Random Selection With vs. Without Replacement

What does “with replacement” mean?

With replacement means the selected Entry remains eligible for the next draw. If a Wheel contains five names, each draw still begins with those same five eligible Entries unless somebody edits or disables the list.

Imagine five discussion prompts labeled A through E. The Wheel selects B. With replacement enabled, B stays in the pool, so the next Selection can be B again. Each draw answers the same question from the same set of eligible choices.

This setting fits activities where a repeat is harmless or useful. A warm-up prompt can produce a different answer from a different person. A movement break can return later in the day. The facilitator still needs to check that every Entry remains suitable each time it appears.

What does “without replacement” mean?

Without replacement means a selected Entry becomes ineligible for the rest of the current round. The pool gets smaller after each Selection, so every enabled Entry can appear once before the round is complete.

Take the same five Entries. If B is selected first, the next Selection comes from A, C, D, and E. Continue selecting and the Tool produces a repeat-free sequence. Reset begins a new round and makes the Entries eligible again.

Penn State’s probability materials use the same plain definition: an object selected without replacement is set aside instead of returned before the next selection. NIST’s random-permutation documentation likewise describes selecting all items without replacement to create a random ordering.

How the probabilities change after a Selection

Suppose four distinct Entries each appear once. On the first draw, each has a one-in-four chance. With replacement, those odds remain one in four on the second draw. Without replacement, the selected Entry has no chance in that round and each of the three remaining Entries has a one-in-three chance next.

Without replacement does not make the later Selections unfair. Every Entry had the same chance to occupy each position before the sequence began. The changing denominator reflects the smaller eligible pool.

The distinction matters when somebody asks why an Entry appeared twice. A repeat is a normal possible outcome with replacement. A repeat during a correctly run no-repeat round signals that the session was reset, the policy changed, the list contains duplicate labels, or the setup needs checking.

Choose the setting from the job

Use replacement when each draw should be a fresh choice from the same list. Use no replacement when the group needs unique turns, broad participation, a shortlist without duplicates, or a complete random order.

Duplicates are separate from the repeat setting

The repeat policy controls what happens after a Selection. Duplicate Entries affect the eligible pool before a Selection. If “Blue” appears twice in a four-row list, those two rows together receive two of the four eligible positions on the first draw.

Turning repeats off does not merge duplicate labels. One Blue row can be selected and excluded while the other Blue row remains eligible. Remove accidental duplicates when each distinct person or option should receive an equal chance.

Sometimes two people genuinely share a name. Keep both Entries and add a neutral identifier that the group already knows, such as a team or first initial. Do not add email addresses, private notes, or other sensitive details merely to distinguish them.

How to run a no-repeat Wheel in Randomly

Open the Wheel, add one row for each eligible Entry, leave “Allow repeat Winners” turned off, and make the first Selection. The Winner is excluded from the current round, and the status shows how many eligible Entries remain.

1. Review the list for missing, disabled, or duplicated Entries before starting.
2. Leave “Allow repeat Winners” off and explain when the round will end.
3. Make a Selection and record the Winner if you are building an order.
4. Continue until every eligible Entry has had a turn or the required number has been selected.
5. Use Undo for the latest genuine mistake, or Reset when the group is ready for a new round.

What this setting does not decide

Replacement changes repeat behavior; it does not decide whether the starting list is appropriate. The facilitator remains responsible for eligibility, consent, accommodations, privacy, and the consequences of the Selection.

Keep random selection to low-stakes tasks. A no-repeat setting can distribute ordinary speaking turns, but it cannot make a hiring, medical, legal, disciplinary, financial, safeguarding, or safety process fair or compliant.

State correction rules before the first Selection. If a missing person or duplicate row is discovered, pause, explain the correction, and restart or continue according to the announced rule. Do not quietly reset because the group dislikes a valid result.