feat(hint): unify the vs_ai idle hint online + offline (server-enforced, monotonic)

Online vs_ai hints were broken: #207 made the vs_ai hint button always-enabled and
wallet-free (assuming all vs_ai = the offline idle-gate), but the backend still served
online vs_ai from the allowance/wallet, so over-clicking hit ErrNoHintsLeft -> a generic
error toast. Now online vs_ai uses the SAME idle-gate model as offline.

Backend: Hint() for a vs_ai game skips the allowance/wallet and increments no hints_used
(owner: vs_ai counts toward no hint statistic), and is idle-gated from the SERVER clock --
it returns ErrHintLocked (code hint_locked) until the robot's last move + 30 min, else
serves the top move. GameState/StateView expose hint_unlock_left_seconds (server-computed
seconds remaining; 0 for a human game / first move / not-your-turn). Pure helper
hintUnlockLeftSeconds unit-tested.

Wire: StateView gains hint_unlock_left_seconds (FlatBuffers, additive); pkg/wire + gateway
transcode carry it (round-trip test).

Client: the gate counts down from a MONOTONIC clock (performance.now()) anchored to the
source's seconds-left when it lands (on load from the view; to the full window when the
robot moves), so a client clock change cannot skew it and a relaunch re-reads a fresh
value. The vs_ai hint button (online + offline) shows the lock + toast; doHint handles the
hint_locked backstop by re-syncing. Replaces #207's absolute hintUnlockAtMs on the
wire/model/delta (the offline record keeps the absolute for persistence; the view exposes
seconds-left).

Docs FUNCTIONAL(+_ru)/ARCHITECTURE updated. Verified: go build/vet + game/server/transcode
tests (+ new hintUnlockLeftSeconds); ui check 0 / unit 490 / e2e 198 (one pre-existing
webkit offline flake) / app entry 114.2/115.

backend/internal/game/helpers_test.go

@@ -69,6 +69,29 @@ func TestHintsRemaining(t *testing.T) {
 	}
 }
 
+func TestHintUnlockLeftSeconds(t *testing.T) {
+	now := time.Now()
+	// A gated vs_ai game on the caller's turn, the robot having moved 10 min ago (turn started then).
+	gated := Game{VsAI: true, ToMove: 0, MoveCount: 2, TurnStartedAt: now.Add(-10 * time.Minute)}
+	cases := []struct {
+		name string
+		g    Game
+		seat int
+		want int
+	}{
+		{"non-vs_ai is open", Game{VsAI: false, ToMove: 0, MoveCount: 2, TurnStartedAt: now.Add(-10 * time.Minute)}, 0, 0},
+		{"not the caller's turn is open", gated, 1, 0},
+		{"human first move (no robot move) is open", Game{VsAI: true, ToMove: 0, MoveCount: 0, TurnStartedAt: now}, 0, 0},
+		{"robot moved 10 min ago leaves 20 min", gated, 0, 20 * 60},
+		{"robot moved past the window is open", Game{VsAI: true, ToMove: 0, MoveCount: 2, TurnStartedAt: now.Add(-40 * time.Minute)}, 0, 0},
+	}
+	for _, c := range cases {
+		if got := hintUnlockLeftSeconds(c.g, c.seat, now); got != c.want {
+			t.Errorf("%s: hintUnlockLeftSeconds = %d, want %d", c.name, got, c.want)
+		}
+	}
+}
+
 func TestAllowedTimeout(t *testing.T) {
 	if !allowedTimeout(24 * time.Hour) {
 		t.Error("24h must be allowed")

backend/internal/game/service.go

@@ -1058,10 +1058,31 @@ func (svc *Service) MarkChangesApplied(ctx context.Context, variant engine.Varia
 	return svc.store.MarkChangesApplied(ctx, variant.String(), version)
 }
 
