Decision Wheel

Many spinner tools work backward from the animation: they rotate the wheel to some visually pleasing stopping angle first, then read off whichever slice happens to be under the pointer as the result. This sounds harmless but introduces a subtle statistical bias, because converting a continuous rotation angle into a discrete winning slice involves floating-point arithmetic that does not divide evenly across an arbitrary number of options — certain slices end up landing under the pointer marginally more often than others purely as an artefact of the rounding involved, not from any genuine unfairness in the spin itself. This tool works the other way around: the winner is selected first, using a proper source of cryptographic randomness, and the wheel's spinning animation is purely a visual flourish landing on a result that was already determined — the animation never has any influence on which option actually wins.

The most common way to turn a random number into "pick one of N options" is to take a random integer and compute its remainder when divided by N — but unless N happens to evenly divide the range the random number was drawn from, this introduces a small, genuine bias where some options become fractionally more likely to be picked than others, purely as an artefact of the division not landing evenly. Rejection sampling avoids this entirely: it draws a random value, and if that value would fall into the tiny unevenly-distributed remainder, discards it and draws again, repeating until a value lands in the evenly divisible portion of the range. Every option ends up with a probability that is exactly, not just approximately, equal — a real fairness guarantee rather than a close approximation of one.

Leaving every option in the pool after each spin is the right choice when repetition is fine or even desirable — deciding what to have for dinner tonight does not require ruling out yesterday's answer. Removing the winner after each spin instead models what statisticians call sampling without replacement, which is the fair and appropriate mode whenever each option is meant to be selected at most once across a series of spins — assigning a fixed set of tasks among a team, drawing multiple distinct prize winners from one list, or calling on students in a class without repeating the same name before everyone else has had a turn.

A wheel with only a handful of entries can give each one a generously sized slice with plenty of room for a full label, while the same wheel divided among fifty entries gives each slice only a thin sliver of the circle to work with, and text set inside a narrow wedge shrinks or truncates quickly. Around fifty options is roughly where labels start becoming genuinely hard to read on a typically sized wheel — the underlying random selection stays exactly as fair regardless of how many entries are added, but the visual presentation is the practical limit worth keeping in mind for a long list.