Lottery Number Generator

Formula

How this is calculated

Enter how many numbers you want to pick (k) and the size of the number pool (N), where balls are numbered 1 through N. Optionally add a bonus ball drawn from the remaining N−k numbers. The generator draws k distinct values without replacement by inserting random integers into a set until it holds k unique numbers (a rejection-sampling form of the partial Fisher–Yates shuffle), guaranteeing no duplicates, then sorts them ascending for display.

The jackpot odds are the number of equally likely combinations, C(N, k) = N! / (k!·(N−k)!), so your chance of matching every main number is 1 in C(N, k). For the classic 6-from-49 game that is 1 in 13,983,816. The bonus ball, when enabled, is selected from the numbers not already drawn, mirroring how many real lotteries pick a supplementary ball from the same pool.

Inputs must be whole numbers with k ≥ 1 and k ≤ N; a bonus ball additionally requires at least one leftover number (N − k ≥ 1). Each draw is independent and uniformly random, so this tool only produces "quick picks" — it cannot improve your odds, which are fixed by N and k alone.