[Feature] Add ladder picker

[yeleepark]

Summary

Add a Ladder Picker mini-game for randomly matching participants to outcomes using a visual ladder.

Why

Ladder games are familiar decision and draw tools in Korea and Japan, and they are useful for assigning small tasks, picking winners, deciding order, or matching people to options. This adds a fun but practical randomization feature to oddkit.

Proposed scope

• Enter participant names
• Enter matching outcomes or prizes/tasks
• Generate a randomized ladder
• Reveal one participant result at a time or reveal all results
• Regenerate the ladder
• Copy the final matching results
• Process everything locally in the browser

UX notes

• Use the English name Ladder Picker for clarity across locales
• Keep the ladder visually readable on desktop and mobile
• Consider simple animation for tracing a selected participant path
• Suggested microcopy: // the lines have spoken

Acceptance criteria

• Participants and outcomes can be entered and matched
• Generated ladders produce one deterministic result per participant for that ladder
• Users can reveal individual results and all results
• Results can be copied to the clipboard
• No participant or outcome data is uploaded to a server