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.
The mechanic is guaranteed by the rules; its strategic importance still needs testing.
Mechanically plausible and ready for controlled simulation, but not yet proven optimal.
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 swingRule 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.
01Position Your captured home and soft frontier touch a broad neutral lane.
02Wasteful overlap - Useful columns
- 2
Three columns sit over territory you already own; only two columns reach forward.
03One anchor, four forward - Useful columns
- 4
One cube anchors the construction while the remaining footprint opens the lane.
Placements that minimize redundant coverage of your own territory will usually claim more useful columns.
A valid construction needs enough contact to connect to your territory; covering cells you already own often spends footprint without changing ownership.
A broad neutral lane beyond one stable edge of your territory.
Overlap is justified when it supplies a bridge, exact height, capture closure, or defense of a critical hinge.
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.
01Flat reach - New columns
- 5
Five low columns spread through open neutral territory.
02Stack without payoff - New columns
- 3
The same five-cube piece occupies only three columns and matches no height or protected crossing.
03Stack with a reason - Vertical payoff
- height + bridge
Here the lost footprint earns an exact two-dot match and clears a black tile.
Low, wide constructions will advance territory faster unless verticality unlocks a specific payoff.
The same cubes can cover more distinct columns when they lie flat. Vertical cubes become valuable only when height, bridging, or connectivity needs them.
Several neutral cells are reachable without a protected obstacle or exact-height target.
Some dealt shapes and connected constructions force stacking; judge the useful footprint, not a blanket height limit.
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.
01Open center - Supports needed
- 8
An interior claim needs all eight neighboring positions satisfied.
02Edge and corner - Corner / edge
- 3 / 5
The edge supplies three exempt positions; the corner supplies five.
03Black wall - Free wall
- 3 black neighbors
Uncleared black tiles satisfy part of the enclosure without belonging to either player.
04Close the diagonal - One cell closes
- the pocket
The marked diagonal is the last unsatisfied neighbor; claiming it hardens the center.
Claims beside helpful boundaries will convert with fewer supporting cells than equivalent interior claims.
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.
An edge or corner pocket, or a nearly enclosed cluster with one missing diagonal.
A boundary can become a mobility dead end, and an opponent may contest the same inexpensive pocket.
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.
01Thin ribbon - Shape
- long + soft
Six claims reach far, but almost every cell is exposed and the route depends on one narrow line.
02Compact lobe - Shape
- shared supports
The same number of claims share neighbors and prepare several closure cells.
03Two useful faces - Live launches
- 2
A good lobe stays compact while preserving two outward launches toward real objectives.
Compact lobes with two useful outward faces will retain more value than equally large ribbons or sealed blobs.
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.
A choice between extending a one-cell corridor and widening a cluster toward two objectives.
A ribbon can be correct when racing to an awkward neutral, a peak, or a strategically vital corridor.
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.
01Single-purpose reach - Jobs completed
- expand
This move claims open cells but changes no enclosure or future objective.
02Expand and close - Jobs completed
- expand + close
The marked footprint claims neutrals and supplies the missing side of an existing pocket.
Moves with two immediate, independently useful consequences will outperform single-purpose moves of similar score.
One footprint can expand ordinary territory while closing a capture, opening a route, defending a hinge, or creating a threat.
A neutral cell that is also the missing neighbor of a claim or the next step toward height.
Do not invent a speculative second benefit that needs several uncontested turns to matter.
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.
01Claim neutral - You
- +5
A neutral cell becomes your soft territory.
02Harden your claim - You
- +5 more
Enclosure converts an existing 5-point claim into a protected 10-point capture.
03Steal a soft claim - Head-to-head
- +10 swing
Ownership flips without a bridge: you gain 5 while the rival loses 5.
04Bridge a capture - 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.
Players who count the relative swing and protection cost will reject attractive-looking but strategically empty exchanges.
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.
A choice among neutral expansion, closing your claim, stealing a patterned claim, or bridging a solid tile.
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 takeRule 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.
01Replayed public board - Source
- turn 9
- Search
- 120 candidates
Balanced to move at 61.9% territory completion. The ringed tile is height 2.
02B: reaches, but misses - Exact match
- no
- Engine score
- +10
- Territory
- +0
This legal construction reaches H at height 3; the printed requirement is 2.
03A: match and support - 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.
04Receipt, not prophecy - 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.
Height plans that include approach, exact match, and capture will bank more bonuses than plans that merely reach the tile.
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.
An unawarded dotted tile with a short approach and visible surrounding-cell requirement.
Ignore a peak when its route consumes too many turns, is easily cut, or loses a more valuable ordinary-territory race.
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.
01Same public position - 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.
02Nearest: secure work - 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.
03Raw ROI: exposed promise - 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.
04Archived replay receipt - 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.
Routes with better total return per committed turn will outperform simple nearest-peak or highest-peak selection.
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.
A short useful route to a modest peak and a long exposed route to a larger peak.
A distant high peak can still dominate when the route is unusually safe or denies an opponent’s only major award.
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.
01Same hand, same board - 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.
02Take the visible 50 - 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.
03Spend five on the pocket - 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.
04One hand cashes both - 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.
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.
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.
Two reachable dotted tiles whose eight-neighbor enclosures overlap, with a hand that can match both heights without leaving a long exposed seam.
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.
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.
01Soft connection - Routes depending on H
- 3
One patterned cell joins two lobes and supports a nearby pocket.
02Harden the hinge - Routes secured
- 3
One closure turns the shared connection into protected infrastructure.
03Bridge or go around - Rival cost
- bridge required
The rival can no longer cover H directly and must pay for a bridge or a longer route.
Capturing high-leverage hinge cells will preserve more routes and territory than maximizing peripheral capture count.
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.
