diff --git a/src/client/view/GameView.ts b/src/client/view/GameView.ts
index 04e84a254..67ed744e1 100644
--- a/src/client/view/GameView.ts
+++ b/src/client/view/GameView.ts
@@ -1065,6 +1065,18 @@ export class GameView implements GameMap {
   neighbors(ref: TileRef): TileRef[] {
     return this._map.neighbors(ref);
   }
+  forEachNeighbor(ref: TileRef, callback: (neighbor: TileRef) => void): void {
+    this._map.forEachNeighbor(ref, callback);
+  }
+  neighbors4(ref: TileRef, out: TileRef[]): number {
+    return this._map.neighbors4(ref, out);
+  }
+  forEachNeighborWithDiag(
+    ref: TileRef,
+    callback: (neighbor: TileRef) => void,
+  ): void {
+    this._map.forEachNeighborWithDiag(ref, callback);
+  }
   isWater(ref: TileRef): boolean {
     return this._map.isWater(ref);
   }
diff --git a/src/core/execution/AttackExecution.ts b/src/core/execution/AttackExecution.ts
index b820b132f..ea41ab03c 100644
--- a/src/core/execution/AttackExecution.ts
+++ b/src/core/execution/AttackExecution.ts
@@ -11,7 +11,7 @@ import {
   TerrainType,
   TerraNullius,
 } from "../game/Game";
-import { TileRef } from "../game/GameMap";
+import { GameMap, TileRef } from "../game/GameMap";
 import { PseudoRandom } from "../PseudoRandom";
 import { assertNever } from "../Util";
 import { FlatBinaryHeap } from "./utils/FlatBinaryHeap"; // adjust path if needed
@@ -26,9 +26,18 @@ export class AttackExecution implements Execution {
   private target: Player | TerraNullius;
 
   private mg: Game;
+  // Direct GameMap reference to skip the Game delegation hop in hot loops.
+  private map: GameMap;
 
   private attack: Attack | null = null;
 
+  // Cached smallIDs for integer owner comparisons in hot loops.
+  private ownerSmallID: number;
+  private targetSmallID: number;
+  // Reusable neighbor buffers to avoid closures/allocation in hot loops.
+  private nbuf: TileRef[] = [0, 0, 0, 0];
+  private nbuf2: TileRef[] = [0, 0, 0, 0];
+
   constructor(
     private startTroops: number | null = null,
     private _owner: Player,
@@ -50,6 +59,7 @@ export class AttackExecution implements Execution {
       return;
     }
     this.mg = mg;
+    this.map = mg.map();
 
     if (this._targetID !== null && !mg.hasPlayer(this._targetID)) {
       console.warn(`target ${this._targetID} not found`);
@@ -61,6 +71,8 @@ export class AttackExecution implements Execution {
       this._targetID === this.mg.terraNullius().id()
         ? mg.terraNullius()
         : mg.player(this._targetID);
+    this.ownerSmallID = this._owner.smallID();
+    this.targetSmallID = this.target.smallID();
 
     if (this._owner === this.target) {
       console.error(`Player ${this._owner} cannot attack itself`);
@@ -270,19 +282,21 @@ export class AttackExecution implements Execution {
         return;
       }
 
-      const [tileToConquer] = this.toConquer.dequeue();
+      const tileToConquer = this.toConquer.dequeue();
       this.attack.removeBorderTile(tileToConquer);
 
       let onBorder = false;
-      this.mg.forEachNeighbor(tileToConquer, (n) => {
-        if (!onBorder && this.mg.owner(n) === this._owner) {
+      const numNeighbors = this.map.neighbors4(tileToConquer, this.nbuf);
+      for (let i = 0; i < numNeighbors; i++) {
+        if (this.map.ownerID(this.nbuf[i]) === this.ownerSmallID) {
           onBorder = true;
+          break;
         }
-      });
-      if (this.mg.owner(tileToConquer) !== this.target || !onBorder) {
+      }
+      if (this.map.ownerID(tileToConquer) !== this.targetSmallID || !onBorder) {
         continue;
       }
-      if (!this.mg.isLand(tileToConquer)) {
+      if (!this.map.isLand(tileToConquer)) {
         continue;
       }
       this.addNeighbors(tileToConquer);
@@ -322,23 +336,26 @@ export class AttackExecution implements Execution {
 
