There are two honest ways for a name wheel to avoid being unfair, and they are not the same thing. Understanding the difference is the whole answer to “is a no-repeat wheel really fair?”
Two ways to be fair
No-repeat rounds (a full rotation): the wheel deals every name out once before anyone repeats. With 25 names, spins 1 through 25 are those 25 names in a random order, then the round resets and reshuffles. Everyone gets exactly one turn per round.
Plain reshuffle (independent picks): every spin is a fresh, independent uniform draw from all names. Any name can come up at any time — including twice in a row — because the wheel has no memory of what it just picked.
What “fair” should mean for taking turns
For calling on students or setting an order, “fair” is not only “each name is equally likely on a single spin” — both methods pass that. It also means good coverage (everyone actually gets picked soon), no clustering (no one is picked twice while someone else waits), and bounded waiting (no unlucky person waits forever). No-repeat rounds win all three by construction; plain reshuffle wins none of them with certainty.
I simulated both — here is the data
I ran a Monte Carlo simulation of both methods for classes of 10, 25, and 40 names (over 100,000 trials each) and cross-checked the coverage numbers against the exact coupon-collector formula, N × (1 + 1/2 + … + 1/N). The simulation and the formula agree to the first decimal, which is the check that the numbers below are right.
| Class size (N) | No-repeat: spins to cover all | Plain reshuffle: average / 90th pct | Perfect round by luck | Back-to-back repeat rate |
|---|---|---|---|---|
| 10 | 10 (guaranteed) | 29 / 44 | about 1 in 2,800 | 10% per spin |
| 25 | 25 (guaranteed) | 95 / 135 | about 1 in 5.7 billion | 4% per spin |
| 40 | 40 (guaranteed) | 171 / 236 | about 1 in 15 quadrillion | 2.5% per spin |
Wait times tell the same story. With no-repeat rounds, the longest anyone can go between turns is bounded to at most 2N−1 spins (at most 49 for a class of 25). With plain reshuffle the wait has a heavy tail: over a 200-spin session with 25 names, the longest gap for a single name averaged 58 spins and reached 88 at the 90th percentile — someone routinely waits far longer than one rotation.
Reading the results
- Coverage: no-repeat covers the whole class in exactly N spins. Plain reshuffle needs about N × ln(N) on average — nearly four rounds' worth of spins to be confident everyone has had a turn.
- Clustering: plain reshuffle repeats a name back-to-back about 1 in N spins. In a busy 30-spin session with 25 names that is roughly one back-to-back repeat every session; with 10 names it is about three.
- A “perfect” fair round happening by chance is effectively impossible past a handful of names — 1 in billions by 25 names — so if you want guaranteed turns, you have to enforce them, not hope for them.
- Bounded vs unbounded waits: no-repeat caps the worst wait; plain reshuffle's worst wait keeps growing with a long session.
So which should you use?
Use no-repeat rounds when the goal is turns: calling on every student, setting a stand-up order, rotating who goes first. It guarantees coverage and caps waiting, which is exactly what “fair turns” means.
Use plain reshuffle when each draw must be genuinely independent of the last — a raffle, a coin-flip-style yes/no, or any single decision where past outcomes should not constrain the next one. Here a no-repeat rule would actually be wrong, because it would make later draws depend on earlier ones.
One honest caveat: no-repeat is not “more random” on a single spin. Within a round it is deliberately less independent — that dependency is the mechanism that guarantees everyone a turn. Both methods are uniform per spin; they differ in what they guarantee over many spins.