Ladder Game
A fun Korean-style random selection game (사다리타기)
How to Play
- Add player names (2-8 players)
- Add the same number of results or prizes
- Click "Start Game" to generate the ladder
- Click "Reveal Results" to see who gets what!
What is a Ladder Game?
The ladder game (사다리타기) is a popular Korean random selection method. Players start at the top and follow the path down, moving horizontally whenever they encounter a rung. The random horizontal rungs ensure a fair and unpredictable outcome!
Why a ladder (사다리타기) actually produces a uniform permutation
A 사다리타기 with n columns maps the n start positions to a permutation of the n results at the bottom. Each horizontal rung between two adjacent columns is a transposition — it swaps whichever two paths pass through it. The full mapping is just the composition of all those swaps, evaluated top to bottom. Because every permutation of n items can be built from adjacent transpositions (the symmetric group S_n is generated by adjacent swaps), enough randomly placed rungs produce a permutation distribution that approaches uniform — i.e., each of the n! possible outcomes becomes equally likely.
Here "enough" matters. For 4 players there are 4! = 24 permutations and any permutation is reachable in at most 6 adjacent swaps (the diameter of S_4). If this tool places too few rungs, nearby columns will over-map to nearby outcomes: column 1 will hit result 1 or 2 more often than it should. A reasonable target is ~1.5× the worst-case number of needed swaps per column pair. For 6 players that's roughly 15–20 rungs total to get within ~1% of uniform by chi-square test.
Edge case: rungs that share a horizontal level must not overlap on the same column pair — two rungs stacked at the same y between columns 2 and 3 would cancel out (swap twice = identity). Any correct implementation (including this one) either offsets levels or skips overlapping placements. If you're drawing one on paper, keep each level to one rung.