Weighted picking is sold with adjectives — "boost," "favor," "give Ava a better chance." Nobody says the number. So we computed it: 20,000 seeded draws through the same weighted picker the site runs, plus 2,000 simulated classroom weeks to answer the question every teacher actually asks — how long until everyone has had a turn?
Both simulations below ran through the same engine that powers the random name picker — the same weighted-pick function, the same seeded randomness, deterministic seeds throughout. Nothing here is a hand-typed example.
20,000 weighted picks: theory vs measured
| Name | Weight | Theoretical win rate | Measured (20,000 picks) |
|---|---|---|---|
| Ava | 5× | 71.43% | 71.42% (14,284 wins) |
| Bob | 1× | 14.29% | 14.54% (2,907 wins) |
| Cat | 1× | 14.29% | 14.04% (2,809 wins) |
A 5× weight is not "five times more likely than each rival" — it is five-sevenths of everything, leaving barely a seventh apiece for the other two names. That gap between "5× more likely" and "71% of all draws" is the single most common misunderstanding of weighted drawing, and the table is the correction. The measured column landing within 0.2 points of the exact value is the engine's implementation check.
How long until everyone has been called on?
Equal weights, 12 students, five call-ons a day, list reset every morning — the honest version of the question teachers actually ask. The naive answer comes from the coupon-collector formula: covering everyone by pure chance needs about 12 × H(12) ≈ 37.2 draws in expectation, which naively divides to ≈ 7.4 school days. But a daily-reset picker never repeats a name within the same day, and that no-repeat pool covers measurably faster: 2,000 simulated classroom histories, each a fresh sequence of daily shuffles, averaged 6.5 days to full coverage.
The full distribution makes the practical point: most classes cover everyone in about a week, but a meaningful tail runs past two weeks — individual trials where one quiet student evades the wheel for days on end are not malfunction, they are the math being honest. That tail is exactly what the session, daily and weekly no-repeat modes are for: they convert "probably soon" into a guarantee, which for classroom trust matters more than any single draw's fairness.
What weighting is — and is not — for
Weighting answers a real need: some draws should favor someone, openly and checkably. A teacher boosting a quiet student's airtime, a standup rotation where the lead speaks first. The seed makes the favoritism explicit instead of sneaky — anyone can re-run the draw and confirm the weights did what they said.
But weighted randomness is a participation tool, not a lottery tool. The moment money, prizes or selection-out consequences attach to a draw, uneven weights stop being a feature and become the exact rigging our methodology exists to rule out. If every entrant can't verify equal treatment, don't weight — and if you do weight, show the seed.