When a ladder draw is the right tool
A ladder draw (called amidakuji in Japan and often "ghost leg" in English) hands out a set of outcomes to a group so that every person gets exactly one and no outcome is used twice. That covers a single loser in a coffee bet, a full presentation order from first to last, or a rota of chores. The tool draws a ladder from the names and outcomes you type and, when you click a name, shows the path from the top to the bottom. Nothing you enter is sent to a server or saved in the browser, so a refresh clears it all.
Why a ladder always matches people and outcomes one to one
Every rung connects two neighbouring vertical lines, and walking over it swaps the positions of the two walkers on those lines. Think of each rung as a swap between two adjacent seats. A swap can be undone by swapping again, so any chain of swaps can be undone too, which means two different people can never land in the same slot and no slot can be left empty. In mathematical terms the combined effect of all rungs is a permutation, a one-to-one mapping. The condition that keeps this true is that rungs on the same row never share a vertical line; the generator places them left to right and skips a column after each rung.
There is one more known property. A single rung is one swap, so a ladder with an even number of rungs produces an even permutation, and a ladder with an odd number produces an odd permutation. Everyone can finish exactly under their starting line after an even number of rungs, but never after an odd number.
How many assignments are possible
| Participants | Places for a rung in one row | Possible assignments (n!) |
|---|---|---|
| 2 | 1 | 2 |
| 3 | 2 | 6 |
| 4 | 3 | 24 |
| 5 | 4 | 120 |
| 6 | 5 | 720 |
| 7 | 6 | 5,040 |
| 8 | 7 | 40,320 |
With 8 people there are 40,320 ways to give everyone a different outcome, and a ladder is a visual way of picking one of them.
Example 1: following four people through eight rungs
Four vertical lines, numbered 0 to 3 from the left, start with Alex, Jamie, Taylor, Morgan. The bottom slots, left to right, hold Dishes, Pass, Pass, Coffee. The ladder has 8 rungs, and the trails below were traced with the same rule the tool uses. Each number is the line the person stands on after crossing one more row.
| Name | Line after each row (top to bottom) | Finishing slot | Outcome |
|---|---|---|---|
| Alex | 0 β 1 β 2 β 2 β 3 β 3 β 3 β 2 β 1 | 1 | Pass |
| Jamie | 1 β 0 β 0 β 0 β 1 β 2 β 2 β 3 β 3 | 3 | Coffee |
| Taylor | 2 β 2 β 1 β 1 β 0 β 0 β 1 β 1 β 2 | 2 | Pass |
| Morgan | 3 β 3 β 3 β 3 β 2 β 1 β 0 β 0 β 0 | 0 | Dishes |
The finishing slots are 1, 3, 2, 0, with no repeats, so the one-to-one property holds here. Eight rungs is an even number, and the overall arrangement (line 0 to slot 1, line 1 to slot 3, line 3 to slot 0, line 2 unchanged) is a rotation of three people, which is an even permutation, consistent with the parity rule above.
Example 2: three rungs that reverse three people
With only three rungs placed left, right, left across three lines, line 0 ends in slot 2, line 1 in slot 1 and line 2 in slot 0, so the order is fully reversed. Few rungs does not mean a mild shuffle; what matters is how the rungs overlap in height. This reversal uses three rungs, an odd number, and a reversal of three items is a single swap of the outer pair, an odd permutation, which again matches the parity rule.
Random rungs alone do not make every slot equally likely
Being one-to-one is a different thing from being equally likely. A ladder with randomly placed rungs tends to send a person to a slot near their starting line slightly more often than to a far one. The next table gives the exact finishing distribution for four people with a 35% chance of a rung, 20 rows, and rungs placed left to right, computed when the page is built (values in percent).
| Start \ Finish | Slot 0 | Slot 1 | Slot 2 | Slot 3 |
|---|---|---|---|---|
| Line 0 | 26.4% | 25.8% | 24.3% | 23.5% |
| Line 1 | 25.8% | 25.4% | 24.6% | 24.2% |
| Line 2 | 24.3% | 24.6% | 25.3% | 25.7% |
| Line 3 | 23.5% | 24.2% | 25.7% | 26.6% |
Line 0 reaches slot 0 with a probability of 26.4% and slot 3 with 23.5%, instead of an even 25%. To remove that bias, this tool shuffles the outcomes with a Fisher-Yates shuffle before assigning them to the bottom slots. Which outcome sits under which slot is therefore uniformly random, and every person has the same chance of every outcome. The rungs are there to make the path something you can follow with your eyes; the fairness comes from the shuffle.
How to use it
- Type one participant per line and one outcome per line. Both lists need the same number of lines, from 2 to 8.
- Decide whether outcomes stay hidden, then press "Build the ladder". With hiding on, only the slot a path reaches is revealed.
- Click a name to follow its path and reveal its result, or press "Reveal all" to open everything.
- To run it again, press "Redraw the ladder". New rungs are drawn and the outcomes are shuffled again.
Common mistakes and limits
- If the outcomes are visible before people choose, someone can pick the line that leads to the outcome they want, because following a path by eye is easy. For bets, keep the outcomes hidden.
- Duplicate names or duplicate outcomes still work, but identical names are hard to tell apart on screen, so add a number or initial.
- The random numbers come from the browser's Math.random, which is a general-purpose generator and is not meant for security. It is fine for a friendly bet but not for a giveaway or lottery where you must prove the draw was fair.
- The participant count and outcome count must match. A stray blank line is ignored, but a missing outcome stops the build with a message.
- Before sharing a screenshot, check whether outcomes are still hidden and how much of the paths are already shown.
Ways to use the result
For a bet where one person loses, mix one "Buy the coffee" with several "Nothing" outcomes. For presentation order, write 1st, 2nd, 3rd and so on as outcomes. For chores, list the tasks as outcomes, and if there are more people than tasks, pad the list with entries such as "Day off". When you repeat a draw, build a fresh ladder each time so nobody can study an old one.
Frequently Asked Questions
Can the result be rigged?
The rungs and the outcome order are generated randomly in your browser at the moment you press the build button, and nothing is sent to a server. As with any web page, someone with developer tools can inspect values on their own screen, so for a draw that needs trust, have everyone watch the same screen.
What is the maximum number of participants?
The tool supports 2 to 8 people so the ladder stays readable. For bigger groups, a team divider or random number generator is a better fit.
Do more rungs make the draw fairer?
No. Fairness here comes from shuffling the outcomes before they are assigned to the slots, so every slot is equally likely however many rungs there are. Rungs just make the path visible and hard to predict from the top.
Can two people end up at the same outcome?
No. Each rung swaps two neighbouring paths, so everyone finishes in a different slot. If you typed the same wording for several outcomes, they are still separate slots that merely share a label.
Are my names and outcomes saved?
No. The page does not use cookies or local storage, and refreshing or closing the tab clears the inputs and the ladder. There is no syncing between devices either.
Related tools
- Team Divider - split a group into random teams
- Random Number Generator - draw a single number
- Coin & Dice Roller - quick yes/no or number draws