Guides/Draw without replacement

Drawing without replacement from a list

“Without replacement” means once a name (or ticket) is drawn, it cannot win again in that round. That is the right model for 1st / 2nd / 3rd place, or for dealing unique tasks from a checklist.

Equal odds at each step

• With n remaining entries, each should have chance 1/n for the next draw.
• After a removal, renormalize: now 1/(n−1) for each survivor.
• A full fair shuffle then reading top-to-bottom is one way to get an ordered without-replacement sequence —seeded shuffle.

Worked example

1. List: Ada, Bo, Cam, Di (4 people). First prize: each 1/4.
2. Suppose Bo wins first. Second prize among Ada, Cam, Di: each 1/3.
3. Do not keep Bo in the hat “for fairness” — that would allow a double win unless you want that.

Duplicates and tickets

• If someone has three tickets, list their name three times (or weight the draw) before removing winners.
• After they win once, remove only one ticket — or all tickets — depending on your published rules.
• Raffle setup:fair raffle·giveaway lists.

With vs without replacement

With replacement (put the name back) is for independent daily picks where repeats are OK —pick without bias. Habit rotation may shuffle then walk the order:shuffle checklists.

Try a single fair draw

Random List Picker— for multiple unique winners, remove each pick from the list before drawing again.