Voltorb Flip Optimizer

A small helper for the 5x5 Voltorb Flip puzzle that enumerates all valid boards given row/column sums and bomb counts, computes exact posterior probabilities P(0/1/2/3) and expected values (EV) for each unopened cell, and recommends the cell with the lowest probability of being a bomb.

Key features

• Exact enumeration of all boards consistent with provided constraints.
• Per-cell posteriors and EV calculation using DFS and pruning.
• Recommends the safest next cell (min P(0), tiebreaker: max EV).
• Interactive CLI to step through a game.

Quick start

1. Inspect the main implementation and helpers in voltorb.py:

   • core enumerator: _enumerate_all_boards
   • row pattern generator: _enumerate_row_patterns
   • posterior & EV calculator: compute_posteriors
   • choice logic: choose_next_safest
   • input validation: sanity_check
   • interactive loop: interactive_game
   • simple board printer: print_board

2. Run interactively:

python voltorb.py

Follow prompts to enter 5 row sums, 5 row bomb counts, 5 column sums, and 5 column bomb counts. The program verifies basic consistency (e.g. total sums and bomb counts) before enumerating solutions.

Constraints (mathematical)

• Total sum constraint: $\sum_{r=0}^{4} \text{row\_sums}[r] = \sum_{c=0}^{4} \text{col\_sums}[c]$
• Total bombs constraint: $\sum_{r=0}^{4} \text{row\_bombs}[r] = \sum_{c=0}^{4} \text{col\_bombs}[c]$
• Each non-bomb cell ∈ {1,2,3} so per-row/column sums must be achievable given non-bomb counts.

Notes on implementation

• The solver generates all possible length-5 row patterns that meet row sum/bomb constraints (see _enumerate_row_patterns) and then composes full boards row-by-row while pruning using column partial bounds (see _col_bounds_so_far inside the file).
• Because the board is fixed at 5×5, exhaustive search with pruning is practical and yields exact probabilities.

When to use

• Use this tool when you want an exact probabilistic recommendation (not a heuristic) for the next flip in Voltorb Flip given full row/column constraints and any already-opened cells.

Contributing

• Improvements welcome: add a small GUI, caching of intermediate results, or optimized pruning heuristics.

License

• MIT