What Is Amidakuji? The Mechanics and Uses of a Fair Lottery Method

Amidakuji is a Japanese lottery method that uses a diagram of vertical and horizontal lines to fairly assign outcomes to participants. All you need is paper and a pen, and it remains widely used in various settings today.

This article explains the history and origin of amidakuji's name, the mechanism that ensures its fairness, and how it differs from other lottery methods.

History and Origin of the Name

The origins of amidakuji date back to the Muromachi period in Japan. At the time, it was called "Amida kuji" and involved drawing radial lines on paper, with each person pulling from an end. The completed diagram resembled the halo (light rays) behind Amida Buddha, which is how it got its name -- the circular rays of light behind the Buddhist statue overlapped with the radial pattern of the lines.

During the Edo period, the radial format evolved into the current style of parallel vertical lines connected by horizontal rungs. This change made it possible to use paper space more efficiently even with large groups, and the method spread widely among common people. Amidakuji came to be used in all manner of everyday situations, from assigning festival duties to determining the order of merchant transactions.

Names Around the World

Similar lottery methods to amidakuji are used across Asia. In Korea, it is called Sadaritagi, meaning "ladder climbing." In China, it is known as Guijiaotu (Ghost Leg Diagram), and in English-speaking countries, it goes by Ghost Leg or Ladder Lottery. While the names differ, the structure using vertical and horizontal lines is largely the same, showing that this method has been accepted across regional boundaries.

How Amidakuji Works

The structure of amidakuji consists of vertical lines equal to the number of participants and horizontal lines (rungs) connecting adjacent vertical lines. Start points are placed at the top and goals (outcomes) at the bottom. You trace down your chosen vertical line from top to bottom. Whenever you encounter a horizontal line, you must cross over to the adjacent vertical line, then continue downward. You repeat this process until you reach the bottom, and the goal you arrive at is your result.

For a detailed guide on how to create and use one, see the Amidakuji beginner's guide.

The Mathematical Basis of Fairness

The reason amidakuji is fair lies in the mathematical concept of "permutations."

Adding one horizontal line swaps the destinations of two adjacent vertical lines. In mathematics, this is called an "adjacent transposition" -- the most basic permutation that exchanges the positions of two elements. An entire amidakuji is built from a series of these adjacent transpositions, which creates a one-to-one correspondence between start points and goals.

This one-to-one correspondence has an important implication: every start point leads to a different goal, no two people reach the same goal, and no goal is left unassigned. With just a few horizontal lines, the paths become rapidly complex, making it virtually impossible for the human eye to predict the outcome. This unpredictability is what guarantees amidakuji's fairness at an experiential level as well.

For more on the mathematical proof, see this article.

How Amidakuji Differs from Other Lottery Methods

Amidakuji has fundamental structural differences from other lottery methods.

Drawing lots is simple, but there's a possibility of multiple winners or only losing tickets remaining. It doesn't inherently guarantee assigning different outcomes to everyone. Amidakuji guarantees a one-to-one correspondence, so duplicates and omissions never occur.

Rock-paper-scissors requires no tools and is convenient, but ties happen frequently. With large groups especially, multiple rounds of do-overs are needed, consuming considerable time. Amidakuji determines everyone's outcome in a single round.

Roulette wheels and lottery apps are convenient, but since their internal workings are hidden, doubts about "is it really random?" tend to linger. Amidakuji proceeds visibly to everyone -- from drawing the horizontal lines to tracing the paths -- making transparency its greatest strength.

See a detailed comparison of various lottery methods here

Where Amidakuji Shines

Amidakuji is particularly effective for role assignment. It's ideal for fairly distributing tasks that someone must take on -- like choosing the organizer for a get-together, assigning project roles, or allocating duties. Everyone can easily accept the result, leaving little room for dissatisfaction.

It also works well for event lotteries. For cases like selecting prize winners or distributing gifts where you want to assign a different outcome to each participant, amidakuji distributes without duplication.

Team division and order determination are other great use cases. For group work teams, presentation order, or karaoke turns, amidakuji assigns outcomes to everyone while eliminating arbitrary selection.

Challenges of Paper Amidakuji and the Move Online

Paper-based amidakuji has its challenges: all participants need to be in the same place, management becomes difficult with large groups, and recording and sharing results is cumbersome.

Online amidakuji solves these problems. Participants can join remotely, getting started is as simple as sharing a URL, and results are automatically recorded for easy later review.

See a detailed comparison of offline vs. online here

Amida-san: Free Online Amidakuji

Amida-san is a service that lets you use amidakuji online for free. No registration is required -- just share the URL with participants to start a lottery. It works on smartphones, tablets, and PCs alike, maintaining the same fairness and transparency as traditional amidakuji. It also offers features like 3D visualization (paid option), multi-language support, and QR code sharing.

Learn more about how to use it

Frequently Asked Questions

Is amidakuji really fair?

Yes, it is mathematically proven. Every start point leads to a different goal, guaranteeing a one-to-one correspondence.

How many horizontal lines are needed?

With paper amidakuji, adding more horizontal lines makes prediction harder, but achieving a mathematically fair distribution requires a very large number of lines. Amida-san guarantees fairness through its algorithm.

Is fairness maintained in the online version?

Yes. Amida-san uses the same mechanism as traditional amidakuji, and the process where everyone adds horizontal lines is completely transparent.

Summary

Amidakuji is a lottery method born in the Muromachi period that has been used in Japan for centuries. Its mathematical one-to-one correspondence guarantees fairness, and the visibility of the entire process makes transparency its greatest feature. Today, using the online version Amida-san, you can easily conduct a fair lottery with large groups regardless of location.

Try Amida-san and experience fair selection for yourself.