feat(offline): port robot move-choice strategy to TS (parity-pinned)

Phase A (2/2) of PWA offline mode: the offline robot picks its move exactly as the
server does, so a local vs_ai game plays the same. Builds on the move generator
from #188; not wired into a game loop yet (Phase B).

- ui/src/lib/robot/strategy.ts: port of backend/internal/robot/strategy.go's
  move-choice slice — mix (FNV-1a, via BigInt for bit-exact uint64), playToWin
  (~40% play-to-win), deviates (the fading off-strategy wobble) and selectMove
  (pick the candidate whose resulting margin lands closest to the +/-[1,30] band,
  conservative tie-break), composed by decide(). The generator's ranked moves feed
  straight in. Think-time/sleep/nudge scheduling is server-only and not ported.
- backend/internal/robot/strategyfixture_test.go: an in-package, env-gated emitter
  (EMIT_STRATEGY_FIXTURES=1) writing golden fixtures from the real Go strategy — it
  reaches the unexported mix/playToWin/deviates/selectMove.
- strategy.parity.test.ts: 21 mix + 56 decision cases match Go exactly (play/
  exchange/pass, the deviate flip, tie-break, band overshoot).

Pure additive library code; no runtime behavior change (unused at runtime, so the
bundle is unchanged).

ui/src/lib/robot/strategy.parity.test.ts

@@ -0,0 +1,68 @@
+import { describe, it, expect } from 'vitest';
+import { readFileSync } from 'node:fs';
+import { mix, playToWin, deviates, decide, DEFAULT_BAND } from './strategy';
+
+// Conformance gate for the ported robot strategy: the client must fold the game seed and
+// choose its action exactly as backend/internal/robot/strategy.go does, so a local vs_ai
+// game plays the same. Golden fixtures come from the in-package emitter
+// (backend/internal/robot/strategyfixture_test.go).
+
+interface MixCase {
+  seed: string;
+  salt: string;
+  nums: number[];
+  value: string;
+}
+interface DecisionCase {
+  seed: string;
+  moveCount: number;
+  myScore: number;
+  oppScore: number;
+  candScores: number[];
+  rackLen: number;
+  bagLen: number;
+  playToWin: boolean;
+  win: boolean;
+  kind: string;
+  index: number;
+}
+interface Fixture {
+  playToWinPercent: number;
+  mix: MixCase[];
+  decisions: DecisionCase[];
+}
+
+const fx = JSON.parse(
+  readFileSync(new URL('./testdata/strategy.json', import.meta.url), 'utf8'),
+) as Fixture;
+
+describe('robot strategy parity vs Go', () => {
+  it('mix folds the seed like Go FNV-1a', () => {
+    for (const c of fx.mix) {
+      expect(mix(BigInt(c.seed), c.salt, ...c.nums), `${c.seed}/${c.salt}/${c.nums}`).toBe(BigInt(c.value));
+    }
+  });
+
+  it('chooses the same action as the Go robot', () => {
+    for (const c of fx.decisions) {
+      const seed = BigInt(c.seed);
+      const cands = c.candScores.map((score, index) => ({ score, index }));
+      const rack = new Array<string>(c.rackLen).fill('a');
+
+      expect(playToWin(seed), `playToWin ${c.seed}`).toBe(c.playToWin);
+
+      // the per-turn intent after the occasional off-strategy deviation
+      let win = playToWin(seed);
+      if (deviates(seed, c.moveCount, c.bagLen)) win = !win;
+      expect(win, `win ${c.seed}/${c.moveCount}/${c.bagLen}`).toBe(c.win);
+
+      const dec = decide(seed, c.moveCount, cands, c.myScore, c.oppScore, rack, c.bagLen, DEFAULT_BAND);
+      expect(dec.kind, `kind ${JSON.stringify(c)}`).toBe(c.kind);
+      if (dec.kind === 'play') {
+        expect(dec.move.index, `index ${JSON.stringify(c)}`).toBe(c.index);
+      } else if (dec.kind === 'exchange') {
+        expect(dec.exchange.length).toBe(c.rackLen);
+      }
+    }
+  });
+});