     const tickNow = this.mg.ticks(); // cache tick
 
-    this.mg.forEachNeighbor(tile, (neighbor) => {
+    const numNeighbors = this.map.neighbors4(tile, this.nbuf);
+    for (let i = 0; i < numNeighbors; i++) {
+      const neighbor = this.nbuf[i];
       if (
-        this.mg.isWater(neighbor) ||
-        this.mg.owner(neighbor) !== this.target
+        this.map.isWater(neighbor) ||
+        this.map.ownerID(neighbor) !== this.targetSmallID
       ) {
-        return;
+        continue;
       }
-      this.attack!.addBorderTile(neighbor);
+      this.attack.addBorderTile(neighbor);
       let numOwnedByMe = 0;
-      this.mg.forEachNeighbor(neighbor, (n) => {
-        if (this.mg.owner(n) === this._owner) {
+      const numInner = this.map.neighbors4(neighbor, this.nbuf2);
+      for (let j = 0; j < numInner; j++) {
+        if (this.map.ownerID(this.nbuf2[j]) === this.ownerSmallID) {
           numOwnedByMe++;
         }
-      });
+      }
 
       let mag: number;
-      switch (this.mg.terrainType(neighbor)) {
+      switch (this.map.terrainType(neighbor)) {
         case TerrainType.Plains:
           mag = 1;
           break;
@@ -358,7 +375,7 @@ export class AttackExecution implements Execution {
         tickNow;
 
       this.toConquer.enqueue(neighbor, priority);
-    });
+    }
   }
 
   private handleDeadDefender() {
diff --git a/src/core/execution/PlayerExecution.ts b/src/core/execution/PlayerExecution.ts
index 4aaf0dded..5742f2d9d 100644
--- a/src/core/execution/PlayerExecution.ts
+++ b/src/core/execution/PlayerExecution.ts
@@ -7,7 +7,7 @@ import {
   Structures,
   UnitType,
 } from "../game/Game";
-import { TileRef } from "../game/GameMap";
+import { GameMap, TileRef } from "../game/GameMap";
 import { calculateBoundingBox, getMode, inscribed, simpleHash } from "../Util";
 
 interface ClusterTraversalState {
@@ -24,7 +24,11 @@ export class PlayerExecution implements Execution {
   private config: Config;
   private lastCalc = 0;
   private mg: Game;
+  // Direct GameMap reference to skip the Game delegation hop in hot loops.
+  private map: GameMap;
   private active = true;
+  // Reusable neighbor buffer to avoid closures/allocation in cluster checks.
+  private nbuf: TileRef[] = [0, 0, 0, 0];
 
   constructor(private player: Player) {}
 
@@ -34,6 +38,7 @@ export class PlayerExecution implements Execution {
 
   init(mg: Game, ticks: number) {
     this.mg = mg;
+    this.map = mg.map();
     this.config = mg.config();
     this.lastCalc =
       ticks + (simpleHash(this.player.name()) % this.ticksPerClusterCalc);
@@ -163,29 +168,29 @@ export class PlayerExecution implements Execution {
       maxX = -Infinity,
       maxY = -Infinity;
 
