OverGrid / Field Guide

Beginner → advanced · a field manual of working theories

Learn to see the next board.

This playbook turns OverGrid’s unusual geometry into decisions you can recognize at the table. Each maneuver plate shows the position, the choice, and what the choice is trying to preserve or convert.

Research boundary: these are working strategies, not solved play. Rule facts are certain; measured cards show completed tests, while reserved cards remain hypotheses for later simulation.

Rule fact

The mechanic is guaranteed by the rules; its strategic importance still needs testing.

Strong theory

Mechanically plausible and ready for controlled simulation, but not yet proven optimal.

Open question

A useful idea with a real chance of being wrong; treat it as an experiment at the table.

Level 1 of 3

Beginner

Place efficiently · close cheap pockets · understand the swing
01.01

Rule factBeginner maneuver

Use one anchor; spend the rest forward

Contact is a requirement, not the objective.

At the tableTouch your territory with the smallest useful anchor, then project the rest toward neutral cells, a closure, or a height route.

  1. 01Position
    PositionYour captured home and soft frontier touch a broad neutral lane.

    Your captured home and soft frontier touch a broad neutral lane.

  2. 02Wasteful overlap
    Wasteful overlapThree columns sit over territory you already own; only two columns reach forward.
    Useful columns
    2

    Three columns sit over territory you already own; only two columns reach forward.

  3. 03One anchor, four forward
    One anchor, four forwardOne cube anchors the construction while the remaining footprint opens the lane.
    Useful columns
    4

    One cube anchors the construction while the remaining footprint opens the lane.

Concept plateThe same contact rule can either spend footprint on owned cells or project it into useful space.
Prediction

Placements that minimize redundant coverage of your own territory will usually claim more useful columns.

Why it could work

A valid construction needs enough contact to connect to your territory; covering cells you already own often spends footprint without changing ownership.

Pattern to spot

A broad neutral lane beyond one stable edge of your territory.

When to break it

Overlap is justified when it supplies a bridge, exact height, capture closure, or defense of a critical hinge.

01.02

Rule factBeginner maneuver

Build flat until height earns the sacrifice

Every stacked cube gives up a board column.

At the tableStay flat unless stacking buys exact height, protected-tile access, a capture, or another immediate positional gain.

  1. 01Flat reach
    Flat reachFive low columns spread through open neutral territory.
    New columns
    5

    Five low columns spread through open neutral territory.

  2. 02Stack without payoff
    Stack without payoffThe same five-cube piece occupies only three columns and matches no height or protected crossing.
    New columns
    3

    The same five-cube piece occupies only three columns and matches no height or protected crossing.

  3. 03Stack with a reason
    Stack with a reasonHere the lost footprint earns an exact two-dot match and clears a black tile.
    Vertical payoff
    height + bridge

    Here the lost footprint earns an exact two-dot match and clears a black tile.

Concept plateVerticality spends footprint; the comparison asks what that sacrifice purchases.
Prediction

Low, wide constructions will advance territory faster unless verticality unlocks a specific payoff.

Why it could work

The same cubes can cover more distinct columns when they lie flat. Vertical cubes become valuable only when height, bridging, or connectivity needs them.

Pattern to spot

Several neutral cells are reachable without a protected obstacle or exact-height target.

When to break it

Some dealt shapes and connected constructions force stacking; judge the useful footprint, not a blanket height limit.

01.03

Rule factBeginner maneuver

Let the board close the pocket

Edges, corners, black tiles, and diagonals rewrite the cost of enclosure.

At the tableSearch the boundary before surrounding open space, then check every diagonal for the cheapest closing cell.

  1. 01Open center
    Open centerAn interior claim needs all eight neighboring positions satisfied.
    Supports needed
    8

    An interior claim needs all eight neighboring positions satisfied.

  2. 02Edge and corner
    Edge and cornerThe edge supplies three exempt positions; the corner supplies five.
    Corner / edge
    3 / 5

    The edge supplies three exempt positions; the corner supplies five.