ui/src/lib/robot/strategy.ts

@@ -0,0 +1,180 @@
+// The offline robot's move choice, ported from backend/internal/robot/strategy.go so a
+// local vs_ai game plays exactly as the server robot does: it picks the candidate whose
+// resulting score margin lands closest to a target band (playing to win ~40% of games and
+// to lose the rest), with an occasional off-strategy "wobble" that fades as the bag empties.
+//
+// Everything derives deterministically from the game's bag seed, folded by FNV-1a (mix),
+// so the choice is reproducible. The 64-bit hash is computed with BigInt to stay bit-exact
+// with Go's uint64 arithmetic; faithfulness is pinned by strategy.parity.test.ts against
+// golden fixtures. Only the move-choice slice of strategy.go is ported — the server's
+// think-time, sleep-window and nudge scheduling are irrelevant to on-device play.
+
+// playToWinPercent is the probability, in percent, that the robot plays to win for a whole
+// game; the rest of the time it plays to lose, so the human wins about 60% of games.
+const playToWinPercent = 40;
+
+// deviateMaxProb is the peak probability of a single off-strategy move, held through the
+// opening and midgame; it tapers linearly to 0 over the last deviateTaperTiles bag tiles.
+const deviateMaxProb = 0.2;
+const deviateTaperTiles = 14;
+
+const FNV_OFFSET = 14695981039346656037n;
+const FNV_PRIME = 1099511628211n;
+const TWO_POW_64 = 1n << 64n;
+const MASK64 = TWO_POW_64 - 1n;
+
+// u64le returns the 8 little-endian bytes of v reduced mod 2^64, matching Go's
+// binary.LittleEndian.PutUint64(uint64(int64(v))) — negatives wrap two's-complement.
+function u64le(v: bigint): number[] {
+  let x = ((v % TWO_POW_64) + TWO_POW_64) % TWO_POW_64;
+  const out: number[] = [];
+  for (let i = 0; i < 8; i++) {
+    out.push(Number(x & 0xffn));
+    x >>= 8n;
+  }
+  return out;
+}
+
+/**
+ * mix folds the game seed and a salt (a label plus optional integers such as the move
+ * index) into a stable 64-bit value, mirroring robot.mix (FNV-1a over the seed's 8 bytes,
+ * the salt bytes, then each number's 8 bytes). seed is the game's bag seed.
+ */
+export function mix(seed: bigint, salt: string, ...nums: number[]): bigint {
+  let h = FNV_OFFSET;
+  const feed = (b: number): void => {
+    h = ((h ^ BigInt(b & 0xff)) * FNV_PRIME) & MASK64;
+  };
+  for (const b of u64le(seed)) feed(b);
+  for (let i = 0; i < salt.length; i++) feed(salt.charCodeAt(i));
+  for (const n of nums) for (const b of u64le(BigInt(n))) feed(b);
+  return h;
+}
+
+/** unitFloat maps a mixed value to a float in [0, 1), mirroring robot.unitFloat. */
+export function unitFloat(v: bigint): number {
+  return Number(v) / Number(TWO_POW_64);
+}
+
+/**
+ * playToWin reports the robot's once-per-game decision to play to win, derived from the
+ * seed so it is fixed for the whole game. Mirrors robot.playToWin.
+ */
+export function playToWin(seed: bigint): boolean {
+  return mix(seed, 'win') % 100n < BigInt(playToWinPercent);
+}
+
+// deviateProb is the probability of a single off-strategy move given the tiles left in the
+// bag: deviateMaxProb through the midgame, tapering to 0 over the last deviateTaperTiles.
+function deviateProb(bagLen: number): number {
+  if (bagLen <= 0) return 0;
+  if (bagLen >= deviateTaperTiles) return deviateMaxProb;
+  return (deviateMaxProb * bagLen) / deviateTaperTiles;
+}
+
+/**
+ * deviates reports whether the robot plays a single move against its per-game intent at
+ * moveCount, given the tiles left in the bag — a deterministic per-turn draw, never firing
