Is a random pick from a list actually fair?

"Pick one at random" sounds simple, but the only thing that makes a pick actually fair is that every item has exactly the same probability of being chosen: 1 ÷ N for a list of N items. That's the whole test — no item should be more or less likely than 1/N, and you can check it with one division rather than trusting a tool's word for it.

The method

1. Count the non-empty items in the list. Blank lines and extra spaces around entries don't count as options.
2. Divide 1 by that count to get each item's probability of being picked on a single draw.
3. For the chance a specific item is picked at least once across several independent draws, it's easier to work with the opposite: the chance it's missed every time is ((N-1)/N)^k for k draws, so the chance it's picked at least once is 1 - ((N-1)/N)^k.
4. For the chance of picking the same item twice in a row, multiply: the first draw picks something with probability 1 (anything counts), and the second draw matches it with probability 1/N — so the answer is just 1/N again, independent of what the first pick was.
5. If the observed frequency across many real runs drifts far from 1/N per item, that's a sign the generator isn't actually uniform — worth checking, not assuming.

A worked example

Five coworkers go into this site's random-pick tool to choose who takes the next support rotation: Alex, Blair, Casey, Drew, Emery.

• Each person's chance on a single pick: 1 ÷ 5 = 20%.
• Run the pick three separate times (say, for three different weeks) to see Casey's odds of being picked at least once: the chance Casey is missed each time is 4/5, so missed all three times is (4/5)^3 = 0.512, meaning picked at least once is 1 - 0.512 = 48.8% — not 60% (3 × 20%), because that naive sum double-counts the cases where Casey gets picked more than once.
• Chance the tool picks the same person two weeks running: 1/5 = 20%, exactly the same as any single pick, because the second draw doesn't know or care what the first one returned.

That last point trips people up: after Casey gets picked once, a lot of people expect the odds to shift ("surely it's someone else's turn"), but a fair, memoryless picker has no concept of turns — every draw restarts at 1/N for everyone, including whoever just won.

Where this actually matters

If the stakes are "who goes first in a board game," a true 1-in-N tool is exactly what you want — nobody should be able to argue it was rigged. If the stakes are "who takes the unpleasant task every single week," a memoryless picker is mathematically fair per draw but can feel deeply unfair over time, because nothing stops the same name coming up three weeks running — the 20% chance from the worked example above is real, not a glitch. For a rotation where repeats should be ruled out by design rather than left to chance, a tool that removes each name after it's picked (or cycles through a fixed order) is the better fit, not a fresh independent draw every time. The Random Pick tool here does a fresh, independent, uniform draw every time you run it — which is the right tool for "settle it right now," not for "share it out evenly over time."