  3. 03Black wall
    Black wallUncleared black tiles satisfy part of the enclosure without belonging to either player.
    Free wall
    3 black neighbors

    Uncleared black tiles satisfy part of the enclosure without belonging to either player.

  4. 04Close the diagonal
    Close the diagonalThe marked diagonal is the last unsatisfied neighbor; claiming it hardens the center.
    One cell closes
    the pocket

    The marked diagonal is the last unsatisfied neighbor; claiming it hardens the center.

Concept plateCapture cost changes with geometry, and one missing diagonal can keep a whole pocket soft.
Prediction

Claims beside helpful boundaries will convert with fewer supporting cells than equivalent interior claims.

Why it could work

Capture checks all eight neighbors. Off-board positions and uncleared black tiles count as satisfied, while one overlooked diagonal can keep an entire pocket soft.

Pattern to spot

An edge or corner pocket, or a nearly enclosed cluster with one missing diagonal.

When to break it

A boundary can become a mobility dead end, and an opponent may contest the same inexpensive pocket.

01.04

Strong theoryBeginner maneuver

Grow a lobe, not a ribbon

Compact claims can share enclosure work without surrendering every launch direction.

At the tableExpand in a compact lobe, but preserve two genuinely useful faces pointed toward future objectives.

  1. 01Thin ribbon
    Thin ribbonSix claims reach far, but almost every cell is exposed and the route depends on one narrow line.
    Shape
    long + soft

    Six claims reach far, but almost every cell is exposed and the route depends on one narrow line.

  2. 02Compact lobe
    Compact lobeThe same number of claims share neighbors and prepare several closure cells.
    Shape
    shared supports

    The same number of claims share neighbors and prepare several closure cells.

  3. 03Two useful faces
    Two useful facesA good lobe stays compact while preserving two outward launches toward real objectives.
    Live launches
    2

    A good lobe stays compact while preserving two outward launches toward real objectives.

Concept plateEqual expansion can create very different exposure and future launch geometry.
Prediction

Compact lobes with two useful outward faces will retain more value than equally large ribbons or sealed blobs.

Why it could work

Nearby claims reuse surrounding cells and can capture in chains. Thin fronts expose more soft territory, while over-compact blobs may fit too few future hands.

Pattern to spot

A choice between extending a one-cell corridor and widening a cluster toward two objectives.

When to break it

A ribbon can be correct when racing to an awkward neutral, a peak, or a strategically vital corridor.

01.05

Strong theoryBeginner maneuver

Make one move do two jobs

The strongest cells often sit at the intersection of objectives.

At the tableBefore placing, name the move’s first job and second job.

  1. 01Single-purpose reach
    Single-purpose reachThis move claims open cells but changes no enclosure or future objective.
    Jobs completed
    expand

    This move claims open cells but changes no enclosure or future objective.

  2. 02Expand and close
    Expand and closeThe marked footprint claims neutrals and supplies the missing side of an existing pocket.
    Jobs completed
    expand + close

    The marked footprint claims neutrals and supplies the missing side of an existing pocket.

Concept plateThe useful footprint is the one whose cells participate in more than one immediate plan.
Prediction

Moves with two immediate, independently useful consequences will outperform single-purpose moves of similar score.

Why it could work

One footprint can expand ordinary territory while closing a capture, opening a route, defending a hinge, or creating a threat.

Pattern to spot

A neutral cell that is also the missing neighbor of a claim or the next step toward height.

When to break it

Do not invent a speculative second benefit that needs several uncontested turns to matter.

01.06

Rule factBeginner maneuver

Know what the swing is worth

A tile’s value depends on what both players gain and lose.

At the tableCount the immediate change for both players, then ask whether your new value survives the reply.

  1. 01Claim neutral
    Claim neutralA neutral cell becomes your soft territory.
    You
    +5

    A neutral cell becomes your soft territory.

