Random Number Generator Widget

How it works

The range is turned into a count of equal steps - whole numbers, or tenths, hundredths and so on when decimals are chosen - and each draw picks one step with the browser's cryptographic random generator. Rejection sampling removes the small bias that the common random-number-mod-range shortcut introduces, and ranges larger than four billion values combine two random words into 53 bits. With "No repeats" on, the widget shuffles when you ask for most of the range (for example a whole lottery draw) and otherwise redraws duplicates, so the result is still a uniform pick of distinct numbers.

Method

• Steps: lo = ceil(min x 10^d), hi = floor(max x 10^d), n = hi - lo + 1; value = (lo + k) / 10^d
• k uniform in [0, n): 32-bit word redrawn while >= 2^32 - (2^32 mod n); for n > 2^32 a 53-bit value redrawn while >= 2^53 - (2^53 mod n)
• No repeats: partial Fisher-Yates shuffle when drawing more than half of a range up to 100,000 values, otherwise redraw duplicates
• Limits: 1 to 500 numbers, 0 to 6 decimal places, bounds within +/- 10^15

Limitations

• Only uniform draws: no weighted, normal (bell-curve) or other distributions.
• Results are not seeded or logged, so a draw cannot be reproduced or audited afterwards; record public draws on video.
• It is not a certified gaming or lottery random number generator and should not be used where regulation requires one.
• Decimal draws are multiples of 10^-d between the bounds; a bound that is not such a multiple is moved inward to the nearest one.

Where publishers use it

• Giveaway and contest pages picking a winning entry number in public
• Teachers generating practice sums, seat numbers or random groups
• Board-game, tabletop and dice-roll pages (1 to 6, 1 to 20 and so on)
• Researchers and QA teams drawing random sample IDs from a numbered list

Questions

Sources

1. Web Cryptography API - Crypto.getRandomValues() - W3C . cryptographically secure random words behind every draw
2. Algorithm 235: Random permutation (R. Durstenfeld, Communications of the ACM 7(7), 1964) - ACM . the in-place Fisher-Yates shuffle used for draws without repeats

Cite or recommend this tool

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