diff --git a/superpowers/src/game/pathfinder.ts b/superpowers/src/game/pathfinder.ts
new file mode 100644
index 0000000..25362da
--- /dev/null
+++ b/superpowers/src/game/pathfinder.ts
@@ -0,0 +1,155 @@
+import { Board, Point } from "../types";
+
+function isEmpty(board: Board, row: number, col: number): boolean {
+  const rows = board.length;
+  const cols = board[0].length;
+  if (row < 0 || row >= rows || col < 0 || col >= cols) {
+    return row >= -1 && row <= rows && col >= -1 && col <= cols;
+  }
+  return board[row][col] === null;
+}
+
+const DIRS: [number, number][] = [
+  [0, 1],
+  [0, -1],
+  [1, 0],
+  [-1, 0],
+];
+
+function raycast(
+  board: Board,
+  row: number,
+  col: number,
+  dr: number,
+  dc: number
+): Point[] {
+  const points: Point[] = [];
+  let r = row + dr;
+  let c = col + dc;
+  const rows = board.length;
+  const cols = board[0].length;
+  while (r >= -1 && r <= rows && c >= -1 && c <= cols && isEmpty(board, r, c)) {
+    points.push({ row: r, col: c });
+    r += dr;
+    c += dc;
+  }
+  return points;
+}
+
+function canConnectStraight(
+  board: Board,
+  a: Point,
+  b: Point
+): boolean {
+  if (a.row === b.row) {
+    const minC = Math.min(a.col, b.col);
+    const maxC = Math.max(a.col, b.col);
+    for (let c = minC + 1; c < maxC; c++) {
+      if (!isEmpty(board, a.row, c)) return false;
+    }
+    return true;
+  }
+  if (a.col === b.col) {
+    const minR = Math.min(a.row, b.row);
+    const maxR = Math.max(a.row, b.row);
+    for (let r = minR + 1; r < maxR; r++) {
+      if (!isEmpty(board, r, a.col)) return false;
+    }
+    return true;
+  }
+  return false;
+}
+
+export function findPath(
+  board: Board,
+  a: Point,
+  b: Point
+): Point[] | null {
+  const tileA = board[a.row]?.[a.col];
+  const tileB = board[b.row]?.[b.col];
+  if (!tileA || !tileB || tileA.emoji !== tileB.emoji) return null;
+  if (a.row === b.row && a.col === b.col) return null;
+
+  // 0 bends: direct straight line
+  if (canConnectStraight(board, a, b)) {
+    return [a, b];
+  }
+
+  // 1 bend: check two possible corners
+  const corner1: Point = { row: a.row, col: b.col };
+  if (
+    isEmpty(board, corner1.row, corner1.col) &&
+    canConnectStraight(board, a, corner1) &&
+    canConnectStraight(board, corner1, b)
+  ) {
+    return [a, corner1, b];
+  }
+
+  const corner2: Point = { row: b.row, col: a.col };
+  if (
+    isEmpty(board, corner2.row, corner2.col) &&
+    canConnectStraight(board, a, corner2) &&
+    canConnectStraight(board, corner2, b)
+  ) {
+    return [a, corner2, b];
+  }
+
+  // 2 bends: try all lines from A, for each reachable cell, try 1-bend to B
+  for (const [dr, dc] of DIRS) {
+    const reachable = raycast(board, a.row, a.col, dr, dc);
+    for (const mid of reachable) {
+      const cornerA: Point = { row: mid.row, col: b.col };
+      if (
+        isEmpty(board, cornerA.row, cornerA.col) &&
+        canConnectStraight(board, mid, cornerA) &&
+        canConnectStraight(board, cornerA, b)
+      ) {
+        return [a, mid, cornerA, b];
+      }
+
+      const cornerB: Point = { row: b.row, col: mid.col };
+      if (
+        isEmpty(board, cornerB.row, cornerB.col) &&
+        canConnectStraight(board, mid, cornerB) &&
+        canConnectStraight(board, cornerB, b)
+      ) {
+        return [a, mid, cornerB, b];
+      }
+
+      if (canConnectStraight(board, mid, b)) {
+        return [a, mid, b];
+      }
+    }
+  }
+
+  return null;
+}
+
+export function hasAnyValidMove(board: Board): boolean {
+  const tiles: { pos: Point; emoji: string }[] = [];
+  for (let r = 0; r < board.length; r++) {
+    for (let c = 0; c < board[r].length; c++) {
+      if (board[r][c] !== null) {
+        tiles.push({ pos: { row: r, col: c }, emoji: board[r][c]!.emoji });
