feat(offline): randomise the hotseat seating (random first mover)

The 2-4 hotseat players now start in a random seating order (so who goes
first, and the turn order, is random) — matching the online games. The
engine starts at seat 0, so shuffling the seats at creation picks the
starter; the shuffle is seed-driven (a distinct derivation from the tile
bag), so replay reproduces it. Scoped to hotseat — vs_ai stays human-first.
- lib/roster.ts: shuffleSeeded (unit-tested); NewGame shuffles buildSeats
  with the game seed before create.
- e2e: pin a seed that keeps the roster order so the lock assertions stay
  deterministic.

ui/src/lib/roster.test.ts

@@ -1,5 +1,5 @@
 import { describe, expect, it } from 'vitest';
-import { buildSeats, commitName, rosterReady, type RosterRow } from './roster';
+import { buildSeats, commitName, rosterReady, shuffleSeeded, type RosterRow } from './roster';
 
 describe('commitName (keep-last-valid)', () => {
   it('commits a valid, trimmed name', () => {
@@ -48,3 +48,21 @@ describe('buildSeats', () => {
     expect(seats.every((s) => !('accountId' in s) || s.accountId === undefined)).toBe(true);
   });
 });
+
+describe('shuffleSeeded', () => {
+  it('is deterministic for the same seed', () => {
+    expect(shuffleSeeded([0, 1, 2, 3], 42n)).toEqual(shuffleSeeded([0, 1, 2, 3], 42n));
+  });
+
+  it('keeps every element (a permutation) and does not mutate the input', () => {
+    const input = [0, 1, 2, 3];
+    const out = shuffleSeeded(input, 7n);
+    expect([...out].sort((a, b) => a - b)).toEqual([0, 1, 2, 3]);
+    expect(input).toEqual([0, 1, 2, 3]); // input untouched
+  });
+
+  it('varies the order across seeds (not always the identity)', () => {
+    const orders = new Set([1n, 2n, 3n, 4n, 5n, 6n, 7n, 8n].map((s) => shuffleSeeded([0, 1, 2, 3], s).join('')));
+    expect(orders.size).toBeGreaterThan(1);
+  });
+});

ui/src/lib/roster.ts

@@ -30,3 +30,25 @@ export function rosterReady(rows: RosterRow[]): boolean {
 export function buildSeats(rows: RosterRow[]): Seat[] {
   return rows.map((r): Seat => ({ kind: 'human', name: r.committed, pin: r.pin }));
 }
+
+/**
+ * shuffleSeeded returns a deterministic shuffle of items driven by seed — a Fisher-Yates over a small
+ * in-house PRNG (a distinct seed derivation from the tile bag, so the seating is not correlated with
+ * the tile draws). Used to randomise the hotseat seating at game start, so the first mover is random;
+ * being seed-driven keeps it reproducible for replay and tests.
+ */
+export function shuffleSeeded<T>(items: readonly T[], seed: bigint): T[] {
+  const out = [...items];
+  let a = (Number(BigInt.asUintN(32, seed ^ 0x9e3779b9n)) >>> 0) || 1;
+  const rand = (): number => {
+    a = (a + 0x6d2b79f5) | 0;
+    let t = Math.imul(a ^ (a >>> 15), 1 | a);
+    t = (t + Math.imul(t ^ (t >>> 7), 61 | t)) ^ t;
+    return ((t ^ (t >>> 14)) >>> 0) / 4294967296;
+  };
+  for (let i = out.length - 1; i > 0; i--) {
+    const j = Math.floor(rand() * (i + 1));
+    [out[i], out[j]] = [out[j], out[i]];
+  }
+  return out;
+}