How Amidakuji (Ghost Leg) Works and Whether It's Fair | Making One Online
Amidakuji, the Japanese “ghost leg” lottery, is a classic way to assign roles or seats. This guide explains, from the underlying maths, why every player always ends up with exactly one result and whether it is really fair, then walks through making one online.
The basic rules of amidakuji
Amidakuji is made of vertical lines and horizontal rungs connecting neighbouring vertical lines. You start at the top, go down, and every time you meet a rung you cross over to the next vertical line. That's the whole rule. In English it's often called “ghost leg”, and in Japan it's also known as the ladder lottery.
- Number of vertical lines = number of players = number of results
- Rungs only connect neighbouring vertical lines
- No two rungs are drawn at the same height on the same line
- Go from top to bottom, and always cross over when you reach a rung
Why everyone always gets exactly one result
The neat thing about amidakuji is that however complicated the rungs, two people never reach the same result, and no result is left unchosen. This isn't luck; it's guaranteed by the structure.
Drawing one rung is the same as swapping the positions of two neighbouring players. A swap can always be undone. The whole amidakuji is just a series of these swaps stacked from top to bottom, and no matter how many undoable steps you stack, the whole thing can still be undone. That is why the starting points and the end points match up exactly one to one.
Is amidakuji really fair?
“Matches one to one” and “is fair” are different things. In short, an amidakuji with only a few rungs is not fair.
With no rungs at all, the result is decided entirely by where you start. With only a few rungs, you can't travel far from your starting point, so destinations cluster nearby. In other words, someone starting at the edge is clearly more likely to land on an edge result.
On the other hand, if you draw plenty of rungs at random positions, that bias fades quickly and the chance of going from any start to any result gets close to equal. Hand-drawn amidakuji feel predictable because they have few, short paths. If fairness is what you want, more rungs is better.
- Few rungs → short moves, so the result stays close to the starting position
- Many random rungs → every start spreads out almost evenly
- Tall layout with many branches → hard to follow by eye, and hard to predict
Why deciding the results first helps
Our amidakuji maker has you lay out the results first to create the frame, then enter a name at each starting point. This order has practical advantages.
- You can prepare the results (winner, tasks, prizes) in advance, so setup is done before everyone arrives
- The structure is already fixed when names are entered, so nobody can suspect that a rung was added later to favour someone
- The amidakuji is regenerated every time you rebuild the frame, so the same set of results gives a different pairing each time
How to make one online and when to use it
- 1
Enter the results and build the frame
List the results you want to assign first, such as “win / lose”, “task A / task B” or prize names.
- 2
Enter a name at each starting point
Type each player's name at a starting point. The structure of the amidakuji is already fixed at this stage.
- 3
Show the amidakuji
Press the show button to draw tall routes with plenty of branches. Everyone can follow the routes together to see the results.
Typical uses include assigning roles or tasks at a party or meeting, handing out prizes, and splitting teams or deciding turn order in games. A simple rule: use amidakuji when you want to give one result to each person, and a wheel when you want to pick just one.
Amidakuji vs. wheel vs. dice
“Decide randomly” covers different needs: assigning, picking one, or getting a number. When in doubt, choose based on how the number of results compares to the number of people.
| Method | Best for | Kind of result | Duplicates |
|---|---|---|---|
| Amidakuji | Assigning tasks, seats or prizes | Gives one result to each person, one to one | Never |
| Wheel | Picking one person or one idea | Draws one item each spin | Possible |
| Dice | When you need a number: order, moves, points | A number from 1 to 6 | Possible |
For duties repeated every month, rotating a schedule is less hassle than redrawing each time. See how to set up a duty rotation for that approach, and how to split teams if you want to divide people into groups.
Common mistakes when drawing one on paper
When a paper amidakuji is unfair, the cause is the way it was drawn, not the method itself. These four mistakes are the typical reasons results get read on the spot or the draw has to be redone.
- Too few rungs: with only 3 or 4 rungs, start and end points line up almost straight down
- Rungs at the same height: when two neighbouring rungs share a height, people disagree on which to take first
- The person who drew it enters names last: they can see the structure when placing names, which invites suspicion
- The fold hiding the results is too shallow: results can show through from above
FAQ
- Can two people get the same result in amidakuji?
- No. Each rung swaps two neighbouring positions, and stacking swaps still keeps starts and ends matched one to one. So results are never duplicated and no result is left over.
- Is amidakuji fair?
- It depends on the number of rungs. With few rungs, results are biased by starting position, but with plenty of randomly placed rungs every start has an almost equal chance. If fairness matters, choose a layout with many rungs and tall lines.
- How many players can take part?
- Our amidakuji maker supports as many as fit across the screen. In practice, 2 to 8 players is easiest to read.
- Does the result change every time?
- Yes. The amidakuji is randomly regenerated every time you rebuild the frame, so even the same set of results gives a different pairing each time.
- How many rungs should I draw?
- Aim for at least three times the number of players: about 12 for 4 people. With too few, the starting position directly affects the result, but with more rungs at random heights the bias almost disappears.
- Should I use amidakuji or a wheel?
- Use amidakuji to give one result to each person, and a wheel to pick just one from the whole group. Amidakuji never duplicates results but needs as many results as people; a wheel can be spun any number of times, but the same item can come up twice in a row.
- Can I make one on my phone?
- Yes. It runs in the browser, so there's nothing to install. With many players, turning your phone sideways makes the routes easier to follow.
Tools in this article
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