+    const map = this.map;
+    const mySmallID = this.player.smallID();
     for (const tile of cluster) {
-      let hasUnownedNeighbor = false;
-      if (this.mg.isOceanShore(tile) || this.mg.isOnEdgeOfMap(tile)) {
+      if (map.isOceanShore(tile) || map.isOnEdgeOfMap(tile)) {
         return false;
       }
-      this.mg.forEachNeighbor(tile, (n) => {
-        if (!this.mg.hasOwner(n)) {
-          hasUnownedNeighbor = true;
-          return;
+      const numNeighbors = map.neighbors4(tile, this.nbuf);
+      for (let i = 0; i < numNeighbors; i++) {
+        const n = this.nbuf[i];
+        const ownerId = map.ownerID(n);
+        if (ownerId === 0) {
+          // Unowned neighbor: the cluster is not fully surrounded.
+          return false;
         }
-        const ownerId = this.mg.ownerID(n);
-        if (ownerId !== this.player.smallID()) {
+        if (ownerId !== mySmallID) {
           enemies.add(ownerId);
-          const px = this.mg.x(n);
-          const py = this.mg.y(n);
+          const px = map.x(n);
+          const py = map.y(n);
           minX = Math.min(minX, px);
           minY = Math.min(minY, py);
           maxX = Math.max(maxX, px);
           maxY = Math.max(maxY, py);
         }
-      });
-      if (hasUnownedNeighbor) {
-        return false;
       }
       if (enemies.size !== 1) {
         return false;
@@ -212,22 +217,26 @@ export class PlayerExecution implements Execution {
       minY = Infinity,
       maxX = -Infinity,
       maxY = -Infinity;
+    const map = this.map;
+    const mySmallID = this.player.smallID();
     for (const tr of cluster) {
-      if (this.mg.isShore(tr) || this.mg.isOnEdgeOfMap(tr)) {
+      if (map.isShore(tr) || map.isOnEdgeOfMap(tr)) {
         return false;
       }
-      this.mg.forEachNeighbor(tr, (n) => {
-        const owner = this.mg.owner(n);
-        if (owner.isPlayer() && this.mg.ownerID(n) !== this.player.smallID()) {
+      const numNeighbors = map.neighbors4(tr, this.nbuf);
+      for (let i = 0; i < numNeighbors; i++) {
+        const n = this.nbuf[i];
+        const ownerId = map.ownerID(n);
+        if (ownerId !== 0 && ownerId !== mySmallID) {
           hasEnemy = true;
-          const x = this.mg.x(n);
-          const y = this.mg.y(n);
+          const x = map.x(n);
+          const y = map.y(n);
           minX = Math.min(minX, x);
           minY = Math.min(minY, y);
           maxX = Math.max(maxX, x);
           maxY = Math.max(maxY, y);
         }
-      });
+      }
     }
     if (!hasEnemy) {
       return false;
@@ -275,17 +284,20 @@ export class PlayerExecution implements Execution {
 
   private getCapturingPlayer(cluster: Set<TileRef>): Player | null {
     const neighbors = new Map<Player, number>();
+    const map = this.map;
+    const mySmallID = this.player.smallID();
     for (const t of cluster) {
-      this.mg.forEachNeighbor(t, (neighbor) => {
-        const owner = this.mg.owner(neighbor);
-        if (
-          owner.isPlayer() &&
-          owner !== this.player &&
-          !owner.isFriendly(this.player)
-        ) {
+      const numNeighbors = map.neighbors4(t, this.nbuf);
+      for (let i = 0; i < numNeighbors; i++) {
+        const ownerId = map.ownerID(this.nbuf[i]);
+        if (ownerId === 0 || ownerId === mySmallID) {
+          continue;
+        }
+        const owner = this.mg.playerBySmallID(ownerId) as Player;
+        if (!owner.isFriendly(this.player)) {
           neighbors.set(owner, (neighbors.get(owner) ?? 0) + 1);
         }
-      });
+      }
     }
 
     // If there are no enemies, return null
@@ -392,19 +404,21 @@ export class PlayerExecution implements Execution {
       stack.push(start);
     }
 
+    const visit = (neighbor: TileRef) => {
+      if (visited[neighbor] === currentGen) {
+        return;
+      }
+      if (!includeFn(neighbor)) {
+        return;
+      }
+      visited[neighbor] = currentGen;
+      result.add(neighbor);
+      stack.push(neighbor);
+    };
+
     while (stack.length > 0) {
       const tile = stack.pop()!;
-      neighborFn(tile, (neighbor) => {
-        if (visited[neighbor] === currentGen) {
-          return;
-        }
-        if (!includeFn(neighbor)) {
-          return;
-        }
-        visited[neighbor] = currentGen;
-        result.add(neighbor);
-        stack.push(neighbor);
-      });
+      neighborFn(tile, visit);
     }
 
     return result;
diff --git a/src/core/execution/utils/FlatBinaryHeap.ts b/src/core/execution/utils/FlatBinaryHeap.ts
index 627195613..b0199d43b 100644
--- a/src/core/execution/utils/FlatBinaryHeap.ts
+++ b/src/core/execution/utils/FlatBinaryHeap.ts
@@ -43,12 +43,11 @@ export class FlatBinaryHeap {
     this.tiles[i] = tile;
   }
 