  2. 02Harden your claim
    Harden your claimEnclosure converts an existing 5-point claim into a protected 10-point capture.
    You
    +5 more

    Enclosure converts an existing 5-point claim into a protected 10-point capture.

  3. 03Steal a soft claim
    Steal a soft claimOwnership flips without a bridge: you gain 5 while the rival loses 5.
    Head-to-head
    +10 swing

    Ownership flips without a bridge: you gain 5 while the rival loses 5.

  4. 04Bridge a capture
    Bridge a captureThe rival loses a 10-point capture and you gain a 5-point claim—but the landing remains soft.
    Immediate swing
    +15
    New tile
    soft

    The rival loses a 10-point capture and you gain a 5-point claim—but the landing remains soft.

Concept plateFour common territory events have different immediate and retained values.
Prediction

Players who count the relative swing and protection cost will reject attractive-looking but strategically empty exchanges.

Why it could work

Neutral claims add 5; capture adds another 5; stealing a claim creates a 10-point head-to-head swing; bridge-stealing a capture creates a 15-point swing but leaves soft territory.

Pattern to spot

A choice among neutral expansion, closing your claim, stealing a patterned claim, or bridging a solid tile.

When to break it

In multiplayer, a large bilateral swing can still benefit an uninvolved leader more than it benefits you.

Level 2 of 3

Intermediate

Convert routes · bank shared height · retain what you take
02.01

Rule factIntermediate maneuver

Treat height as a route, not a destination

Matching the dots starts the job; enclosure cashes it.

At the tablePlan the approach, exact stack, surrounding cells, and conversion turn before committing.

  1. 01Replayed public board
    Replayed public boardBalanced to move at 61.9% territory completion. The ringed tile is height 2.
    Source
    turn 9
    Search
    120 candidates

    Balanced to move at 61.9% territory completion. The ringed tile is height 2.

  2. 02B: reaches, but misses
    B: reaches, but missesThis legal construction reaches H at height 3; the printed requirement is 2.
    Exact match
    no
    Engine score
    +10
    Territory
    +0

    This legal construction reaches H at height 3; the printed requirement is 2.

  3. 03A: match and support
    A: match and supportThe alternative lands at exact height 2 and removes 2 missing support cells in the same legal move.
    Exact match
    yes
    Engine score
    +25
    Opponent damage
    +20

    The alternative lands at exact height 2 and removes 2 missing support cells in the same legal move.

  4. 04Receipt, not prophecy
    Receipt, not prophecyAcross this cluster’s 8 complete-route and 53 reach-only candidates, completion improved immediate ordinary score but not mobility.
    Score excl. height
    +6.86
    Territory
    +2.03
    Mobility
    -0.70

    Across this cluster’s 8 complete-route and 53 reach-only candidates, completion improved immediate ordinary score but not mobility.

Concept plateHistorical pre-v8 public position · official-2p-bigger:68371 · accepted source-era engine outcomes at turn 9, not a simulated future or current-policy result.
Prediction

Height plans that include approach, exact match, and capture will bank more bonuses than plans that merely reach the tile.

Why it could work

Under the default rules, exact height permits the claim, but the one-time 10, 20, or 30-point award arrives only when that tile becomes captured.

Pattern to spot

An unawarded dotted tile with a short approach and visible surrounding-cell requirement.

When to break it

Ignore a peak when its route consumes too many turns, is easily cut, or loses a more valuable ordinary-territory race.

02.02

Strong theoryIntermediate maneuver

Rank peaks by route return

The biggest printed bonus is not necessarily the best climb.

At the tableCompare bonus, useful route territory, captures enabled, contest risk, and turns required.

  1. 01Same public position
    Same public positionAt turn 7, both selectors read this exact public board. N is nearest; R has the larger raw route-return estimate.
    Source
    official-2p-standard · 68371

    At turn 7, both selectors read this exact public board. N is nearest; R has the larger raw route-return estimate.

