Sphere Trace Solver (BETA)

The board is a 5×5 grid of 25 hidden cells. Each cell belongs to exactly one ship (or is blue/empty). Ships are horizontal or vertical contiguous segments with no overlap:

• Teal — length 4, always present, worth 20 sp/cell
• Green — length 3, always present, worth 35 sp/cell
• Yellow — length 3, always present, worth 55 sp/cell
• Orange — length 2, always present, worth 90 sp/cell
• Rare ships — length 2 each, worth ~90 sp/cell; 0 variable rares in 6-color, 1 in 7-color, 2 in 8-color, 3 in 9-color
• Blue — all remaining cells are empty, worth 10 sp/cell

Click budget: ship hits are free. Only hitting a blue (empty) cell costs from your budget of 4 blue clicks.

Extra Chance: if you’ve hit fewer than 5 ship cells total, each blue click extends the game (the game doesn’t end). Once you’ve hit 5 ship cells, Extra Chance shuts off — the next blue you click ends the game immediately. Use your remaining budget wisely.

Perfect game: use constraint inference to find all blue cells before hitting 5 ships, then collect all remaining ship cells for free.

The solver tracks which board arrangements are consistent with everything you've revealed so far. The Boards consistent count updates after each click.

Phase 1 — Extra Chance available (ships hit < 5):
While you haven't hit 5 ship cells yet, each blue (empty) click uses one of your 4 blue clicks but the game continues. The solver tries to click cells very likely to be blue — avoiding ships early — while gathering information to find ship cells later.

Recommendations come from one of two sources:

• DP policy — an exact precomputed lookup for the current board state (6- and 7-color only)
• heuristic — a weighted scorer used when the policy table doesn't apply; balances the factors below
• greedy fallback — an emergency fallback if the solver data could not be loaded

Phase 2 — 4th blue ends game (ships hit ≥ 5):
Extra Chance is off. The next blue click you make ends the game immediately. The solver picks the cell most likely to be a ship (lowest P(blue)), maximizing your remaining SP.

Cell overlays — shown on unrevealed cells when enabled in the Cell Overlays panel:

• P(B) — probability this cell is blue (empty), as a percentage. High = likely safe to click in Phase 1; low = likely a ship and good to target in Phase 2.
• EV — expected SP from clicking this cell, averaged across all consistent board arrangements. Most useful in Phase 2 to prioritize high-value ships.
• Score — composite heuristic score used to rank cells. Only shown when source is heuristic or phase 2. Higher is better.
• Tooltip — hover over any unrevealed cell to see a per-term breakdown of its Score (only when source is heuristic or phase 2).

Heuristic scoring terms — visible in the per-cell tooltip hover:

• t_blue — P(blue): probability this cell is empty.
• t_info6 / t_gini — information gain: how much clicking this cell is expected to reduce uncertainty about the remaining board. Higher = this click would reveal more about ship positions.
• t_ev / t_var_sp — expected value of this click: how much SP it is likely to yield, accounting for both the average and the variance across consistent board arrangements.
• t_rare_id — bonus for cells likely to help identify which rare color(s) are on this board.