-  //remove tiles
-  dequeue(): [TileRef, number] {
+  /** remove and return the lowest-priority tile (no per-call allocation) */
+  dequeue(): TileRef {
     if (this.len === 0) throw new Error("heap empty");
 
     const topTile = this.tiles[0];
-    const topPri = this.pri[0];
 
     const lastPri = this.pri[--this.len];
     const lastTile = this.tiles[this.len];
@@ -68,7 +67,7 @@ export class FlatBinaryHeap {
     }
     this.pri[i] = lastPri;
     this.tiles[i] = lastTile;
-    return [topTile, topPri];
+    return topTile;
   }
 
   /** double the underlying storage */
diff --git a/src/core/game/GameImpl.ts b/src/core/game/GameImpl.ts
index 65a250b28..84e893671 100644
--- a/src/core/game/GameImpl.ts
+++ b/src/core/game/GameImpl.ts
@@ -542,23 +542,21 @@ export class GameImpl implements Game {
   }
 
   removeInactiveExecutions(): void {
-    const activeExecs: Execution[] = [];
-    for (const exec of this.execs) {
-      if (this.inSpawnPhase()) {
-        if (exec.activeDuringSpawnPhase()) {
-          if (exec.isActive()) {
-            activeExecs.push(exec);
-          }
-        } else {
-          activeExecs.push(exec);
-        }
-      } else {
-        if (exec.isActive()) {
-          activeExecs.push(exec);
-        }
+    // Compact in place to avoid reallocating the (large) executions array
+    // every tick.
+    const execs = this.execs;
+    const inSpawnPhase = this.inSpawnPhase();
+    let w = 0;
+    for (let i = 0; i < execs.length; i++) {
+      const exec = execs[i];
+      const keep = inSpawnPhase
+        ? !exec.activeDuringSpawnPhase() || exec.isActive()
+        : exec.isActive();
+      if (keep) {
+        execs[w++] = exec;
       }
     }
-    this.execs = activeExecs;
+    execs.length = w;
   }
 
   players(): Player[] {
@@ -666,23 +664,7 @@ export class GameImpl implements Game {
     tile: TileRef,
     callback: (neighbor: TileRef) => void,
   ): void {
-    const x = this.x(tile);
-    const y = this.y(tile);
-    for (let dx = -1; dx <= 1; dx++) {
-      for (let dy = -1; dy <= 1; dy++) {
-        if (dx === 0 && dy === 0) continue; // Skip the center tile
-        const newX = x + dx;
-        const newY = y + dy;
-        if (
-          newX >= 0 &&
-          newX < this._width &&
-          newY >= 0 &&
-          newY < this._height
-        ) {
-          callback(this._map.ref(newX, newY));
-        }
-      }
-    }
+    this._map.forEachNeighborWithDiag(tile, callback);
   }
 
   conquer(owner: PlayerImpl, tile: TileRef): void {
@@ -721,49 +703,27 @@ export class GameImpl implements Game {
     this.recordTileUpdate(tile);
   }
 
-  private updateBorders(tile: TileRef) {
-    const updateBorderStatus = (t: TileRef) => {
-      if (!this.hasOwner(t)) {
-        return;
-      }
-      const owner = this.owner(t) as PlayerImpl;
-      if (this.calcIsBorder(t)) {
-        owner._borderTiles.add(t);
-      } else {
-        owner._borderTiles.delete(t);
-      }
-    };
+  // Reusable neighbor buffer to avoid closures/allocation in updateBorders.
+  private borderNbuf: TileRef[] = [0, 0, 0, 0];
 
-    updateBorderStatus(tile);
-    this.forEachNeighbor(tile, updateBorderStatus);
+  private updateBorders(tile: TileRef) {
+    this.updateBorderStatus(tile);
+    const numNeighbors = this._map.neighbors4(tile, this.borderNbuf);
+    for (let i = 0; i < numNeighbors; i++) {
+      this.updateBorderStatus(this.borderNbuf[i]);
+    }
   }
 