-// Hint reveals the top-scoring legal play for the requesting player on their
-// turn, spending one hint from their per-game allowance and then their profile
-// wallet. It returns ErrHintsDisabled, ErrNoHintsLeft or ErrNoHintAvailable as
-// appropriate.
+// hintIdleWindow is how long a vs_ai player must be stuck on a turn (since the robot's last move)
+// before the idle hint unlocks. Mirrors the offline client (lib/hints HINT_GATE_MS = 30 min).
+const hintIdleWindow = 30 * time.Minute
+
+// hintUnlockLeftSeconds is the seconds until g's vs_ai idle hint unlocks for seat, measured from now:
+// the robot's last move (the current turn's start, on the human's turn) plus the window, floored at
+// 0 and ceiled to whole seconds. It is 0 for a non-vs_ai game, when it is not seat's turn, or on the
+// human's first move (MoveCount 0, no robot move yet) — the gate is an anti-frustration aid, not a
+// first-move tax. The client anchors a monotonic countdown to it, so a client clock cannot skew it.
+func hintUnlockLeftSeconds(g Game, seat int, now time.Time) int {
+	if !g.VsAI || g.ToMove != seat || g.MoveCount < 1 {
+		return 0
+	}
+	left := g.TurnStartedAt.Add(hintIdleWindow).Sub(now)
+	if left <= 0 {
+		return 0
+	}
+	return int((left + time.Second - 1) / time.Second) // ceil to whole seconds (no math import)
+}
+
+// Hint reveals the top-scoring legal play for the requesting player on their turn. For a human game
+// it spends one hint from the per-game allowance then the profile wallet (ErrHintsDisabled /
+// ErrNoHintsLeft / ErrNoHintAvailable). For a vs_ai game the hint is unlimited and wallet-free but
+// idle-gated from the server clock (ErrHintLocked until the window elapses) and counts toward no
+// hint statistic.
 func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (HintResult, error) {
 	pre, err := svc.store.GetGame(ctx, gameID)
 	if err != nil {
@@ -1080,6 +1101,26 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 	if !pre.HintsAllowed {
 		return HintResult{}, ErrHintsDisabled
 	}
+	if pre.VsAI {
+		// vs_ai: unlimited and wallet-free, but idle-gated from the server clock — and counted toward
+		// no hint statistic. Enforce the gate (the client normally pre-gates from the view's
+		// HintUnlockLeftSeconds; this is the authoritative backstop), then serve the top move without
+		// touching the allowance, the wallet or hints_used.
+		if hintUnlockLeftSeconds(pre, seat, svc.clock()) > 0 {
+			return HintResult{}, ErrHintLocked
+		}
+		unlock := svc.locks.lock(gameID)
+		defer unlock()
+		g, err := svc.liveGame(ctx, pre)
+		if err != nil {
+			return HintResult{}, err
+		}
+		move, ok := g.HintView()
+		if !ok {
+			return HintResult{}, ErrNoHintAvailable
+		}
+		return HintResult{Move: move}, nil
+	}
 	acc, err := svc.accounts.GetByID(ctx, accountID)
 	if err != nil {
 		return HintResult{}, err
@@ -1208,6 +1249,8 @@ func (svc *Service) GameState(ctx context.Context, gameID, accountID uuid.UUID)
 		BagLen:         g.BagLen(),
 		HintsRemaining: hintsRemaining(pre.HintsPerPlayer, pre.Seats[seat].HintsUsed, acc.HintBalance),
 		WalletBalance:  acc.HintBalance,
+		// vs_ai idle-hint gate (seconds left; 0 for a human game / first move / not your turn).
+		HintUnlockLeftSeconds: hintUnlockLeftSeconds(pre, seat, svc.clock()),
 	}, nil
 }
 

