Random Choice

Ghost Leg (Ladder Game)

Ghost Leg (Ladder Game)

Also called ghost leg or Amidakuji, this ladder game links participants to outcomes at random. Set participants and outcomes, then reveal each path.

Entry mode

Outcomes
1
2
3
4

Ladder board

Enter participant count and outcomes, then create a ladder.

Purpose

Reveal random matches one by one in a familiar ladder-game format.

How to use

  1. Set the participant count.
  2. Enter the same number of outcomes.
  3. Create the ladder.
  4. Select top slots one by one, or reveal all results.

Why two people never collide

A single rung swaps the positions of two adjacent lines. A swap is always reversible, and chaining any number of reversible operations together leaves the whole chain reversible.

That makes the entire ladder a one-to-one mapping. If two people could reach the same outcome, running the ladder backwards from it would have no defined answer, which is a contradiction. However tangled the ladder looks, the property holds.

Rung count is set automatically

With too few rungs, results cluster near their starting positions. Mixing thoroughly takes rungs on the order of the square of the participant count, so five participants want around twenty-five.

This tool scales the rung count to the number of participants, so results mix properly without anyone having to think about it and no starting position carries a bias.

Selection order is irrelevant

The belief that picking first helps, or that middle lines are safer, has no basis. Every connection is fixed the instant the ladder is complete, so each position's outcome already exists regardless of when it is claimed.

Drawing the ladder before people pick, or assigning starting points before drawing it, gives identical probabilities. As long as the rungs are random, no starting point is favoured.

Building trust online

A paper ladder is verifiable because everyone sees the same picture. Online the computation is invisible, which makes the sequence matter: show the complete ladder first, then reveal results.

This tool places rungs randomly first, then draws them, then animates the path being traced. The ladder determines the outcome rather than the outcome determining the ladder.

Matching the number of outcomes

The number of outcomes must equal the number of participants. If there is only one winner, fill the rest with losing entries to balance the count. Setting the count creates that many input boxes, which makes it easy to match.

Keeping the outcomes hidden and revealing them one participant at a time is the more enjoyable format. Showing everything at once removes the tension entirely.

Examples

  • Assign chores
  • Pick small rewards
  • Match people to roles
  • Classroom mini game

Notes

  • The number of outcomes must match the participant count.
  • Participant count is limited so the board remains usable on mobile.

FAQ

Can results be revealed one at a time?

Yes. Select a top slot to reveal only that path and result.

Related tools

Random Team GeneratorRandom team generator — shuffle people into balanced teams.Wheel of NamesWheel of names — spin the wheel to pick one option.List RandomizerList randomizer — shuffle names or items into a random order.Secret Santa GeneratorRandomly match gift-exchange partners, with optional exclusion rules for couples.

Related guides

How to Split a Class into GroupsGroup work is common but forming groups every lesson is a chore. Here is why random assignment helps in the classroom and how to do it fast.How to Decide Meeting OrderChoosing who speaks first seems trivial but shapes the discussion. Here is how random order cuts hesitation and improves meetings.How the Ladder Game WorksA plain explanation of how a ladder connects each participant to a different outcome, and why the result is fair.