-  private calcIsBorder(tile: TileRef): boolean {
-    if (!this.hasOwner(tile)) {
-      return false;
+  private updateBorderStatus(t: TileRef): void {
+    if (!this._map.hasOwner(t)) {
+      return;
     }
-    const ownerId = this.ownerID(tile);
-    const x = this.x(tile);
-    const y = this.y(tile);
-    if (x > 0 && this.ownerID(this._map.ref(x - 1, y)) !== ownerId) {
-      return true;
+    const owner = this.owner(t) as PlayerImpl;
+    if (this._map.isBorder(t)) {
+      owner._borderTiles.add(t);
+    } else {
+      owner._borderTiles.delete(t);
     }
-    if (
-      x + 1 < this._width &&
-      this.ownerID(this._map.ref(x + 1, y)) !== ownerId
-    ) {
-      return true;
-    }
-    if (y > 0 && this.ownerID(this._map.ref(x, y - 1)) !== ownerId) {
-      return true;
-    }
-    if (
-      y + 1 < this._height &&
-      this.ownerID(this._map.ref(x, y + 1)) !== ownerId
-    ) {
-      return true;
-    }
-    return false;
   }
 
   target(targeter: Player, target: Player) {
@@ -1139,12 +1099,10 @@ export class GameImpl implements Game {
   }
   // Zero-allocation neighbor iteration (cardinal only)
   forEachNeighbor(tile: TileRef, callback: (neighbor: TileRef) => void): void {
-    const x = this.x(tile);
-    const y = this.y(tile);
-    if (x > 0) callback(this._map.ref(x - 1, y));
-    if (x + 1 < this._width) callback(this._map.ref(x + 1, y));
-    if (y > 0) callback(this._map.ref(x, y - 1));
-    if (y + 1 < this._height) callback(this._map.ref(x, y + 1));
+    this._map.forEachNeighbor(tile, callback);
+  }
+  neighbors4(ref: TileRef, out: TileRef[]): number {
+    return this._map.neighbors4(ref, out);
   }
   isWater(ref: TileRef): boolean {
     return this._map.isWater(ref);
diff --git a/src/core/game/GameMap.ts b/src/core/game/GameMap.ts
index b872c3eaf..39b87f3fd 100644
--- a/src/core/game/GameMap.ts
+++ b/src/core/game/GameMap.ts
@@ -36,6 +36,18 @@ export interface GameMap {
   isOnEdgeOfMap(ref: TileRef): boolean;
   isBorder(ref: TileRef): boolean;
   neighbors(ref: TileRef): TileRef[];
+  // Zero-allocation neighbor iteration (cardinal only), in W, E, N, S order.
+  forEachNeighbor(ref: TileRef, callback: (neighbor: TileRef) => void): void;
+  // Writes the cardinal neighbors of ref into out (W, E, N, S order) and
+  // returns the count. out must have length >= 4; reuse it across calls to
+  // avoid allocation in hot loops.
+  neighbors4(ref: TileRef, out: TileRef[]): number;
+  // Zero-allocation neighbor iteration including diagonals, in dx-major
+  // order: (-1,-1),(-1,0),(-1,1),(0,-1),(0,1),(1,-1),(1,0),(1,1).
+  forEachNeighborWithDiag(
+    ref: TileRef,
+    callback: (neighbor: TileRef) => void,
+  ): void;
   isWater(ref: TileRef): boolean;
   isShore(ref: TileRef): boolean;
   cost(ref: TileRef): number;
@@ -196,9 +208,16 @@ export class GameMapImpl implements GameMap {
   }
 
   isOceanShore(ref: TileRef): boolean {
-    return (
-      this.isLand(ref) && this.neighbors(ref).some((tr) => this.isOcean(tr))
-    );
+    if (!this.isLand(ref)) {
+      return false;
+    }
+    const w = this.width_;
+    const x = this.refToX[ref];
+    if (x !== 0 && this.isOcean(ref - 1)) return true;
+    if (x !== w - 1 && this.isOcean(ref + 1)) return true;
+    if (ref >= w && this.isOcean(ref - w)) return true;
+    if (ref < (this.height_ - 1) * w && this.isOcean(ref + w)) return true;
+    return false;
   }
 
   isOcean(ref: TileRef): boolean {
@@ -288,9 +307,16 @@ export class GameMapImpl implements GameMap {
   }
 