  2. 02Nearest: secure work
    Nearest: secure workN was already connected: approach cost 0, with 1 support cell left. In the untouched replay, Balanced banked it on turn 7.
    Raw estimate
    30/turn
    Observed owner
    Balanced

    N was already connected: approach cost 0, with 1 support cell left. In the untouched replay, Balanced banked it on turn 7.

  3. 03Raw ROI: exposed promise
    Raw ROI: exposed promiseR looked richer at 45/turn because future route work was counted as return. In the untouched replay, Raider banked it on turn 8.
    Raw estimate
    45/turn
    Observed owner
    Raider

    R looked richer at 45/turn because future route work was counted as return. In the untouched replay, Raider banked it on turn 8.

  4. 04Archived replay receipt
    Archived replay receiptThe accepted pre-v8 artifact records this final public board at turn 46 (flip-war). The source-era reducer is already finished when archived turn 27 begins, so no post-terminal command was replayed. Across 100 historical clusters, this raw ROI ranker selected an eventually won height less often than nearest.
    Nearest
    50%
    Raw ROI
    30%
    Paired gap
    -20pp [-30pp, -10pp]

    The accepted pre-v8 artifact records this final public board at turn 46 (flip-war). The source-era reducer is already finished when archived turn 27 begins, so no post-terminal command was replayed. Across 100 historical clusters, this raw ROI ranker selected an eventually won height less often than nearest.

Concept plateHistorical pre-v8 observed replay counterexample · official-2p-standard:68371 · target rankings are hypothetical; ownership through the observed awards is observational. The archived final is not replayed past the current terminal boundary.
Prediction

Routes with better total return per committed turn will outperform simple nearest-peak or highest-peak selection.

Why it could work

A route also claims ordinary territory, enables captures, consumes time, and risks interception. Once a bonus is awarded, later ownership changes do not award it again.

Pattern to spot

A short useful route to a modest peak and a long exposed route to a larger peak.

When to break it

A distant high peak can still dominate when the route is unusually safe or denies an opponent’s only major award.

02.03

Strong theoryIntermediate maneuver

Bank height in a shared pocket

Make the climb and its closure share the same cells.

At the tableBefore taking the immediate five points, ask whether one compact lobe can claim both dotted tiles and let the next hand close them together.

  1. 01Same hand, same board
    Same hand, same boardTurn 1 on Advanced. The ringed three-dot and two-dot cells share enclosure work; the choice is immediate spread or a compact height pocket.
    Hand
    W · X · T
    Live peaks
    3 nearby
    Source
    Advanced 61057

    Turn 1 on Advanced. The ringed three-dot and two-dot cells share enclosure work; the choice is immediate spread or a compact height pocket.

  2. 02Take the visible 50
    Take the visible 50Incumbent Ender spreads across eight territory cells for 50 immediate points, but its next hand closes only the three-dot award.
    Immediate
    +50
    Next Ender move
    +65

    Incumbent Ender spreads across eight territory cells for 50 immediate points, but its next hand closes only the three-dot award.

  3. 03Spend five on the pocket
    Spend five on the pocketThe alternative exact-matches the ringed three-dot and two-dot cells together. It scores five fewer now, but banks both awards inside one compact lobe.
    Immediate
    +45
    Banked height
    5 dots

    The alternative exact-matches the ringed three-dot and two-dot cells together. It scores five fewer now, but banks both awards inside one compact lobe.

  4. 04One hand cashes both
    One hand cashes bothThe following Z-U-X hand captures both ringed height cells plus four ordinary cells: 110 points instead of the incumbent line’s 65.
    Next Ender move
    +110
    Two-move edge
    +40
    Final replay
    725–525 win

    The following Z-U-X hand captures both ringed height cells plus four ordinary cells: 110 points instead of the incumbent line’s 65.

