Selfo: no colour starts one move away from winning

src/games/selfo.ts

@@ -122,6 +122,12 @@ const after = (board: Board, from: string, to: string): Board => {
     return next;
 };
 
+/** Whether `player` could connect all their pieces with a single move (if it were their turn). */
+const canWinInOne = (graph: HexTriGraph, board: Board, player: playerid): boolean =>
+    piecesOf(board, player).some(from =>
+        graph.neighbours(from).some(to => !board.has(to) && isConnected(graph, after(board, from, to), player))
+    );
+
 /** Whether the move would enclose an opposing piece without winning the game outright. */
 const wouldEnclose = (graph: HexTriGraph, board: Board, from: string, to: string): boolean => {
     const player = board.get(from)!;
@@ -291,7 +297,7 @@ export class SelfoGame extends GameBase {
     /**
      * Random starting position: both colours scattered with no group larger
      * than the board radius (and never one big enough to be connected), no
-     * piece already enclosed, and no immediate win for the first player (and,
+     * piece already enclosed, and no colour one move away from winning (and,
      * with `no-enclosure`, at least one legal move for both).
      */
     private randomStart(): Board {
@@ -307,11 +313,9 @@ export class SelfoGame extends GameBase {
             for (const c of first) { board.set(c, 1); }
             for (const c of second) { board.set(c, 2); }
             if (hasEnclosedPiece(this.graph, board, 1) || hasEnclosedPiece(this.graph, board, 2)) { continue; }
-            // the first player must not be able to win on their first move
-            const wins = piecesOf(board, 1).some(from =>
-                this.graph.neighbours(from).some(to => !board.has(to) && isConnected(this.graph, after(board, from, to), 1))
-            );
-            if (wins) { continue; }
+            // neither colour may be one move away from winning (the second player
+            // could otherwise win at once, or take that colour with the pie rule)
+            if (canWinInOne(this.graph, board, 1) || canWinInOne(this.graph, board, 2)) { continue; }
             fallback = board;
             if (!this.noEnclosure) { return board; }
             if (legalMoves(this.graph, board, 1, true).length > 0 && legalMoves(this.graph, board, 2, true).length > 0) {

test/games/selfo.test.ts

@@ -29,6 +29,14 @@ const connected = (cells: string[], g: HexTriGraph = graph): boolean => {
     return seen.size === set.size;
 };
 
+// Whether `player` could connect all their pieces with a single move, if it were their turn.
+const canWinInOne = (board: Map<string, playerid>, player: playerid, g: HexTriGraph): boolean => {
+    const own = [...board.entries()].filter(([, p]) => p === player).map(([c]) => c);
+    return own.some(from => g.neighbours(from).some(to =>
+        !board.has(to) && connected(own.map(c => c === from ? to : c), g)
+    ));
+};
+
 const corners = (graph.listCells() as string[]).filter(c => graph.neighbours(c).length === 3);
 
 describe("Selfo", () => {
@@ -59,6 +67,31 @@ describe("Selfo", () => {
             });
         }
 
+        it("never starts with a colour one move away from winning", () => {
+            // the small board is where this used to happen (about 2% of the starts)
+            for (const [variants, radius] of [[["r2f5"], 2], [["r2f5", "no-enclosure"], 2], [[], 3]] as [string[], number][]) {
+                const g = new HexTriGraph(radius + 1, radius * 2 + 1);
+                for (let i = 0; i < 200; i++) {
+                    const game = new SelfoGame(undefined, variants);
+                    expect(canWinInOne(game.board, 1, g), `black, ${variants.join(",")}`).to.be.false;
+                    expect(canWinInOne(game.board, 2, g), `white, ${variants.join(",")}`).to.be.false;
+                }
+            }
+        });
+
+        it("detects a colour that is one move away from winning", () => {
+            // c3 + n0 + t: t can step next to c3 and complete the group (see "moves and winning")
+            const nbrs = graph.neighbours("c3").sort();
+            const n0 = nbrs[0];
+            const n1 = nbrs.find(n => n !== n0 && !graph.neighbours(n0).includes(n))!;
+            const t = graph.neighbours(n1).sort().find(c => c !== "c3" && !nbrs.includes(c))!;
+            const board = new Map<string, playerid>([["c3", 1], [n0, 1], [t, 1]]);
+            expect(canWinInOne(board, 1, graph)).to.be.true;
+            // two pieces at distance 3 or more cannot be joined by a single step
+            const far = corners.find(c => c !== corners[0] && graph.path(corners[0], c)!.length > 3)!;
+            expect(canWinInOne(new Map<string, playerid>([[corners[0], 1], [far, 1]]), 1, graph)).to.be.false;
+        });
+
         it("records the starting position", () => {
             const game = new SelfoGame(undefined, ["r2f5"]);
             const [first, second] = game.getStartingPosition().split("|");