Selection With and Without Replacement

Two different questions

With replacement — every entry stays on the wheel. Each spin is independent and identical. A name can win twice in a row.

Without replacement — the winner comes off the wheel. Each spin draws from a smaller pool, and no entry can win twice.

Wheel Cue calls the second one Remove the winner after each spin. It is on by default on the student picker, the giveaway picker and the raffle wheel, because those three almost always want it.

They answer different questions. "Who answers this question?" is with replacement — the same student *could* be asked twice in a lesson. "Who gets each of the three prizes?" is without — one person should not take two.

What happens to the odds

With ten names and replacement, every spin is 10% for everyone, forever.

Without replacement, the odds climb for whoever is left:

This is not the wheel becoming unfair. Over the whole sequence every name is drawn exactly once, so each has the same chance of ending up in any given position. It is more even than drawing with replacement, not less.

The strip under the wheel and the result window both update as the pool shrinks, so the current odds are always on screen.

Which one you want

Use without replacement when the results have to be different:

• Multiple prizes with one winner each
• Working through a whole class before anyone repeats
• A running order or turn order
• Assigning jobs, roles or dates where duplicates make no sense
• Drawing several distinct numbers

Use with replacement when each event is genuinely separate:

• One question, one student, no relationship to the last lesson
• A yes/no or coin flip
• Picking dinner tonight, which has nothing to do with last night
• Anything where you want the true independent probability each time

The common mistake is leaving replacement on for a multi-prize giveaway and then being surprised when someone wins twice. That is not the wheel misbehaving — it is exactly what independent draws do.

Practical notes

• Reset puts everyone back. The button under the entry list restores the original list, so a class roster returns to full strength for the next round.
• The Results panel is the record. It keeps the order names were drawn in, and Copy exports it with probabilities and timestamps.
• Weights still work. A removed weighted entry takes its tickets with it and the total drops, so everyone else's share rises.
• Shuffling is the same idea, done at once. [Shuffle] under the entry box, or the team generator, rearranges everything in one move instead of draw by draw. A full shuffle and drawing without replacement until the wheel is empty are statistically the same procedure.