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).

backend/internal/robot/strategyfixture_test.go

@@ -0,0 +1,146 @@
+package robot
+
+import (
+	"encoding/json"
+	"os"
+	"path/filepath"
+	"strconv"
+	"testing"
+
+	"scrabble/backend/internal/engine"
+)
+
+// The client-side offline robot (ui/src/lib/robot) reproduces the robot's move choice
+// so a local vs_ai game plays the same way as the server. These golden fixtures pin that
+// TS port to the real Go strategy. Being in-package, this emitter can exercise the
+// unexported mix / playToWin / deviates / selectMove that the port mirrors.
+
+type mixCase struct {
+	Seed  string `json:"seed"`
+	Salt  string `json:"salt"`
+	Nums  []int  `json:"nums"`
+	Value string `json:"value"` // the mix() uint64, as a decimal string (exceeds JS safe ints)
+}
+
+type decisionCase struct {
+	Seed       string `json:"seed"`
+	MoveCount  int    `json:"moveCount"`
+	MyScore    int    `json:"myScore"`
+	OppScore   int    `json:"oppScore"`
+	CandScores []int  `json:"candScores"`
+	RackLen    int    `json:"rackLen"`
+	BagLen     int    `json:"bagLen"`
+	PlayToWin  bool   `json:"playToWin"`
+	Win        bool   `json:"win"` // the per-turn intent after the deviate flip
+	Kind       string `json:"kind"`
+	Index      int    `json:"index"` // chosen candidate index for a play, else -1
+}
+
+type strategyFixture struct {
+	PlayToWinPercent int            `json:"playToWinPercent"`
+	Mix              []mixCase      `json:"mix"`
+	Decisions        []decisionCase `json:"decisions"`
+}
+
+// scenario is one selectMove situation exercised across several seeds.
+type scenario struct {
+	moveCount, myScore, oppScore, rackLen, bagLen int
+	cands                                         []int
+}
+
+// TestEmitStrategyFixtures regenerates ui/src/lib/robot/testdata/strategy.json. It is
+// gated by EMIT_STRATEGY_FIXTURES so a normal `go test` skips it; the committed output is
+// what the TS parity test consumes. Regenerate with:
+//
+//	EMIT_STRATEGY_FIXTURES=1 go test ./backend/internal/robot -run TestEmitStrategyFixtures
+func TestEmitStrategyFixtures(t *testing.T) {
+	if os.Getenv("EMIT_STRATEGY_FIXTURES") == "" {
+		t.Skip("set EMIT_STRATEGY_FIXTURES=1 to regenerate ui/src/lib/robot/testdata/strategy.json")
+	}
+
+	seeds := []int64{1, 42, -7, 1000003, 9999999999, 123456789, -123456789}
+
+	mixCases := []mixCase{}
+	addMix := func(seed int64, salt string, nums ...int) {
+		mixCases = append(mixCases, mixCase{
+			Seed:  strconv.FormatInt(seed, 10),
+			Salt:  salt,
+			Nums:  append([]int{}, nums...),
+			Value: strconv.FormatUint(mix(seed, salt, nums...), 10),
+		})
+	}
+	for _, sd := range seeds {
+		addMix(sd, "win")
+		addMix(sd, "deviate", 0)
+		addMix(sd, "deviate", 7)
+	}
+
+	scenarios := []scenario{
+		{3, 40, 55, 7, 20, []int{30, 12, 8}},   // behind, mid-game
+		{10, 120, 90, 7, 8, []int{25, 18, 5}},  // ahead, late
+		{1, 0, 0, 7, 30, []int{60, 30, 15, 7}}, // first move, big spread
+		{20, 200, 40, 5, 2, []int{50, 20}},     // big lead, bag near empty (no deviate)
+		{5, 30, 30, 7, 14, []int{20, 20, 20}},  // equal margins (tie-break)
+		{8, 50, 60, 7, 20, []int{}},            // no play, bag can refill -> exchange
+		{8, 50, 60, 3, 2, []int{}},             // no play, bag can't refill -> pass
+		{15, 300, 10, 7, 6, []int{80, 40, 10}}, // overshoots the band -> nearest to +30
+	}
+
+	decisions := []decisionCase{}
+	for _, sd := range seeds {
+		for _, sc := range scenarios {
+			cands := make([]engine.MoveRecord, len(sc.cands))
+			for i, s := range sc.cands {
+				cands[i] = engine.MoveRecord{Score: s, Player: i}
+			}
+			rack := make([]string, sc.rackLen)
+			for i := range rack {
+				rack[i] = "a"
+			}
+
+			ptw := playToWin(sd)
+			win := ptw
+			if deviates(sd, sc.moveCount, sc.bagLen) {
+				win = !win
+			}
+			d := selectMove(cands, sc.myScore, sc.oppScore, win, defaultBand, rack, sc.bagLen)
+
+			kind, index := "pass", -1
+			switch d.kind {
+			case decidePlay:
+				kind, index = "play", d.move.Player
+			case decideExchange:
+				kind = "exchange"
+			}
+
+			decisions = append(decisions, decisionCase{
+				Seed:       strconv.FormatInt(sd, 10),
+				MoveCount:  sc.moveCount,
+				MyScore:    sc.myScore,
+				OppScore:   sc.oppScore,
+				CandScores: append([]int{}, sc.cands...),
+				RackLen:    sc.rackLen,
+				BagLen:     sc.bagLen,
+				PlayToWin:  ptw,
+				Win:        win,
+				Kind:       kind,
+				Index:      index,
+			})
+		}
+	}
+
+	fx := strategyFixture{PlayToWinPercent: playToWinPercent, Mix: mixCases, Decisions: decisions}
+	dir := filepath.Join("..", "..", "..", "ui", "src", "lib", "robot", "testdata")
+	if err := os.MkdirAll(dir, 0o755); err != nil {
+		t.Fatalf("mkdir %s: %v", dir, err)
+	}
+	data, err := json.MarshalIndent(fx, "", "  ")
+	if err != nil {
+		t.Fatalf("marshal: %v", err)
+	}
+	path := filepath.Join(dir, "strategy.json")
+	if err := os.WriteFile(path, append(data, '\n'), 0o644); err != nil {
+		t.Fatalf("write %s: %v", path, err)
+	}
+	t.Logf("wrote %s (%d mix, %d decisions)", path, len(mixCases), len(decisions))
+}