One soft cell connects two lobes, supports several claims, or controls access around a black tile.
A hinge is overrated when opponents already have an independent route or an easy legal bridge.
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.
01Bridge raid - Immediate swing
- +15
- Landing
- soft
Blue crosses the black tile and takes one solid red cell as a new soft claim.
02No support: flipped back - After one round
- 0 retained
Red’s reply reaches the landing directly and restores the old frontier.
03Supported raid: held - After one round
- +15 retained
A smaller landing beside blue support survives the direct reply and prepares closure.
Smaller thefts with durable support will outperform larger steals that are immediately reversed.
Bridge-stolen captured territory becomes a soft claim and cannot recapture in the same resolution. The reply can erase the headline score swing.
A bridge can reach solid enemy territory, but the landing area has either strong support or obvious enemy recapture access.
A temporary swing can be correct when it triggers the ending, breaks a route, or forces a reply that creates value elsewhere.
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.
01Five neutrals remain - Remaining
- 5
Four easy cells sit beside blue; one awkward cell lies beyond a narrow rival corridor.
02Tempting cleanup - Remaining
- 1 awkward
Blue takes the four nearby cells and leaves only the awkward coordinate.
03Route closes - Result
- flip-war risk
The table can still trade the contested frontier, but no cheap line reaches the last neutral.
04Hard cell first - Route
- finish preserved
The alternate route secures the awkward coordinate while easy cleanup remains accessible.
Late plans that preserve a route to the hardest remaining coordinate will finish more reliably than greedy neutral-count reduction.
A tempting move can consume easy cells while closing the only practical approach to an isolated neutral, after which profitable recaptures dominate.
Only a few neutral cells remain and one sits beyond a narrow or contested approach.
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 endingOpen 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.
01One public hand, two frontiers - 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.
02Raw-frontier candidate - 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.
03Compatibility candidate - 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.
04Best reply; value unresolved - 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.
Positions with more hand-compatible objective routes will outperform positions with a larger but strategically empty frontier.
The six piece shapes and their orientations fit different launch geometry. Raw frontier size ignores whether a useful connected construction can start there.
A wide irregular edge with few good fits versus a smaller edge aligned with several objectives.
Future hands are uncertain, and preserving excessive flexibility can sacrifice guaranteed score.
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.
01Create the threat - If ignored
- +30 next turn
Blue prepares a capture chain that will harden the marked pocket next turn.
02Reply is forced - Red’s preferred route
- delayed
Red abandons its preferred height route to occupy the only closing cell.
03Spend the tempo - Initiative
- blue keeps it
Blue uses the stolen turn to advance a separate objective while red remains tied to defense.
Threats that force costly replies will create more two-turn value than equally scoring quiet moves.
A height conversion, capture chain, or completion threat can make defense mandatory and erase the opponent’s preferred expansion turn.
You can create a threat that becomes much more valuable if ignored, while preserving a second objective.
A threat is not forcing when the opponent has a stronger counterattack or one reply answers it while advancing their own plan.
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.
01Two critical cells - Threats
- A + B
Height conversion at A and pocket closure at B depend on different coordinates.
02Red blocks A - Surviving threat
- B
The reply reaches the height route, but the separate closure at B remains live.
03B converts - Fork result
- one threat scores
Blue closes the pocket; the defense could save only one side of the fork.
Threat pairs with different critical cells will convert more often than larger threats sharing a single vulnerable hinge.
If height, capture, attack, or completion threats depend on disjoint cells, the defender must choose which future value survives.
Two near-conversions lie in different sectors and no connected reply footprint can cover both critical cells.
The fork fails when both routes share a launch point, the opponent can end the game, or one connected construction intersects both.
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.
01The public decision state - 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.
02Fragile immediate leader - 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.
03Strongest observed reply - 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.
04Quieter line retains score - 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.
Moves with slightly lower immediate value but stronger worst-reply outcomes will perform more consistently across opponents and maps.
Multiple viable continuations and captured infrastructure reduce the damage of any single counter. A brittle plan concentrates value behind one soft cell.
A high-scoring move with one critical dependency versus a quieter move preserving two routes.
Robustness can become expensive caution when opponents cannot find the precise reply or immediate tempo decides the game.
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.
01Trigger now - Owed replies
- R → G → Y
- Score at trigger
- Blue +10
Blue takes the final neutral while red, green, and yellow are still owed turns.
02Replies reverse the lead - Projected finish
- Blue −15
The trigger score looked safe, but three scoring replies leave blue behind.
03Trigger later - Owed replies
- R only
- Projected finish
- Blue +20
After the round advances, an equivalent finish leaves only one rival reply.
04But waiting has a price - Guardrail
- secure access first
Delay only when the route stays yours; otherwise a rival may trigger first or strand the cell.
Seat-aware trigger decisions will avoid more losing finishes than simple finish-now or finish-if-leading rules.
When the last ordinary territory is consumed, particular players are still owed turns. Trigger timing changes both the number and identity of those replies.
One neutral remains, the actor can take it, and several seats still have turns in the current round.
Waiting can let a rival trigger from a worse state, strand the last neutral, or surrender a safe finish already available.
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.
01Attack first place - Standings after
- Green 1st · Blue 3rd
Blue damages red, but green inherits the lead while blue remains third.
02Attack the useful hinge - Standings after
- Blue 1st
A different target removes the cell blocking blue’s route and moves blue into first.
03Change with the board - Phase
- state, not turn number
Early positions reward expansion; middle positions reward conversion; late positions reward safe closure.
Targeting based on attacker rank improvement and route value will outperform leader damage alone in multiplayer.
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.
Several opponents can be damaged, but only one attack changes your rank or opens your winning route.
A runaway leader may still require direct denial even when another player receives some short-term benefit.