Each connector is an adjacent swap
Treat every vertical line as a position. A connector swaps two neighboring positions. Applying all swaps from top to bottom creates a one-to-one mapping between starts and destinations.
A fixed diagram is deterministic
After every line is drawn, each start has a fixed result. Uncertainty comes from not knowing the path or not yet choosing a start, not from the route changing while it is traced.
When chances can be symmetric
Prepare outcomes first, generate the diagram without targeting a person, and let participants choose without seeing paths. That procedure can make opportunities symmetric; a large number of connectors alone does not prove fairness.
A more auditable process
Agree on generation and choice order, freeze the diagram after all choices, then reveal it. A digital tool should retain the round or its seed for checking.
- Fairness comes from procedure, not visual complexity.
- Anyone who knows the full diagram can calculate outcomes.
- More connectors do not automatically remove human bias.