backend/internal/game/types.go

@@ -65,6 +65,10 @@ var (
 	ErrNoHintsLeft = errors.New("game: no hints remaining")
 	// ErrNoHintAvailable is returned when the player has no legal play to reveal.
 	ErrNoHintAvailable = errors.New("game: no legal move to suggest")
+	// ErrHintLocked is returned when a vs_ai game's idle hint is still gated (the player has not yet
+	// been stuck the idle window since the robot's last move). The client normally pre-gates from
+	// StateView.HintUnlockLeftSeconds, so this is the authoritative server-clock backstop.
+	ErrHintLocked = errors.New("game: hint is not available yet")
 	// ErrGameLimitReached is returned when an account already holds MaxActiveQuickGames
 	// simultaneous quick games and tries to create another game (quick or by invitation).
 	ErrGameLimitReached = errors.New("game: simultaneous game limit reached")
@@ -240,6 +244,11 @@ type StateView struct {
 	// WalletBalance is the player's global hint-wallet balance alone (HintsRemaining folds
 	// it in with the per-game allowance), so the client keeps the wallet live across games.
 	WalletBalance int
+	// HintUnlockLeftSeconds is, for a vs_ai game on the requesting player's turn, the seconds left
+	// until the idle hint unlocks (the robot's last move plus the idle window, from the server clock);
+	// 0 for the human's first move, when it is not their turn, or a non-vs_ai game. The vs_ai hint is
+	// unlimited and wallet-free; this idle gate replaces the allowance/wallet for it.
+	HintUnlockLeftSeconds int
 }
 
 // HistoryMove is one decoded journal row, independent of any dictionary.

backend/internal/server/dto.go

@@ -163,13 +163,16 @@ type alphabetEntryDTO struct {
 // stateDTO is a player's view of a game. Rack carries wire alphabet indices (a
 // blank is engine.BlankIndex). Alphabet is present only when the request asked for it.
 type stateDTO struct {
-	Game           gameDTO            `json:"game"`
-	Seat           int                `json:"seat"`
-	Rack           []int              `json:"rack"`
-	BagLen         int                `json:"bag_len"`
-	HintsRemaining int                `json:"hints_remaining"`
-	WalletBalance  int                `json:"wallet_balance"`
-	Alphabet       []alphabetEntryDTO `json:"alphabet,omitempty"`
+	Game           gameDTO `json:"game"`
+	Seat           int     `json:"seat"`
+	Rack           []int   `json:"rack"`
+	BagLen         int     `json:"bag_len"`
+	HintsRemaining int     `json:"hints_remaining"`
+	WalletBalance  int     `json:"wallet_balance"`
+	// HintUnlockLeftSeconds is the vs_ai idle-hint gate: seconds until the hint unlocks (0 for a human
+	// game / first move / not your turn). The client anchors a monotonic countdown to it.
+	HintUnlockLeftSeconds int                `json:"hint_unlock_left_seconds"`
+	Alphabet              []alphabetEntryDTO `json:"alphabet,omitempty"`
 }
 
 // matchDTO reports whether the caller has been paired into a game.
@@ -315,12 +318,13 @@ func stateDTOFrom(v game.StateView, includeAlphabet bool) (stateDTO, error) {
 		return stateDTO{}, err
 	}
 	dto := stateDTO{
-		Game:           gameDTOFromGame(v.Game),
-		Seat:           v.Seat,
-		Rack:           rack,
-		BagLen:         v.BagLen,
-		HintsRemaining: v.HintsRemaining,
-		WalletBalance:  v.WalletBalance,
+		Game:                  gameDTOFromGame(v.Game),
+		Seat:                  v.Seat,
+		Rack:                  rack,
+		BagLen:                v.BagLen,
+		HintsRemaining:        v.HintsRemaining,
+		WalletBalance:         v.WalletBalance,
+		HintUnlockLeftSeconds: v.HintUnlockLeftSeconds,
 	}
 	if includeAlphabet {
 		tab, err := engine.AlphabetTable(v.Game.Variant)

backend/internal/server/handlers.go

@@ -239,6 +239,9 @@ func statusForError(err error) (int, string) {
 		return http.StatusConflict, "no_hint_available"
 	case errors.Is(err, game.ErrHintsDisabled), errors.Is(err, game.ErrNoHintsLeft):
 		return http.StatusConflict, "hint_unavailable"
+	case errors.Is(err, game.ErrHintLocked):
+		// A vs_ai idle hint is still gated (the server-clock backstop); the client shows the lock.
+		return http.StatusConflict, "hint_locked"
 	case errors.Is(err, engine.ErrIllegalPlay), errors.Is(err, engine.ErrTilesNotOnRack), errors.Is(err, engine.ErrGameOver):
 		return http.StatusUnprocessableEntity, "illegal_play"
 	case errors.Is(err, account.ErrEmailTaken), errors.Is(err, account.ErrIdentityTaken):