generate random numbers without bias
Drawing "a number between 1 and 60" sounds simple, but the naive path (take a random integer and apply modulo) introduces a real bias, even if small. This page shows which random number generator this tool uses, how modulo bias actually shows up, and what changes when you exclude numbers or ask for no repeats.
When the requested count equals the range size, the result is always a full permutation of the interval, no number is left out or repeated.
The range from 1 to 6 only holds 6 distinct values, so asking for 7 without repeats is mathematically impossible and the tool refuses the draw instead of quietly forcing a repeat.
Without rejection sampling, the first 967,296 values of the range would appear slightly more often than the rest; with it, all 1 million values end up exactly equally likely.
Yes. We use crypto.getRandomValues, the browser's cryptographic random number generator, with rejection sampling to eliminate modulo bias. This guarantees a uniform distribution, every number in the range has equal odds, with no tilt toward the smaller values as happens in more naive generators.
Yes, in theory. Math.random is a deterministic PRNG: the whole sequence comes from an internal state, and observing enough output can, in adversarial scenarios, let someone reconstruct that state and predict the next numbers. That is why this tool defaults to crypto.getRandomValues, and only falls back to Math.random if the Web Crypto API does not exist.
It is the distortion that shows up when you take a large random integer and apply modulo by a range that does not divide that space evenly. Some values of the final range end up receiving an extra slice of the raw outcomes, even though the underlying generator itself is perfectly fair.
Because the range from 1 to 6 only contains 6 distinct possible values, and without repeats there is no seventh different number left to draw. The tool detects that impossibility before attempting to generate anything and returns an error instead of silently repeating a value.
Yes. In no-repeat mode, every drawn number leaves the available pool, so the odds of the remaining numbers rise with each round: the first pick has a 1-in-N chance, the second has a 1-in-N-minus-1 chance among what is left, and so on.