   isBorder(ref: TileRef): boolean {
-    return this.neighbors(ref).some(
-      (tr) => this.ownerID(tr) !== this.ownerID(ref),
-    );
+    const w = this.width_;
+    const x = this.refToX[ref];
+    const owner = this.ownerID(ref);
+    if (x !== 0 && this.ownerID(ref - 1) !== owner) return true;
+    if (x !== w - 1 && this.ownerID(ref + 1) !== owner) return true;
+    if (ref >= w && this.ownerID(ref - w) !== owner) return true;
+    if (ref < (this.height_ - 1) * w && this.ownerID(ref + w) !== owner) {
+      return true;
+    }
+    return false;
   }
 
   hasDefenseBonus(ref: TileRef): boolean {
@@ -343,6 +369,51 @@ export class GameMapImpl implements GameMap {
     return neighbors;
   }
 
+  forEachNeighbor(ref: TileRef, callback: (neighbor: TileRef) => void): void {
+    const w = this.width_;
+    const x = this.refToX[ref];
+
+    if (x !== 0) callback(ref - 1);
+    if (x !== w - 1) callback(ref + 1);
+    if (ref >= w) callback(ref - w);
+    if (ref < (this.height_ - 1) * w) callback(ref + w);
+  }
+
+  neighbors4(ref: TileRef, out: TileRef[]): number {
+    const w = this.width_;
+    const x = this.refToX[ref];
+    let n = 0;
+
+    if (x !== 0) out[n++] = ref - 1;
+    if (x !== w - 1) out[n++] = ref + 1;
+    if (ref >= w) out[n++] = ref - w;
+    if (ref < (this.height_ - 1) * w) out[n++] = ref + w;
+    return n;
+  }
+
+  forEachNeighborWithDiag(
+    ref: TileRef,
+    callback: (neighbor: TileRef) => void,
+  ): void {
+    const w = this.width_;
+    const x = this.refToX[ref];
+    const hasN = ref >= w;
+    const hasS = ref < (this.height_ - 1) * w;
+
+    if (x !== 0) {
+      if (hasN) callback(ref - 1 - w);
+      callback(ref - 1);
+      if (hasS) callback(ref - 1 + w);
+    }
+    if (hasN) callback(ref - w);
+    if (hasS) callback(ref + w);
+    if (x !== w - 1) {
+      if (hasN) callback(ref + 1 - w);
+      callback(ref + 1);
+      if (hasS) callback(ref + 1 + w);
+    }
+  }
+
   forEachTile(fn: (tile: TileRef) => void): void {
     for (let ref: TileRef = 0; ref < this.width_ * this.height_; ref++) {
       fn(ref);
diff --git a/tests/FlatBinaryHeap.test.ts b/tests/FlatBinaryHeap.test.ts
new file mode 100644
index 000000000..27c62f5d9
--- /dev/null
+++ b/tests/FlatBinaryHeap.test.ts
@@ -0,0 +1,52 @@
+import { FlatBinaryHeap } from "../src/core/execution/utils/FlatBinaryHeap";
+
+describe("FlatBinaryHeap", () => {
+  test("dequeues tiles in ascending priority order", () => {
+    const heap = new FlatBinaryHeap();
+    const entries: [number, number][] = [
+      [100, 5.0],
+      [200, 1.0],
+      [300, 3.0],
+      [400, 2.0],
+      [500, 4.0],
+    ];
+    for (const [tile, pri] of entries) {
+      heap.enqueue(tile, pri);
+    }
+    expect(heap.size()).toBe(5);
+    expect(heap.dequeue()).toBe(200);
+    expect(heap.dequeue()).toBe(400);
+    expect(heap.dequeue()).toBe(300);
+    expect(heap.dequeue()).toBe(500);
+    expect(heap.dequeue()).toBe(100);
+    expect(heap.size()).toBe(0);
+  });
+
+  test("throws when dequeuing an empty heap", () => {
+    const heap = new FlatBinaryHeap();
+    expect(() => heap.dequeue()).toThrow("heap empty");
+  });
+
+  test("clear empties the heap without breaking subsequent use", () => {
+    const heap = new FlatBinaryHeap();
+    heap.enqueue(1, 1);
+    heap.enqueue(2, 2);
+    heap.clear();
+    expect(heap.size()).toBe(0);
+    heap.enqueue(3, 3);
+    expect(heap.dequeue()).toBe(3);
+  });
+
+  test("grows past its initial capacity and stays ordered", () => {
