Why random picking keeps missing the same people

Picking one name at random from a class of thirty, thirty times, leaves about eleven students unpicked. Each individual has a 36.17 per cent chance of never being drawn, because each draw is independent and the picker has no memory of who has already had a turn. Random and fair are not the same word as even.

This surprises people because the intuition for "random" is closer to "shuffled" — and a shuffle does guarantee everyone. The fix is to use a shuffle, which is what the remove-once-picked option does.

How bad is the coverage problem?

Worse than it feels, and it gets worse with the size of the group. The number of draws needed to expect everyone to have appeared at least once grows faster than the group does.

A class of thirty needs about 120 draws before everyone can be expected to have been picked once. At one question a lesson that is most of a school year, and the last few students are the slowest to arrive: after 60 draws about four are still untouched, and after 90 there is still roughly one.

This is the coupon collector problem, and its shape is why the tail is so long. Early draws almost always find someone new; late draws almost always find someone who has already been picked.

What does remove-once-picked change?

Everything about the coverage, and nothing about the fairness of any single draw. With removal on, the picker samples without replacement: each name comes out exactly once, and thirty draws cover thirty students.

Each individual draw is still uniform over whoever is left. The first pick is one in thirty, the second is one in twenty-nine, and the last is a certainty — which is fair in the sense that matters for a rota, and is not the same statistical object as thirty independent draws.

For a classroom register or a standup order, removal is almost always what you want. For anything where a repeat is legitimate — drawing a topic, picking a warm-up exercise — it is not.

Why does the same name come up twice in a row?

Because with thirty names it happens 3.33 per cent of the time, which is about once a month at one pick a day. Independence means the previous result has no influence on the next, and the picker has no rule against it because such a rule would make the draw less random rather than more.

A room reads a back-to-back repeat as evidence the tool is broken. It is the opposite: a picker that never repeated would be one that remembered, and a picker that remembers is one that can be predicted.

What actually makes a rota feel fair?

Visible state rather than better randomness. Three things do most of the work.

• Show the remaining list. If everyone can see who is still in, nobody has to trust the arithmetic.
• Show who has been picked. The history is what settles the argument about whether someone has had two turns.
• Reset deliberately. Starting a fresh round is a decision worth announcing, because it is the moment the coverage guarantee restarts.

A picker that removes names and shows both lists needs no explanation at all. One that draws independently and shows only the winner needs the entire argument above, every time.

There is a middle option worth knowing about: draw with removal, but reset the round early. Working through twenty of thirty names and then restarting keeps the coverage benefit while stopping the last few draws from being predictable — by name twenty-eight everyone in the room knows who the remaining two are, and the draw has stopped being a draw.

Does the order within a round matter?

Only if the position carries an advantage. Going first on a cold-call question is harder than going tenth; presenting first in a review is different from presenting last. Where that is true, sampling without replacement solves coverage and leaves a second fairness question about position untouched.

The usual answer is to reverse or re-draw the order each round, so a student who went first this week does not go first next week. That is a scheduling decision rather than a randomness one, and it is the part a picker cannot do for you.

Questions people ask

Is each pick genuinely random? Yes — drawn from the browser cryptographic random source, not from a simple pseudo-random function. The uniformity holds over whoever is currently in the list.

Will it remember my list between visits? No. Nothing is stored and nothing is sent anywhere, which means pasting the register takes a moment at the start and leaves nothing behind afterwards.

How many names can I paste? A full class list or a department, without trouble. The practical limit is how many you can read on screen rather than anything in the tool.

Can I pick more than one at a time? Yes, and with removal on that draws a distinct group rather than a name that might appear twice in the same group.

Turn removal on and the coverage problem disappears; leave it off and expect eleven students in thirty to slip through. The random person picker is the plain-list version, spin the wheel is the same draw with an audience attached, and the random number generator handles the case where the list lives somewhere else and you only need an index.