Measured opening comparison
Turtle Opening Case Study: Three Legal First Moves
Seed 20260614 begins with 35 free tiles and 16 legal matching pairs. That gives many valid clicks, but the immediate access change is not the same for every pair.
This case study holds the board assignment constant and compares three genuine first moves: a cap-and-edge pair, two outer row ends, and a pair that removes an upper tile without immediately freeing another position. Tile IDs and internal half-tile coordinates are included so the observations can be repeated against the project rules.
What was measured
For each candidate, the test removed exactly two free matching tiles. It then counted positions that changed from blocked to free, all free positions remaining, and all legal matching pairs in the resulting state. A move can remove an upper blocker yet still show zero newly free positions because other cover or side constraints remain.
Coordinates are written as x, y, z in the project's half-tile grid. Adjacent same-row tiles differ by two x units; z zero is the base and z four is the single Turtle cap.
Results for three legal openings
The initial baseline was 35 free tiles and 16 legal pairs. Every row below comes from the same generated assignment before any other move was made.
| Opening pair | IDs and coordinates | Newly free | Free tiles after | Legal pairs after |
|---|---|---|---|---|
| 6 of characters: cap plus east row end | 29 (24,4,0) + 143 (13,7,4) | 5: IDs 28, 139, 140, 141, 142 | 38 | 19 |
| North winds: two west row ends | 0 (4,0,0) + 72 (4,14,0) | 2: IDs 1 and 73 | 35 | 16 |
| 9 of characters: base plus layer one | 20 (6,4,0) + 105 (8,8,1) | 0 | 33 | 15 |
Read the access delta, not just the removed pair
initial state 35 free tiles | 16 legal pairs 29 + 143 (cap) -2 +5 = 38 free | 19 legal pairs 0 + 72 (ends) -2 +2 = 35 free | 16 legal pairs 20 + 105 (upper) -2 +0 = 33 free | 15 legal pairs
Pair 29 plus 143 has the largest immediate release in this sample. Removing the cap makes all four layer-three tiles pass the cover test, while removing base tile 29 opens its neighboring row position 28. The next state therefore has three more free tiles and three more legal pairs than the baseline.
That result is evidence about one transition, not proof that the pair is part of every successful path. Immediate mobility is a useful comparison signal, but later face dependencies still matter.
The row-end pair keeps the option count level
Tiles 0 and 72 are north winds at the left ends of two different base rows. Removing them releases tiles 1 and 73. Because two free positions leave and two become free, the total returns to 35; the number of legal pairs also returns to 16.
This is not a wasted move. It advances two independent rows and keeps the measured choice count stable. It simply creates a smaller immediate access change than removing the cap on this seed.
An upper-layer removal can have no immediate unlock
Tiles 20 and 105 are both 9 of characters and both are free initially. Tile 105 overlaps lower geometry, so the impact analyzer records that an upper blocker was removed. Even so, no position becomes free immediately: the affected lower positions still fail another cover or side condition.
The resulting state has 33 free tiles and 15 legal pairs. This distinction matters when using Learn Mode: removing a top-layer tile and newly unlocking a tile are related observations, but they are not synonymous.
How to reproduce the comparison
Generate the Turtle layout with numeric seed 20260614, keep every position present, and enumerate matching pairs only among positions that pass the free-tile test. Confirm the 35-free-tile and 16-legal-pair baseline. For each row in the table, begin again from that untouched state, remove the listed IDs, and recount.
In the playable interface, Replay Same Board returns to the same initial assignment. Learn Mode can confirm the qualitative unlock message, while the published IDs and counts provide a stricter check against the implemented analyzer.
- Do not test the three pairs one after another; each is an alternative first move.
- Treat x and y as half-tile units, not pixel positions.
- Compare the complete resulting state rather than assuming any cap removal is automatically best.