+      }
+    }
+  }
+
+  const groups = new Map<string, Point[]>();
+  for (const t of tiles) {
+    if (!groups.has(t.emoji)) groups.set(t.emoji, []);
+    groups.get(t.emoji)!.push(t.pos);
+  }
+
+  for (const [, positions] of groups) {
+    for (let i = 0; i < positions.length; i++) {
+      for (let j = i + 1; j < positions.length; j++) {
+        if (findPath(board, positions[i], positions[j]) !== null) {
+          return true;
+        }
+      }
+    }
+  }
+
+  return false;
+}
diff --git a/superpowers/tests/game/pathfinder.test.ts b/superpowers/tests/game/pathfinder.test.ts
new file mode 100644
index 0000000..1720a89
--- /dev/null
+++ b/superpowers/tests/game/pathfinder.test.ts
@@ -0,0 +1,113 @@
+import { describe, it, expect } from "vitest";
+import { findPath, hasAnyValidMove } from "../../src/game/pathfinder";
+import { Board } from "../../src/types";
+
+function makeBoard(grid: (string | null)[][]): Board {
+  let id = 0;
+  return grid.map((row) =>
+    row.map((cell) => (cell !== null ? { emoji: cell, id: id++ } : null))
+  );
+}
+
+describe("findPath", () => {
+  it("finds direct horizontal connection", () => {
+    const board = makeBoard([
+      ["A", null, "A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 0, col: 2 });
+    expect(path).not.toBeNull();
+    expect(path!.length).toBe(2);
+  });
+
+  it("finds direct vertical connection", () => {
+    const board = makeBoard([
+      ["A"],
+      [null],
+      ["A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 2, col: 0 });
+    expect(path).not.toBeNull();
+    expect(path!.length).toBe(2);
+  });
+
+  it("finds one-bend connection", () => {
+    const board = makeBoard([
+      ["A", null],
+      [null, "A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 1, col: 1 });
+    expect(path).not.toBeNull();
+    expect(path!.length).toBe(3);
+  });
+
+  it("finds two-bend connection", () => {
+    const board = makeBoard([
+      ["A", "B", null],
+      [null, null, null],
+      [null, "B", "A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 2, col: 2 });
+    expect(path).not.toBeNull();
+    expect(path!.length).toBe(4);
+  });
+
+  it("returns null when no valid path exists", () => {
+    const board = makeBoard([
+      ["A", "B", "C"],
+      ["D", "E", "F"],
+      ["C", "B", "A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 2, col: 2 });
+    expect(path).toBeNull();
+  });
+
+  it("returns null when tiles are not the same emoji", () => {
+    const board = makeBoard([
+      ["A", null, "B"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 0, col: 2 });
+    expect(path).toBeNull();
+  });
+
+  it("finds path through border (empty surround)", () => {
+    const board = makeBoard([
+      ["A", "B", "A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 0, col: 2 });
+    expect(path).not.toBeNull();
+  });
+
+  it("adjacent identical tiles connect", () => {
+    const board = makeBoard([
+      ["A", "A"],
+    ]);
+    const path = findPath(board, { row: 0, col: 0 }, { row: 0, col: 1 });
+    expect(path).not.toBeNull();
+    expect(path!.length).toBe(2);
+  });
+});
+
+describe("hasAnyValidMove", () => {
+  it("returns true when moves exist", () => {
+    const board = makeBoard([
+      ["A", "A"],
+    ]);
+    expect(hasAnyValidMove(board)).toBe(true);
+  });
+
+  it("returns false when no moves exist", () => {
+    const board = makeBoard([
+      ["A", "B"],
+      ["C", "D"],
+    ]);
+    expect(hasAnyValidMove(board)).toBe(false);
+  });
+
+  it("returns false for empty board", () => {
+    const board = makeBoard([
+      [null, null],
+      [null, null],
+    ]);
+    expect(hasAnyValidMove(board)).toBe(false);
+  });
+});