Prajwal Prathiksh
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Gift exchange draw

Make a draw for your group, then tell each person who they got.

Used in copied messages. You can change it after drawing.

1

People

Use distinct names so you know who is who. Everyone gives and receives one gift.

2

Exclusions optional

Keep two people from drawing each other. Useful for partners or housemates.

    A new draw replaces the last one.
    3

    Pairings

    Your pairings will appear here.

    Only the person viewing this screen can see them. Share each result yourself.

    How many draws are possible? A quick explanation and the maths
    People entered
    0
    No exclusions
    Add at least two names
    Exclusion pairs
    0
    With these exclusions
    Add at least two names

    The short version

    A draw means the whole set of pairings, not one person's pick. Everyone gives once and receives once. The "No exclusions" total rules out self-draws. The other total also rules out any pair you've excluded.

    These are counts of possible draws, not odds. The tool finds a valid draw at random, but it does not give every valid draw exactly the same chance.

    A four-person example

    Say Alex, Blair, Casey, and Devon are exchanging gifts. There are 24 ways to hand out all four names. Once you remove draws where somebody gets their own name, nine remain.

    1. 24ways to hand out four names
    2. 9after removing self-draws
    3. 4after also excluding Alex and Blair

    Why four at the end? Alex and Blair must get Casey and Devon, in either order. Casey and Devon then get Alex and Blair, also in either order. That's 2 × 2 = 4 complete draws.

    One of the four: Alex → Casey, Blair → Devon, Casey → Blair, Devon → Alex.

    This is a fixed example. The totals above use the names and exclusions you entered.

    Show the formulas For the mathematically curious

    Let n be the number of people. Before any restrictions, there are n! assignments. After removing self-draws, the count is called a derangement.

    Dn=n! ∑k=0n (−1)kk!

    For exclusions, mark every self-draw and both directions of each excluded pair as forbidden. Let rk count the ways to choose k forbidden giver-to-recipient spots without repeating a giver or recipient. Inclusion-exclusion then counts the valid draws:

    N= ∑k=0n (−1)k rk (n−k)!

    The overlap matters. A complete draw can break several restrictions at once, so subtracting one fixed amount per exclusion would count some draws more than once.