Ladder Game (Ghost Leg)

The ladder game — ghost leg in English, amidakuji (あみだくじ) in Japan and 사다리타기 in Korea — is a quick way to hand out prizes, chores or roles. Names go at the top, outcomes at the bottom, and horizontal rungs connect the vertical lines. Each player follows their line down, crossing every rung they meet, until they reach an outcome. This page draws the ladder for you and animates every path in its own colour.

How to use this tool

1. Type the players, one per line.
2. Type the outcomes in the same number of lines — use “X” for blanks. Missing lines become X.
3. Pick how many rungs you want and whether to show the animated picture.
4. Press the button, watch the paths trace down, and read the result table.

Formula

Outcome of player i = σ(i), with σ a uniformly random permutation; ladder = random rungs, then the adjacent swaps that finish at σ

A ladder with only randomly placed rungs is not quite fair — outcomes near your own column are more likely. So this page draws the assignment first with unbiased secure random numbers, then builds the ladder in two parts: rungs on random gaps at the top, and below them the swaps of an odd–even transposition sort that carry every player from where the top left them to their drawn outcome. Two rungs never meet the same line at the same height.

Example

With 5 players and the outcomes “Buys coffee”, X, X, “Washes up”, X, every player has exactly a 1 in 5 chance of buying the coffee and a 1 in 5 chance of washing up, whatever column they start in. A normal ladder for 5 players has 10 random rungs plus up to 10 finishing rungs.