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/store.go

@@ -3,6 +3,7 @@ package game
 import (
 	"context"
 	"database/sql"
+	"encoding/json"
 	"errors"
 	"fmt"
 	"hash/fnv"
@@ -12,6 +13,7 @@ import (
 	"github.com/go-jet/jet/v2/qrm"
 	"github.com/google/uuid"
 
+	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/postgres/jet/backend/model"
 	"scrabble/backend/internal/postgres/jet/backend/table"
@@ -53,13 +55,22 @@ type gameInsert struct {
 }
 
 // statDelta is one account's contribution to its statistics on a game finish.
+// bestVariant/bestScore/bestTiles describe the game's best play for this account when
+// it scored (bestVariant empty otherwise): the variant label, the play's total score and
+// its main word as rendering tiles. They feed the per-variant account_best_move upsert,
+// which keeps only the account's highest-scoring play per variant.
 type statDelta struct {
-	accountID  uuid.UUID
-	wins       int
-	losses     int
-	draws      int
-	gamePoints int
-	wordPoints int
+	accountID   uuid.UUID
+	wins        int
+	losses      int
+	draws       int
+	gamePoints  int
+	wordPoints  int
+	moves       int // plays this game (tile placements), summed into account_stats.moves
+	hintsUsed   int // hints used this game (allowance + wallet), summed into account_stats.hints_used
+	bestVariant string
+	bestScore   int
+	bestTiles   []account.BestMoveTile
 }
 
 // commit is everything a single committed transition persists: the journal row,
@@ -633,6 +644,9 @@ func (s *Store) CommitMove(ctx context.Context, c commit) error {
 				if err := upsertStats(ctx, tx, d, c.now); err != nil {
 					return err
 				}
+				if err := upsertBestMove(ctx, tx, d, c.now); err != nil {
+					return err
+				}
 			}
 		}
 		return nil
@@ -662,6 +676,9 @@ func (s *Store) VoidGame(ctx context.Context, v voidCommit) error {
 			if err := upsertStats(ctx, tx, d, v.now); err != nil {
 				return err
 			}
+			if err := upsertBestMove(ctx, tx, d, v.now); err != nil {
+				return err
+			}
 		}
 		return nil
 	})
@@ -714,13 +731,17 @@ func upsertStats(ctx context.Context, tx *sql.Tx, d statDelta, now time.Time) er
 	draws := row.Draws + int32(d.draws)
 	maxGame := max(row.MaxGamePoints, int32(d.gamePoints))
 	maxWord := max(row.MaxWordPoints, int32(d.wordPoints))
+	moves := row.Moves + int32(d.moves)
+	hintsUsed := row.HintsUsed + int32(d.hintsUsed)
 
 	upd := table.AccountStats.UPDATE(
 		table.AccountStats.Wins, table.AccountStats.Losses, table.AccountStats.Draws,
 		table.AccountStats.MaxGamePoints, table.AccountStats.MaxWordPoints, table.AccountStats.UpdatedAt,
+		table.AccountStats.Moves, table.AccountStats.HintsUsed,
 	).SET(
 		postgres.Int(int64(wins)), postgres.Int(int64(losses)), postgres.Int(int64(draws)),
 		postgres.Int(int64(maxGame)), postgres.Int(int64(maxWord)), postgres.TimestampzT(now),
+		postgres.Int(int64(moves)), postgres.Int(int64(hintsUsed)),
 	).WHERE(table.AccountStats.AccountID.EQ(postgres.UUID(d.accountID)))
 	if _, err := upd.ExecContext(ctx, tx); err != nil {
 		return fmt.Errorf("update stats %s: %w", d.accountID, err)
@@ -728,8 +749,41 @@ func upsertStats(ctx context.Context, tx *sql.Tx, d statDelta, now time.Time) er
 	return nil
 }
 
-// SpendHintAllowance increments a seat's per-game hint counter by one.
-func (s *Store) SpendHintAllowance(ctx context.Context, gameID uuid.UUID, seat int) error {
+// upsertBestMove records the account's best play for a variant, keeping only the
+// highest-scoring one: a first play inserts, a later one replaces it only when it scored
+// strictly higher (the conditional DO UPDATE makes the upsert atomic under concurrent
+// finishes without a separate lock). It is a no-op when the finish carries no scoring play
+// for the account (a draw with no plays, or an exchange/pass-only game).
+func upsertBestMove(ctx context.Context, tx *sql.Tx, d statDelta, now time.Time) error {
+	if d.bestVariant == "" || len(d.bestTiles) == 0 {
+		return nil
+	}
+	tiles, err := json.Marshal(d.bestTiles)
+	if err != nil {
+		return fmt.Errorf("marshal best move %s/%s: %w", d.accountID, d.bestVariant, err)
+	}
+	stmt := table.AccountBestMove.
+		INSERT(
+			table.AccountBestMove.AccountID, table.AccountBestMove.Variant,
+			table.AccountBestMove.Score, table.AccountBestMove.Tiles, table.AccountBestMove.UpdatedAt,
+		).
+		VALUES(d.accountID, d.bestVariant, d.bestScore, string(tiles), postgres.TimestampzT(now)).
+		ON_CONFLICT(table.AccountBestMove.AccountID, table.AccountBestMove.Variant).
+		DO_UPDATE(postgres.SET(
+			table.AccountBestMove.Score.SET(table.AccountBestMove.EXCLUDED.Score),
+			table.AccountBestMove.Tiles.SET(table.AccountBestMove.EXCLUDED.Tiles),
+			table.AccountBestMove.UpdatedAt.SET(table.AccountBestMove.EXCLUDED.UpdatedAt),
+		).WHERE(table.AccountBestMove.EXCLUDED.Score.GT(table.AccountBestMove.Score)))
+	if _, err := stmt.ExecContext(ctx, tx); err != nil {
+		return fmt.Errorf("upsert best move %s/%s: %w", d.accountID, d.bestVariant, err)
+	}
+	return nil
+}
+
+// IncHintsUsed increments a seat's per-game hints-used counter by one. It is called for
+// every hint — both the free per-game allowance and the wallet-charged ones — so the counter
+// is the seat's total hints used this game (the first HintsPerPlayer being the allowance).
+func (s *Store) IncHintsUsed(ctx context.Context, gameID uuid.UUID, seat int) error {
 	stmt := table.GamePlayers.
 		UPDATE(table.GamePlayers.HintsUsed).
 		SET(table.GamePlayers.HintsUsed.ADD(postgres.Int(1))).
@@ -738,7 +792,7 @@ func (s *Store) SpendHintAllowance(ctx context.Context, gameID uuid.UUID, seat i
 				AND(table.GamePlayers.Seat.EQ(postgres.Int(int64(seat)))),
 		)
 	if _, err := stmt.ExecContext(ctx, s.db); err != nil {
-		return fmt.Errorf("game: spend hint allowance: %w", err)
+		return fmt.Errorf("game: increment hints used: %w", err)
 	}
 	return nil
 }