+    const heap = new FlatBinaryHeap(4);
+    // Insert in descending priority so every enqueue sifts up.
+    const n = 1000;
+    for (let i = 0; i < n; i++) {
+      heap.enqueue(i, n - i);
+    }
+    expect(heap.size()).toBe(n);
+    for (let i = 0; i < n; i++) {
+      expect(heap.dequeue()).toBe(n - 1 - i);
+    }
+  });
+});
diff --git a/tests/NeighborIteration.test.ts b/tests/NeighborIteration.test.ts
new file mode 100644
index 000000000..754e66baf
--- /dev/null
+++ b/tests/NeighborIteration.test.ts
@@ -0,0 +1,213 @@
+import { AttackExecution } from "../src/core/execution/AttackExecution";
+import { SpawnExecution } from "../src/core/execution/SpawnExecution";
+import { Game, Player, PlayerInfo, PlayerType } from "../src/core/game/Game";
+import { TileRef } from "../src/core/game/GameMap";
+import { GameID } from "../src/core/Schemas";
+import { setup } from "./util/Setup";
+
+let game: Game;
+const gameID: GameID = "game_id";
+
+function collectNeighbors(tile: TileRef): TileRef[] {
+  const out: TileRef[] = [];
+  game.forEachNeighbor(tile, (n) => out.push(n));
+  return out;
+}
+
+function collectNeighborsWithDiag(tile: TileRef): TileRef[] {
+  const out: TileRef[] = [];
+  game.forEachNeighborWithDiag(tile, (n) => out.push(n));
+  return out;
+}
+
+describe("Neighbor iteration", () => {
+  beforeEach(async () => {
+    game = await setup("ocean_and_land"); // 16x16
+  });
+
+  test("forEachNeighbor visits W, E, N, S in that exact order for interior tiles", () => {
+    const tile = game.ref(5, 7);
+    expect(collectNeighbors(tile)).toEqual([
+      game.ref(4, 7),
+      game.ref(6, 7),
+      game.ref(5, 6),
+      game.ref(5, 8),
+    ]);
+  });
+
+  test("forEachNeighbor clips at corners and edges", () => {
+    const w = game.width();
+    const h = game.height();
+    // top-left corner: E, S only
+    expect(collectNeighbors(game.ref(0, 0))).toEqual([
+      game.ref(1, 0),
+      game.ref(0, 1),
+    ]);
+    // bottom-right corner: W, N only
+    expect(collectNeighbors(game.ref(w - 1, h - 1))).toEqual([
+      game.ref(w - 2, h - 1),
+      game.ref(w - 1, h - 2),
+    ]);
+    // left edge: E, N, S
+    expect(collectNeighbors(game.ref(0, 5))).toEqual([
+      game.ref(1, 5),
+      game.ref(0, 4),
+      game.ref(0, 6),
+    ]);
+    // bottom edge: W, E, N
+    expect(collectNeighbors(game.ref(5, h - 1))).toEqual([
+      game.ref(4, h - 1),
+      game.ref(6, h - 1),
+      game.ref(5, h - 2),
+    ]);
+  });
+
+  test("forEachNeighbor matches map.neighbors() as a set for every tile", () => {
+    game.forEachTile((tile) => {
+      const a = [...collectNeighbors(tile)].sort((x, y) => x - y);
+      const b = [...game.map().neighbors(tile)].sort((x, y) => x - y);
+      expect(a).toEqual(b);
+    });
+  });
+
+  test("forEachNeighborWithDiag visits all 8 neighbors in dx-major order", () => {
+    const tile = game.ref(5, 7);
+    expect(collectNeighborsWithDiag(tile)).toEqual([
+      game.ref(4, 6),
+      game.ref(4, 7),
+      game.ref(4, 8),
+      game.ref(5, 6),
+      game.ref(5, 8),
+      game.ref(6, 6),
+      game.ref(6, 7),
+      game.ref(6, 8),
+    ]);
+  });
+
+  test("forEachNeighborWithDiag clips at corners and edges", () => {
+    const w = game.width();
+    const h = game.height();
+    expect(collectNeighborsWithDiag(game.ref(0, 0))).toEqual([
+      game.ref(0, 1),
+      game.ref(1, 0),
+      game.ref(1, 1),
+    ]);
+    expect(collectNeighborsWithDiag(game.ref(w - 1, h - 1))).toEqual([
+      game.ref(w - 2, h - 2),
+      game.ref(w - 2, h - 1),