+ * once the bag is empty. Mirrors robot.deviates.
+ */
+export function deviates(seed: bigint, moveCount: number, bagLen: number): boolean {
+  const p = deviateProb(bagLen);
+  if (p <= 0) return false;
+  return unitFloat(mix(seed, 'deviate', moveCount)) < p;
+}
+
+/** MarginBand is an inclusive target range for the resulting score margin (own score after
+ *  the move minus the opponent's). */
+export interface MarginBand {
+  lo: number;
+  hi: number;
+}
+
+/** DEFAULT_BAND aims to lead by 1..30 when playing to win (negated when playing to lose),
+ *  matching robot.defaultBand. */
+export const DEFAULT_BAND: MarginBand = { lo: 1, hi: 30 };
+
+/**
+ * Decision is the robot's chosen action: a play (the picked candidate), an exchange of the
+ * listed tiles, or a pass. Generic over the candidate type (needs only a score) and the
+ * rack tile type.
+ */
+export type Decision<C, R> =
+  | { kind: 'play'; move: C }
+  | { kind: 'exchange'; exchange: R[] }
+  | { kind: 'pass' };
+
+// distanceToBand is how far m lies outside [lo, hi], or 0 when inside.
+function distanceToBand(m: number, lo: number, hi: number): number {
+  if (m < lo) return lo - m;
+  if (m > hi) return m - hi;
+  return 0;
+}
+
+/**
+ * selectMove chooses the robot's action from the ranked candidate plays and the current
+ * scores. With at least one legal play it picks the candidate whose resulting margin
+ * (myScore + score - oppScore) is closest to the band (negated when not playing to win),
+ * breaking ties toward the conservative edge (smallest lead when winning, smallest deficit
+ * when losing). With no legal play it exchanges the whole rack when the bag can refill it,
+ * else passes. Mirrors robot.selectMove.
+ */
+export function selectMove<C extends { score: number }, R>(
+  cands: readonly C[],
+  myScore: number,
+  oppScore: number,
+  win: boolean,
+  band: MarginBand,
+  rack: readonly R[],
+  bagLen: number,
+): Decision<C, R> {
+  if (cands.length === 0) {
+    if (rack.length > 0 && bagLen >= rack.length) {
+      return { kind: 'exchange', exchange: [...rack] };
+    }
+    return { kind: 'pass' };
+  }
+
+  let lo = band.lo;
+  let hi = band.hi;
+  if (!win) {
+    lo = -band.hi;
+    hi = -band.lo;
+  }
+
+  const margin = (c: C): number => myScore + c.score - oppScore;
+  let best = 0;
+  let bestDist = Infinity;
+  for (let i = 0; i < cands.length; i++) {
+    const m = margin(cands[i]);
+    const dist = distanceToBand(m, lo, hi);
+    if (dist < bestDist) {
+      best = i;
+      bestDist = dist;
+    } else if (dist === bestDist) {
+      // Conservative tie-break: keep the lead (win) or the deficit (lose) small.
+      if ((win && m < margin(cands[best])) || (!win && m > margin(cands[best]))) best = i;
+    }
+  }
+  return { kind: 'play', move: cands[best] };
+}
+
+/**
+ * decide is the robot's whole per-turn choice: the once-per-game play-to-win intent, flipped
+ * for this move by the occasional deviation, fed to selectMove. Mirrors the decision slice of
+ * robot (*Service).act. seed is the game's bag seed; cands are the ranked legal plays.
+ */
+export function decide<C extends { score: number }, R>(
+  seed: bigint,
+  moveCount: number,
+  cands: readonly C[],
+  myScore: number,
+  oppScore: number,
+  rack: readonly R[],
+  bagLen: number,
+  band: MarginBand = DEFAULT_BAND,
+): Decision<C, R> {
+  let win = playToWin(seed);
+  if (deviates(seed, moveCount, bagLen)) win = !win;
+  return selectMove(cands, myScore, oppScore, win, band, rack, bagLen);
+}