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30 Names, 30 Spins: Who Actually Gets Picked, Computed

Teachers and party hosts tell us the same story: they spin a name wheel to be fair, and somehow the same three people keep coming up while a quarter of the room never hears their name. That is not a broken wheel — it is the birthday paradox wearing a costume. We ran the numbers through the site's own sampler, 20,000 simulated class-size draws per row, and tabulated exactly how uneven a "fair" wheel really is, plus the one switch that makes it exact.

By Nan Liang
October 28, 2026 · 7 min read

Two kinds of numbers below, and they agree. The exact columns are closed-form: a name sits out all 30 spins with probability (29/30)³⁰, coverage needs follow the harmonic numbers, and the first-repeat figure is plain binomial survival. The simulation columns are the site's own sampler — weightedPick over a uniform 30-slice wheel, driven by seeded mulberry32, 20,000 class-size sessions per row.

The table: n names, n spins, no elimination

Group sizeNever picked (expected)Picked twice+ (expected)First pick repeats (exact)First pick repeats (sim)Spins to cover everyone (mean)Spins to cover 90%
103.53.561.3%89.1%29.322
207.27.262.3%94.4%72.045
3010.810.862.6%97.1%119.968

A curious identity: with exactly n spins, "picked twice or more" and "never picked" have the same expectation, n × (1−1/n)ⁿ — both ≈ 36% of the group at n=30. The simulation column lands within half a point of theory, which is the sampler confirming its own math.

What this means for your next session

Your wheel is not broken; your sample is short. A 30-name class needs about 119.9 spins on average before every name has appeared once — four times the list length. Spinning 30 times and calling it a day leaves 10.8 people on the bench, every time, by arithmetic rather than luck.

The first spinner is not safe either. The first name drawn has a 62.6% chance of coming up again before the round ends. If your game punishes repeat picks, that is a coin-flip-plus hanging over the opening draw.

Elimination mode is the exact fix. Flip the toggle under the wheel and every name comes up exactly once in n spins, in a uniformly random order — no coverage gap, no repeat penalty, no marathon. The name picker pairs it with the spin history so the room can see who is still waiting. For free-flowing party chaos where repeats are the joke, keep it off — the party wheel is built for that.

Decide in one line

Why do some names never come up on a fair wheel?
Because each spin is independent — the wheel has no memory. With 30 names and 30 spins, each name is missed by every spin with probability (29/30)³⁰ ≈ 36.2%, so about 11 of 30 names are expected to sit out entirely. Independence is what makes single spins fair; it is also what makes the sequence clump. The math is exact, and the simulation column in the post confirms it to the decimal.
Is the wheel biased toward certain names?
No. Every name has exactly a 1/30 chance on every single spin, and the sampler behind this site is a plain weighted draw with a seeded random source you can verify in the browser console. The clumping you see over a session is the expected shape of randomness, not favoritism — the same reason a coin can land heads five times in a row without being crooked.
How many spins until every name has been picked at least once?
For a list of n names the expected count is n × H(n), the n-th harmonic number — about 3× the list for 10 names, 3.6× for 20, and 4× for 30. That is roughly 120 spins to cover a class of 30 with no repeats-allowed spinning. If you need full coverage, do not spin longer — switch modes.
What does elimination mode change, exactly?
It removes each picked name from the pool after it lands, so the draw happens without replacement: every name comes up exactly once in n spins, in a uniformly random order. The trade-off is that the pool shrinks as you go, which is exactly what you want for taking turns — and the spin history keeps a running tally of who is still waiting.

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