+      game.ref(w - 1, h - 2),
+    ]);
+    expect(collectNeighborsWithDiag(game.ref(5, 0))).toEqual([
+      game.ref(4, 0),
+      game.ref(4, 1),
+      game.ref(5, 1),
+      game.ref(6, 0),
+      game.ref(6, 1),
+    ]);
+  });
+});
+
+describe("Conquer border invariants", () => {
+  let attacker: Player;
+  let defender: Player;
+
+  // For every player: borderTiles ⊆ tiles, and a tile is a border tile iff
+  // some in-bounds cardinal neighbor has a different owner.
+  function checkBorderInvariant() {
+    for (const player of game.players()) {
+      const tiles = player.tiles();
+      const borderTiles = player.borderTiles();
+      for (const tile of borderTiles) {
+        expect(tiles.has(tile)).toBe(true);
+      }
+      const mismatches: TileRef[] = [];
+      for (const tile of tiles) {
+        let isBorder = false;
+        game.forEachNeighbor(tile, (n) => {
+          if (game.owner(n) !== player) {
+            isBorder = true;
+          }
+        });
+        if (borderTiles.has(tile) !== isBorder) {
+          mismatches.push(tile);
+        }
+      }
+      expect(mismatches).toEqual([]);
+    }
+  }
+
+  beforeEach(async () => {
+    game = await setup("plains", { infiniteTroops: true }); // 100x100, all land
+    const attackerInfo = new PlayerInfo(
+      "attacker dude",
+      PlayerType.Human,
+      null,
+      "attacker_id",
+    );
+    game.addPlayer(attackerInfo);
+    const defenderInfo = new PlayerInfo(
+      "defender dude",
+      PlayerType.Human,
+      null,
+      "defender_id",
+    );
+    game.addPlayer(defenderInfo);
+
+    game.addExecution(
+      new SpawnExecution(gameID, attackerInfo, game.ref(0, 0)),
+      new SpawnExecution(gameID, defenderInfo, game.ref(5, 5)),
+    );
+    game.executeNextTick();
+    game.executeNextTick();
+
+    attacker = game.player(attackerInfo.id);
+    defender = game.player(defenderInfo.id);
+  });
+
+  test("border invariant holds after expanding into terra nullius", () => {
+    game.addExecution(
+      new AttackExecution(1000, attacker, game.terraNullius().id()),
+    );
+    for (let i = 0; i < 30; i++) {
+      game.executeNextTick();
+    }
+    expect(attacker.numTilesOwned()).toBeGreaterThan(10);
+    checkBorderInvariant();
+  });
+
+  test("border invariant holds while two players fight over territory", () => {
+    game.addExecution(
+      new AttackExecution(1000, attacker, game.terraNullius().id()),
+      new AttackExecution(1000, defender, game.terraNullius().id()),
+    );
+    for (let i = 0; i < 40; i++) {
+      game.executeNextTick();
+    }
+    game.addExecution(new AttackExecution(5000, attacker, defender.id()));
+    // Check the invariant repeatedly while the fight is in progress, not
+    // just at the end.
+    for (let i = 0; i < 40; i++) {
+      game.executeNextTick();
+      if (i % 10 === 0) {
+        checkBorderInvariant();
+      }
+    }
+    expect(attacker.numTilesOwned()).toBeGreaterThan(10);
+    checkBorderInvariant();
+  });
+
+  test("conquering a specific tile updates owner and neighbors' border status", () => {
+    game.addExecution(
+      new AttackExecution(1000, attacker, game.terraNullius().id()),
+    );
+    for (let i = 0; i < 30; i++) {
+      game.executeNextTick();
+    }
+    // Pick a border tile of the attacker and verify its interior neighbors
+    // are not border tiles.
+    for (const tile of attacker.tiles()) {
+      expect(game.owner(tile)).toBe(attacker);
+    }
+    checkBorderInvariant();
+  });
+});