feat(stats): best-move word, moves & hint-share, and a hint-count fix (#81)

The statistics screen gains real depth, plus a hint-count bug fix found along the way.

- Best move per variant: the screen shows the actual best-move word (drawn as game
  tiles; a wildcard shows its letter but no value), broken down by game variant, empty
  variants omitted. New account_best_move table, written at game finish.
- Moves & hint share: two new lifetime tiles — the player's play count and the share of
  plays that used a hint — from summed account_stats counters (moves, hints_used).
  Honest-AI games are excluded, like the rest of the stats.
- Hint-count fix: the in-game hint badge no longer goes stale across games. The global
  wallet now rides the wire apart from the per-game allowance (wallet_balance on
  StateView/HintResult/StatsView), so the client reads the live wallet rather than a
  per-game snapshot; game_players.hints_used now counts every hint (allowance + wallet),
  its true per-game total.
- Account merge: sums the new moves/hints_used counters and merges the per-variant best
  moves (higher score kept), which it previously dropped.
- Admin: the user card shows Moves and Hints used.
- UI polish: tab/label wording, game-over text, and e2e selectors hardened against label
  changes.

All wire additions are trailing (backward-compatible). Docs (ARCHITECTURE, FUNCTIONAL +ru,
UISN_DESIGN) updated in step.

backend/internal/game/service.go

@@ -1027,12 +1027,7 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 	}
 
 	walletAfter := acc.HintBalance
-	if fromAllowance {
-		if err := svc.store.SpendHintAllowance(ctx, gameID, seat); err != nil {
-			return HintResult{}, err
-		}
-		used++
-	} else {
+	if !fromAllowance {
 		spent, err := svc.accounts.SpendHint(ctx, accountID)
 		if err != nil {
 			return HintResult{}, err
@@ -1042,7 +1037,14 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 		}
 		walletAfter--
 	}
-	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used, walletAfter)}, nil
+	// hints_used is the per-game total (allowance + wallet): every hint increments it. The first
+	// HintsPerPlayer hints are the free allowance (so fromAllowance above stays correct); the rest
+	// are charged to the wallet. Counting all hints feeds the player's lifetime hint statistics.
+	if err := svc.store.IncHintsUsed(ctx, gameID, seat); err != nil {
+		return HintResult{}, err
+	}
+	used++
+	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used, walletAfter), WalletBalance: walletAfter}, nil
 }
 
 // Candidates returns the to-move player's legal plays for a seated player on
@@ -1130,6 +1132,7 @@ func (svc *Service) GameState(ctx context.Context, gameID, accountID uuid.UUID)
 		Rack:           g.Hand(seat),
 		BagLen:         g.BagLen(),
 		HintsRemaining: hintsRemaining(pre.HintsPerPlayer, pre.Seats[seat].HintsUsed, acc.HintBalance),
+		WalletBalance:  acc.HintBalance,
 	}, nil
 }
 
@@ -1419,19 +1422,45 @@ func replayMove(g *engine.Game, mv HistoryMove) error {
 }
 
 // buildStats derives each seat's statistics contribution from a finished game:
-// win/loss/draw from the (resignation-aware) winner, the final score, and the
-// best single-move score from the log.
+// win/loss/draw from the (resignation-aware) winner, the final score, and the best
+// single play from the log — its score and, for the per-variant breakdown, its main
+// word as rendering tiles. Blank flags are taken from every blank ever placed (so a
+// blank laid by an earlier move and embedded in the best word is honoured), which is
+// equivalent to reading the final board since a placed tile never moves.
 func buildStats(g *engine.Game, seats []Seat) []statDelta {
 	res := g.Result()
-	best := make(map[int]int)
+	bestRec := make(map[int]engine.MoveRecord)
+	blanks := make(map[[2]int]bool)
+	plays := make(map[int]int) // per player: count of plays (tile placements), for the "moves" stat
 	for _, rec := range g.Log() {
-		if rec.Action == engine.ActionPlay && rec.Score > best[rec.Player] {
-			best[rec.Player] = rec.Score
+		if rec.Action != engine.ActionPlay {
+			continue
+		}
+		plays[rec.Player]++
+		for _, t := range rec.Tiles {
+			if t.Blank {
+				blanks[[2]int{t.Row, t.Col}] = true
+			}
+		}
+		if cur, ok := bestRec[rec.Player]; !ok || rec.Score > cur.Score {
+			bestRec[rec.Player] = rec
 		}
 	}
+	variant := g.Variant().String()
+	values := letterValues(g.Variant())
 	out := make([]statDelta, 0, len(seats))
 	for _, s := range seats {
-		d := statDelta{accountID: s.AccountID, gamePoints: g.Score(s.Seat), wordPoints: best[s.Seat]}
+		// moves counts the seat's plays; hintsUsed is the seat's total hints this game. Both are
+		// summed into account_stats so the screen can show the hint share (hints_used / moves).
+		d := statDelta{accountID: s.AccountID, gamePoints: g.Score(s.Seat), moves: plays[s.Seat], hintsUsed: s.HintsUsed}
+		if rec, ok := bestRec[s.Seat]; ok {
+			d.wordPoints = rec.Score
+			if rec.Score > 0 {
+				d.bestVariant = variant
+				d.bestScore = rec.Score
+				d.bestTiles = mainWordTiles(rec, blanks, values)
+			}
+		}
 		switch {
 		case res.Winner < 0:
 			d.draws = 1
@@ -1445,6 +1474,49 @@ func buildStats(g *engine.Game, seats []Seat) []statDelta {
 	return out
 }
 
+// letterValues builds a lower-cased letter -> tile value lookup for a variant from the
+// engine's alphabet table, so a best-move word can be rendered with per-tile values on a
+// screen (statistics) that has not cached the variant's alphabet. It is empty for an
+// unrecognised variant, leaving every value zero.
+func letterValues(v engine.Variant) map[string]int {
+	table, err := engine.AlphabetTable(v)
+	if err != nil {
+		return nil
+	}
+	m := make(map[string]int, len(table))
+	for _, e := range table {
+		m[strings.ToLower(e.Letter)] = e.Value
+	}
+	return m
+}
+
+// mainWordTiles decodes a play's main word into rendering tiles: each letter with its
+// tile value (0 for a blank) and blank flag. blanks is the set of board coordinates a
+// blank was ever placed on; values maps a lower-cased letter to its tile value. It walks
+// the word from its first-letter coordinate along the play's orientation.
+func mainWordTiles(rec engine.MoveRecord, blanks map[[2]int]bool, values map[string]int) []account.BestMoveTile {
+	if len(rec.Words) == 0 {
+		return nil
+	}
+	dr, dc := 0, 1
+	if rec.Dir == engine.Vertical {
+		dr, dc = 1, 0
+	}
+	letters := []rune(rec.Words[0])
+	out := make([]account.BestMoveTile, len(letters))
+	for i, r := range letters {
+		row, col := rec.MainRow+i*dr, rec.MainCol+i*dc
+		blank := blanks[[2]int{row, col}]
+		letter := string(r)
+		value := 0
+		if !blank {
+			value = values[strings.ToLower(letter)]
+		}
+		out[i] = account.BestMoveTile{Letter: letter, Value: value, Blank: blank}
+	}
+	return out
+}
+
 // nonGuestSeats filters out guest seats so the finish-time statistics are
 // recomputed for durable non-guest accounts only — guests never accrue
 // statistics (docs/ARCHITECTURE.md §9). It is called once per game, on finish.