Concept plateHistorical pre-v8 paired reconstruction · official-2p-advanced × seed 61057 · Ender vs Balanced · same W-X-T opening hand. The plate shows engine outcomes; it is illustrative, not current promotion evidence, and one replay does not establish causality.
Prediction

On height boards, compact constructions that bank several exact-height claims inside one closable pocket will convert more value than wider moves that reach only one award.

Why it could work

Height points arrive only when the tile becomes captured. Nearby exact-height claims can reuse enclosure work, so a small immediate sacrifice can prepare one hand to close several awards while denying those awards to the rival.

Pattern to spot

Two reachable dotted tiles whose eight-neighbor enclosures overlap, with a hand that can match both heights without leaving a long exposed seam.

When to break it

Take the sure score when the rival can cut the pocket before your next turn, the exact stacks cannot share support, or the ordinary-territory race will end first.

02.04

Strong theoryIntermediate maneuver

Capture the hinge

One protected connection can hold an entire position together.

At the tableAsk which single cell changes the most relationships on the board, then harden that cell first.

  1. 01Soft connection
    Soft connectionOne patterned cell joins two lobes and supports a nearby pocket.
    Routes depending on H
    3

    One patterned cell joins two lobes and supports a nearby pocket.

  2. 02Harden the hinge
    Harden the hingeOne closure turns the shared connection into protected infrastructure.
    Routes secured
    3

    One closure turns the shared connection into protected infrastructure.

  3. 03Bridge or go around
    Bridge or go aroundThe rival can no longer cover H directly and must pay for a bridge or a longer route.
    Rival cost
    bridge required

    The rival can no longer cover H directly and must pay for a bridge or a longer route.

Concept plateA hinge is valuable because several routes and claims depend on it at once.
Prediction

Capturing high-leverage hinge cells will preserve more routes and territory than maximizing peripheral capture count.

Why it could work

A captured cell cannot be covered directly. If it joins regions, closes a pocket, or controls a corridor, opponents must bridge it or find another route.

Pattern to spot

One soft cell connects two lobes, supports several claims, or controls access around a black tile.

When to break it

A hinge is overrated when opponents already have an independent route or an easy legal bridge.

02.05

Strong theoryIntermediate maneuver

Raid only with a way to hold

Immediate swing is not retained value.

At the tableAfter imagining the raid, give the opponent one full reply. Discount any value that disappears.

  1. 01Bridge raid
    Bridge raidBlue crosses the black tile and takes one solid red cell as a new soft claim.
    Immediate swing
    +15
    Landing
    soft

    Blue crosses the black tile and takes one solid red cell as a new soft claim.

  2. 02No support: flipped back
    No support: flipped backRed’s reply reaches the landing directly and restores the old frontier.
    After one round
    0 retained

    Red’s reply reaches the landing directly and restores the old frontier.

  3. 03Supported raid: held
    Supported raid: heldA smaller landing beside blue support survives the direct reply and prepares closure.
    After one round
    +15 retained

    A smaller landing beside blue support survives the direct reply and prepares closure.

Concept plateA bridge raid branches into a headline swing that vanishes or a smaller position that survives.
Prediction

Smaller thefts with durable support will outperform larger steals that are immediately reversed.

Why it could work

Bridge-stolen captured territory becomes a soft claim and cannot recapture in the same resolution. The reply can erase the headline score swing.

Pattern to spot

A bridge can reach solid enemy territory, but the landing area has either strong support or obvious enemy recapture access.

When to break it

A temporary swing can be correct when it triggers the ending, breaks a route, or forces a reply that creates value elsewhere.

02.06

Strong theoryIntermediate maneuver

Finish the awkward cell early

The easiest four neutrals can conceal a disastrous fifth.

At the tableRank the remaining neutrals by difficulty and preserve—or take—the hardest route before cleaning up the easy cells.

  1. 01Five neutrals remain
    Five neutrals remainFour easy cells sit beside blue; one awkward cell lies beyond a narrow rival corridor.
    Remaining
    5

    Four easy cells sit beside blue; one awkward cell lies beyond a narrow rival corridor.

