With replacement versus without replacement
With replacement means the winner goes back in. The list is identical before every draw, so every draw is independent: the same entry can win twice in a row, and over many draws some entries will win repeatedly while others never come up. That is correct behaviour for sampling — it is what "pick one at random, every time" literally means.
Without replacement means the winner leaves the pool. Nothing can win twice, and the draw ends when the pool is empty. This is the right model whenever the goal is coverage: every student answering once, every prize going to a different entrant, every task assigned exactly once.
Why the probabilities change after each removal
On an equal wheel every entry's chance is one divided by the number of entries. Remove one and the denominator shrinks, so the survivors' chances grow. A worked example with four names — Amara, Ben, Chloe and Diego:
| Stage | Pool | Amara | Ben | Chloe | Diego |
|---|---|---|---|---|---|
| Before draw 1 | 4 names | 25% | 25% | 25% | 25% |
| Ben wins, is removed | 3 names | 33.3% | — | 33.3% | 33.3% |
| Diego wins, is removed | 2 names | 50% | — | 50% | — |
| One remains | 1 name | 100% | — | — | — |
Two things are true at once here, and they are easy to confuse. Each individual draw is perfectly fair among the entries still in the pool — at every stage the remaining names have identical chances. But the draw is not a sequence of independent events: Ben's chance of winning draw 2 was zero, because he had already won. "Everyone eventually gets picked" describes the whole session, not the conditions of any single draw.
How this maps onto WheelOurNames
On the wheel, drawing without replacement is the auto-remove option (in the behaviour settings). It is off by default — the standard wheel draws with replacement, so a name can genuinely come up twice in a row. Switch auto-remove on and each winner leaves the wheel after a short countdown (five seconds by default, adjustable), the remaining slices resize, and the next spin starts from the recomputed odds. Removed names are not deleted from your list: they sit in the winner history, where you can restore any of them to the wheel individually. When the last name is removed the wheel is empty and the spin button is disabled until you restore or re-add entries — there is no draw from an empty pool.
The Giveaway Wheel uses the same idea for multi-winner draws. With "allow repeat winners" off, each announced winner is removed before the next spin, so ten prizes go to ten different entrants; the tool refuses the draw up front if you ask for more unique winners than the pool contains. Switch repeats on and you are back to sampling with replacement, where one lucky entrant can take two prizes.
The shuffle is the quiet third case
A full-list shuffle — what the List Randomizer does — is also selection without replacement, just performed all at once. Drawing names one by one without replacement until the pool is empty produces exactly the same thing as shuffling the list and reading top to bottom: a random ordering in which every entry appears exactly once. If what you actually need is "everyone, in a random order," the shuffle gets there in one step instead of n spins.
Choosing between the modes
- Classroom cold-calling. Without replacement (auto-remove) when the aim is to hear from everyone once per topic; with replacement when you want every question to feel equally live for every student.
- Giveaways. Without replacement whenever prizes must go to different people; with replacement only when your rules explicitly allow one entrant to win multiple prizes.
- Ordering and rotation. A shuffle — without replacement, done in one pass.
- Repeated sampling and games. With replacement: each round should be independent, like rolling a die again.
Whichever mode you choose, the randomness underneath is the same cryptographically secure, bias-corrected draw documented on the fairness page — the only thing that changes is whether the winner stays in the pool.