How the Ladder Game Works — And Why It's Fair

A ladder game (also known as Amidakuji) is made up of several vertical lines connected by horizontal rungs. Starting from the top, you move downward, and whenever you hit a rung, you cross over to the next line — repeating this until you reach the bottom, which becomes your result.

Why results never overlap

The key property of the ladder game is that different starting points always end up at different destinations. Each vertical line connects to exactly one result on a strict one-to-one basis, so two people can never end up with the same outcome.

This property holds no matter how many rungs you add. Each rung simply swaps the positions of two lines, and swapping positions any number of times still leaves you with a one-to-one pairing — a permutation.

What makes it fair

For a ladder game to be fair, the rungs need to be placed randomly and in sufficient number. Too few rungs, and starting points map almost directly onto their destinations, making the outcome easy to predict.

• More rungs make the paths more complex and harder to predict
• Rungs at the same height shouldn't sit right next to each other, so each path stays unambiguous
• Randomizing the starting positions makes things even fairer

RANDOMBOX's ladder game places plenty of rungs at random based on the number of participants and avoids adjacent overlaps, so every path is always clear and unambiguous.

When to use it

The ladder game is great for deciding "who does what" in a fun way — cleaning duty, presentation order, penalties, or seating assignments. Because results never overlap, it's especially handy for splitting up roles.