14 million — still essentially zero.