  2. 02Tempting cleanup
    Tempting cleanupBlue takes the four nearby cells and leaves only the awkward coordinate.
    Remaining
    1 awkward

    Blue takes the four nearby cells and leaves only the awkward coordinate.

  3. 03Route closes
    Route closesThe table can still trade the contested frontier, but no cheap line reaches the last neutral.
    Result
    flip-war risk

    The table can still trade the contested frontier, but no cheap line reaches the last neutral.

  4. 04Hard cell first
    Hard cell firstThe alternate route secures the awkward coordinate while easy cleanup remains accessible.
    Route
    finish preserved

    The alternate route secures the awkward coordinate while easy cleanup remains accessible.

Concept plateGreedy cleanup can strand the one coordinate that determines whether the game ends.
Prediction

Late plans that preserve a route to the hardest remaining coordinate will finish more reliably than greedy neutral-count reduction.

Why it could work

A tempting move can consume easy cells while closing the only practical approach to an isolated neutral, after which profitable recaptures dominate.

Pattern to spot

Only a few neutral cells remain and one sits beyond a narrow or contested approach.

When to break it

An opponent may be forced to take the awkward cell, or immediate completion timing may outweigh route insurance.

Level 3 of 3

Advanced

Control replies · build robust threats · engineer the ending
03.01

Open questionAdvanced maneuver

Count good launches, not exposed edges

A frontier is valuable only when future hands fit it and lead somewhere.

At the tableFor every launch face, ask which likely hands fit there and what each successful fit reaches.

  1. 01One public hand, two frontiers
    One public hand, two frontiersExact central crop before U–Z–T. Blue can widen the open edge or pack the same hand into a more hand-compatible sector.
    Public hand
    U · Z · T
    Source turn
    6 of 5P

    Exact central crop before U–Z–T. Blue can widen the open edge or pack the same hand into a more hand-compatible sector.

  2. 02Raw-frontier candidate
    Raw-frontier candidateThe observed U–Z–T placement retained 6 raw faces and 56 current-hand-compatible faces in this crop’s full position.
    Raw frontier
    6
    Compatible faces
    56

    The observed U–Z–T placement retained 6 raw faces and 56 current-hand-compatible faces in this crop’s full position.

  3. 03Compatibility candidate
    Compatibility candidateThe alternative uses the same public hand. It raises compatible faces to 59, but narrows raw frontier to 4.
    Compatible faces
    59
    Raw frontier
    4

    The alternative uses the same public hand. It raises compatible faces to 59, but narrows raw frontier to 4.

  4. 04Best reply; value unresolved
    Best reply; value unresolvedBuilder’s strongest observed L–W–U reply lands in another sector. Both frontier choices retained score here; across 43 clusters the utility interval still crosses zero.
    Cluster score Δ
    +10
    43-cluster utility
    CI crosses 0

    Builder’s strongest observed L–W–U reply lands in another sector. Both frontier choices retained score here; across 43 clusters the utility interval still crosses zero.

Concept plateObserved receipt · official-5p-expert × seed 68311. This state gained 3 compatible faces but lost 2 raw routes; its +0.0152 retained-utility difference is one example, while the 43-cluster effect remains unresolved at +0.0044 [−0.0091, +0.0179].
Prediction

Positions with more hand-compatible objective routes will outperform positions with a larger but strategically empty frontier.

Why it could work

The six piece shapes and their orientations fit different launch geometry. Raw frontier size ignores whether a useful connected construction can start there.

Pattern to spot

A wide irregular edge with few good fits versus a smaller edge aligned with several objectives.

When to break it

Future hands are uncertain, and preserving excessive flexibility can sacrifice guaranteed score.

03.02

Strong theoryAdvanced maneuver

Spend moves to force replies

Initiative is the useful turn your opponent no longer gets.

At the tableEvaluate what useful move your threat removes from the opponent, not only what your move scores now.

