Ghost leg

Ghost leg is a technique to randomly match up two groups – assigning a list of chores to a list of people, for example. And all you need is a drawing of a ladder.

A selection of bamboo ladders
Thamizhpparithi Maari, CC BY-SA 3.0, via Wikimedia Commons

Say you have five people, and you have five gifts to distribute between them. Or five roommates and five household chores to allocate. The ghost leg, also known as ladder climbing or the Amida lottery (if you’re of a Buddhist persuasion) is a clever visual way to randomly connect each person with each gift / chore / whatever. As long as the groups are the same size, it doesn’t matter how large those groups get – the ghost leg can randomise them.

(Side note: it can also let you randomise the order of any group, Think of it like matching Person 1, Person 2, Person 3 with first place, second place, third place.)

This can all be done with a pencil and a piece of paper. First, draw a series of parallel vertical lines, one for each item / person in the group. Then, draw horizontal rungs – like the rungs of a ladder – between those lines. You can draw any number of rungs, and with every new rung the level of “randomisation” increases.

To connect the top group to the bottom group, put one member of each group at the top or bottom of the vertical lines, and then you trace a path from one to the other. The rule is simple: every time you meet a rung, the path is redirected along that rung. Consider the following two pathways (in red):

Ghost leg example
임의재, CC BY-SA 4.0, via Wikimedia Commons

Each member of one group, perched at the top of a different vertical line, traces a path to a different member of the other group at the bottom of those vertical lines. It’s quite clever, because each rung effectively swaps the order of two pathways. That means no two pathways will ever end at the same point. The two groups are randomly matched up with no gaps and no overlaps.

The ghost leg is a common technique in East Asia, where it’s common to fold the paper or otherwise hide the middle rungs until it’s time to do the sorting.

[Thanks to David S.]

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