Ladder Draw Generator (Amidakuji)

What this generator does

Draws a set of vertical lines with rungs between neighbours, and matches whatever is at the top of each line to whatever is at the bottom of the line you reach by walking down and crossing every rung you meet. Because each rung only ever swaps two neighbours, the result is always a one-to-one matching — and because the arrangement is drawn first and the ladder built to produce it, every possible matching was equally likely.

How to use this tool

1. Type the names at the top and what they are being matched to at the bottom, the same number of each.
2. Draw the ladder, and let everybody trace their own line before anything is revealed.
3. Cross every rung you meet; carry straight on where there is none.
4. Show who got what to confirm what everybody already worked out.

Understanding the controls

At the top

The names, one a line or separated by commas. They stay in your browser.

At the bottom

What each one is being matched to. The same number as at the top, because a ladder matches them one to one and cannot do anything else.

Extra rows

How many rows of scattered rungs go in before the rows that land the result. More rungs make a longer walk and a better-looking ladder; they do not change the odds, because the answer was settled before they were drawn.

Trace

Highlights one line all the way down, for confirming by eye what somebody has already traced with a finger.

Common use cases

• Deciding who does which job, in front of the people it applies to
• Matching people to secret santa gifts, teams, seats or chores
• A draw where somebody is going to object, and you want the working visible
• Teaching what a one-to-one matching is, with something everybody can trace
• Running a draw on a screen a room can see, without anybody having to trust the screen

How this generator works

Two things are established on the finished drawing rather than on the intention behind it. That everybody is matched one to one is proved by walking the rungs as drawn — down from every line, and then up from every finish, which has to return the line that walks down to it. And that no outcome was favoured is a matter of construction: scattering rungs and seeing what happens is not uniform, because a ladder with few rungs barely moves anybody. So the arrangement is drawn first with a fair shuffle, and rows are then added until the ladder produces it. Those closing rows use a sort that swaps disjoint neighbouring pairs in each round, which is exactly what a row of a ladder can hold, so no round can contain two rungs that touch.

Randomness and fairness

The arrangement and the scattered rungs come from your browser’s secure generator. There is deliberately no repeat word: the names are yours and never go into the address, so a link could carry the ladder but not the people on it — and a link that promised the same draw while giving a different one would be worse than no link at all.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• Names stay in your browser, so there is no link that reproduces a draw. Print it or copy the result if it has to be kept.
• Two to twelve lines. Beyond that the rungs stop being traceable by eye, which is the only reason to use a ladder rather than anything else.
• The top and bottom lists have to be the same length, because a ladder matches one to one and cannot leave anybody out or give anybody two.
• Extra rows change how the drawing looks and not what it does. A ladder that looks busier is not fairer.
• There is no way to keep two particular people apart, or to fix one pairing in advance. A draw that is steered is not a draw.

Privacy and your data

Everything happens in your browser: the names you type are never transmitted, never stored, and never written into the address. What is measured is that a ladder was drawn and how many lines it had — never who was on it.