  1. 01Create the threat
    Create the threatBlue prepares a capture chain that will harden the marked pocket next turn.
    If ignored
    +30 next turn

    Blue prepares a capture chain that will harden the marked pocket next turn.

  2. 02Reply is forced
    Reply is forcedRed abandons its preferred height route to occupy the only closing cell.
    Red’s preferred route
    delayed

    Red abandons its preferred height route to occupy the only closing cell.

  3. 03Spend the tempo
    Spend the tempoBlue uses the stolen turn to advance a separate objective while red remains tied to defense.
    Initiative
    blue keeps it

    Blue uses the stolen turn to advance a separate objective while red remains tied to defense.

Concept plateA forcing move is valuable because it replaces the opponent’s preferred turn with defense.
Prediction

Threats that force costly replies will create more two-turn value than equally scoring quiet moves.

Why it could work

A height conversion, capture chain, or completion threat can make defense mandatory and erase the opponent’s preferred expansion turn.

Pattern to spot

You can create a threat that becomes much more valuable if ignored, while preserving a second objective.

When to break it

A threat is not forcing when the opponent has a stronger counterattack or one reply answers it while advancing their own plan.

03.03

Strong theoryAdvanced maneuver

Fork independent threats

Two threats matter when one construction cannot answer both.

At the tablePair objectives that demand incompatible replies, then confirm that blocking one really leaves the other alive.

  1. 01Two critical cells
    Two critical cellsHeight conversion at A and pocket closure at B depend on different coordinates.
    Threats
    A + B

    Height conversion at A and pocket closure at B depend on different coordinates.

  2. 02Red blocks A
    Red blocks AThe reply reaches the height route, but the separate closure at B remains live.
    Surviving threat
    B

    The reply reaches the height route, but the separate closure at B remains live.

  3. 03B converts
    B convertsBlue closes the pocket; the defense could save only one side of the fork.
    Fork result
    one threat scores

    Blue closes the pocket; the defense could save only one side of the fork.

Concept plateA real fork survives because each defense leaves the other threat intact.
Prediction

Threat pairs with different critical cells will convert more often than larger threats sharing a single vulnerable hinge.

Why it could work

If height, capture, attack, or completion threats depend on disjoint cells, the defender must choose which future value survives.

Pattern to spot

Two near-conversions lie in different sectors and no connected reply footprint can cover both critical cells.

When to break it

The fork fails when both routes share a launch point, the opponent can end the game, or one connected construction intersects both.

03.04

Strong theoryAdvanced maneuver

Prefer plans that survive the best reply

A spectacular line is fragile when one precise answer destroys it.

At the tableBefore choosing the spectacular line, imagine the opponent’s most precise answer and value what remains.

  1. 01The public decision state
    The public decision stateExact contested center crop before Z–U–X. Blue is choosing between a broad immediate sweep and a line that hardens the left pocket.
    Public hand
    Z · U · X
    Source turn
    21 of 4P

    Exact contested center crop before Z–U–X. Blue is choosing between a broad immediate sweep and a line that hardens the left pocket.

  2. 02Fragile immediate leader
    Fragile immediate leaderThis exact construction leads the one-ply evaluator at 0.1271, but most of its new central claims remain soft.
    Immediate utility
    0.1271
    After reply
    +40 score

    This exact construction leads the one-ply evaluator at 0.1271, but most of its new central claims remain soft.

  3. 03Strongest observed reply
    Strongest observed replyBuilder’s T–W–U construction flips the soft center. The crop shows the T and U; the W continues one column beyond the right edge.
    Observed reply
    T · W · U
    Fragile result
    +40 score

    Builder’s T–W–U construction flips the soft center. The crop shows the T and U; the W continues one column beyond the right edge.

  4. 04Quieter line retains score
    Quieter line retains scoreMoving Z one row earlier captures four cells on the left. It starts at 0.1213 utility, then retains 50 score against its best observed reply.
    Immediate utility
    0.1213
    After reply
    +50 score

    Moving Z one row earlier captures four cells on the left. It starts at 0.1213 utility, then retains 50 score against its best observed reply.

