Random Number Generator

How to use the random number generator

Set the range, set how many numbers you want, choose whether repeats are allowed, and the values appear immediately. The defaults draw 5 unique numbers from 1 to 100.

Both ends of the range are inclusive, which is worth stating because it is the single most common off-by-one in this kind of tool: 1 to 100 has 100 possible values, and 0 to 99 also has 100.

A reversed range is normalised rather than refused, so entering 10 as the minimum and 1 as the maximum still draws from 1 to 10. The count is capped at 1,000 numbers per draw and the range at plus or minus one billion.

Unique mode changes what is being asked for. With repeats allowed, each number is an independent draw and duplicates are expected: pull five values from 1 to 100 and there is a real chance two of them match, exactly as there is with five rolls of a hundred-sided die.

With unique on, the tool draws without replacement, which is the lottery model, the raffle model, and the model for picking distinct winners from a list of entrant numbers. If you ask for more unique numbers than the range can supply, the tool says so rather than silently repeating or hanging, because a request for 10 unique values from a range of 5 has no answer at all.

The randomness comes from the browser cryptographic generator, which the operating system seeds from genuine physical entropy, and not from the ordinary pseudo-random function that most scripts reach for. For picking a restaurant it makes no difference. For a prize draw, a security exercise, or anything where a participant has a reason to want the outcome, the difference is the whole point, and there is no cost to using the stronger source, so the tool simply always uses it.

Where do most generators quietly go wrong?

Converting a raw 32-bit value into a number in your range is where most generators quietly go wrong, and where this one takes the slower path. The obvious method is a remainder: take the random value modulo the size of the range. That is biased whenever the range does not divide evenly into the generator period, and it is biased in a specific direction, towards the low end.

This tool instead defines an acceptance window that is an exact multiple of your range, throws away any value above it, and draws again. The retry costs nothing measurable, and the result is a distribution with no lean in it at all.

The formula, worked line by line

A random integer in a range is built in two steps: get a uniform random value from the hardware-backed generator, then map it into the range you asked for. The first step is a library call. The second step is where the interesting decision lives, because the obvious mapping is not uniform.

The generator hands back a 32-bit unsigned integer, uniform across 4,294,967,296 possible values. Your range is almost never a divisor of that number. Taking the remainder directly therefore spreads an unequal number of source values onto each output value, and the surplus always lands on the values at the bottom of the range.

source          = crypto.getRandomValues(Uint32Array(1))   in [0, 2^32)
range           = max - min + 1        (both ends inclusive)
window          = floor(2^32 / range) x range
draw            = redraw while source >= window; then min + (source mod range)
unique mode     = partial Fisher-Yates over a lazy map, O(count)

The bias only becomes visible when the range is large relative to the source. Ask for a number between 1 and 10,000,000 and the arithmetic changes character: ten million divides into 4,294,967,296 only 429 times, leaving 4,967,296 values over.

A plain remainder would hand the first 4,967,296 values in the range a head start of one part in 429, which is 0.233 percent, and a simulation running tens of millions of draws would see it. Rejection sampling here discards those 4,967,296 source values, redraws about one time in 865, and returns a distribution with no lean.

The lesson generalises: modulo bias is invisible at n equals 6 and obvious at n equals ten million, and there is no threshold at which it becomes correct.

Unique mode uses a partial Fisher-Yates shuffle over a lazily built map rather than an array. A textbook shuffle would materialise the whole range, shuffle it, and take the first few entries, which is fine for 1 to 100 and catastrophic for 1 to 10,000,000, where it would try to allocate ten million entries to return five numbers.

Storing only the positions actually swapped makes the work proportional to how many numbers you asked for rather than to how wide the range is, so five unique values from a range of ten million come back instantly. If the request is impossible, more unique values than the range holds, the tool reports that rather than looping forever looking for an answer that does not exist.

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