The 1–3 range
Three is where choosing by hand starts to go wrong. Given three options in a row, people reach for the middle one more often than the ends, a habit shoppers show on supermarket shelves and candidates show on multiple-choice papers.
A 1–3 draw has no middle. Each option carries 33.33 percent, and the generator has no idea which one is sitting at eye level.
Number your options first, then tap. Rock, paper and scissors map onto 1, 2 and 3 as neatly as anything.
- 1 to 3, both included
- 3 whole numbers
- 33.33%, exactly 1 in 3
- 1 to 10 numbers per draw
- None up to 3 numbers, then unavoidable
- Every draw gets a link that replays it
What a 1–3 draw is for
- Throwing rock, paper or scissors blind
- Choosing between three takeaway menus
- Setting turn order for three players, one draw at a time
- Handing out three chores without an argument
- Picking one of three finalists for a spot prize
How the randomness works
Every tap calls crypto.getRandomValues, the browser's cryptographic generator, and asks it for one unsigned 32-bit value. That lands somewhere between 0 and 4,294,967,295, and it then has to be folded down to the 3 numbers in this range.
Folding it down with a plain remainder is where most generators go wrong, an error known as modulo bias. 3 does not divide 4,294,967,296 evenly: 1 value is left over at the top, and wrapping it around would make the first 1 numbers in the range fractionally likelier than the rest. This tool throws away any raw value at or above the last exact multiple of 3 and draws a fresh one instead. That is rejection sampling. It fires about 1 in 4,294,967,296 draws, and it is the difference between 33.33% exactly and 33.33% approximately.
Ask for more than one number and the tool keeps drawing until it holds that many distinct values, then sorts them ascending. Nothing is seeded, nothing is sent anywhere, and each draw is independent of the one before it. The roll history under the tool lives in your browser's local storage, where the clear button empties it. The daily lucky numbers elsewhere on this site work the opposite way on purpose: they use a seeded generator so the same date always returns the same set. How random is random sets the two side by side.
Three is the first range that needs a redraw. Divide 4,294,967,296 by three and exactly one value is left over, so the tool discards that value whenever it appears and draws again. The odds of that are one in 4.3 billion, and it is the difference between a flat 33.33 percent each and a generator that quietly favours 1.
- crypto.getRandomValues, the browser's cryptographic generator
- One unsigned 32-bit value, sometimes more
- Rejection sampling onto 3 slots
- 1 of 4,294,967,296 raw values, redrawn
- No. These tools are never seeded
- Your browser. No server ever sees a draw
1–3 — frequently asked
Write the three options down in a fixed order, number them 1, 2 and 3, then tap Generate. Fixing the order before the draw is the part people skip, and it is the part that makes the result defensible.
Enough to be measurable. Shoppers pick the centre item from a row of identical products more often than the outer ones, and the same pull shows up when people guess which of three envelopes holds the prize. Nobody reports feeling biased, which is exactly the problem.
Yes, and it is a genuine upgrade on throwing by hand. Human players open with rock more often than chance and repeat their last winning throw, both of which a decent opponent learns fast. A blind draw gives away nothing.