Concept plateObserved receipt · official-4p-centered × seed 68311. The quieter Z–U–X line gives up 0.0057 immediate utility and retains 10 more score after the strongest observed legal reply. Across 25 clusters, retained score improves +16.40 [+11.07, +21.73].
Prediction

Moves with slightly lower immediate value but stronger worst-reply outcomes will perform more consistently across opponents and maps.

Why it could work

Multiple viable continuations and captured infrastructure reduce the damage of any single counter. A brittle plan concentrates value behind one soft cell.

Pattern to spot

A high-scoring move with one critical dependency versus a quieter move preserving two routes.

When to break it

Robustness can become expensive caution when opponents cannot find the precise reply or immediate tempo decides the game.

03.05

Strong theoryAdvanced maneuver

Choose when the final round begins

The score at the trigger is not the final score.

At the tableCount every remaining reply and project the score after—not at—the trigger.

  1. 01Trigger now
    Trigger nowBlue takes the final neutral while red, green, and yellow are still owed turns.
    Owed replies
    R → G → Y
    Score at trigger
    Blue +10

    Blue takes the final neutral while red, green, and yellow are still owed turns.

  2. 02Replies reverse the lead
    Replies reverse the leadThe trigger score looked safe, but three scoring replies leave blue behind.
    Projected finish
    Blue −15

    The trigger score looked safe, but three scoring replies leave blue behind.

  3. 03Trigger later
    Trigger laterAfter the round advances, an equivalent finish leaves only one rival reply.
    Owed replies
    R only
    Projected finish
    Blue +20

    After the round advances, an equivalent finish leaves only one rival reply.

  4. 04But waiting has a price
    But waiting has a priceDelay only when the route stays yours; otherwise a rival may trigger first or strand the cell.
    Guardrail
    secure access first

    Delay only when the route stays yours; otherwise a rival may trigger first or strand the cell.

Concept plateThe turn-order strip changes the meaning of an otherwise identical last-neutral move.
Prediction

Seat-aware trigger decisions will avoid more losing finishes than simple finish-now or finish-if-leading rules.

Why it could work

When the last ordinary territory is consumed, particular players are still owed turns. Trigger timing changes both the number and identity of those replies.

Pattern to spot

One neutral remains, the actor can take it, and several seats still have turns in the current round.

When to break it

Waiting can let a rival trigger from a worse state, strand the last neutral, or surrender a safe finish already available.

03.06

Strong theoryAdvanced maneuver

Attack the player who improves your finish

The leader is not always the target whose loss benefits you.

At the tableForecast the standings and board access after the attack, including every uninvolved player.

  1. 01Attack first place
    Attack first placeBlue damages red, but green inherits the lead while blue remains third.
    Standings after
    Green 1st · Blue 3rd

    Blue damages red, but green inherits the lead while blue remains third.

  2. 02Attack the useful hinge
    Attack the useful hingeA different target removes the cell blocking blue’s route and moves blue into first.
    Standings after
    Blue 1st

    A different target removes the cell blocking blue’s route and moves blue into first.

  3. 03Change with the board
    Change with the boardEarly positions reward expansion; middle positions reward conversion; late positions reward safe closure.
    Phase
    state, not turn number

    Early positions reward expansion; middle positions reward conversion; late positions reward safe closure.

Concept plateMultiplayer targeting is about who captures the benefit after standings and routes update.
Prediction

Targeting based on attacker rank improvement and route value will outperform leader damage alone in multiplayer.

Why it could work

Lowering first place can promote an uninvolved player. The useful target is the player whose lost points, route, or tempo produce value the attacker can capture.

Pattern to spot

Several opponents can be damaged, but only one attack changes your rank or opens your winning route.

When to break it

A runaway leader may still require direct denial even when another player receives some short-term benefit.