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.

docs/ARCHITECTURE.md

@@ -203,7 +203,8 @@ arrive from a platform rather than completing a mandatory registration).
   guest is promoted to durable, clearing `is_guest`).
 - **Merge** retires the account that owns the linked identity into the **current**
   account, in a single transaction (`internal/accountmerge`): statistics summed
-  (max points kept), the hint wallet summed, `paid_account` ORed, identities
+  (counters incl. moves/hints added, max points kept, and the per-variant best moves
+  merged keeping the higher-scoring play), the hint wallet summed, `paid_account` ORed, identities
   repointed, games / chat / complaints transferred, friends and blocks
   de-duplicated (friendships keep the strongest status accepted>pending>declined),
   pending invitations/codes dropped, and the secondary kept as an **audit
@@ -347,7 +348,13 @@ Key points:
   placement and leaves the commit to the player. When the rack has no legal move the
   service spends **nothing** and returns `ErrNoHintAvailable` — surfaced as the distinct
   result code `no_hint_available` (separate from `hint_unavailable`) so the UI can say
-  "no options" rather than "no hints left".
+  "no options" rather than "no hints left". The hint count shown to the player is the
+  per-game allowance remaining **plus** the global wallet; because the wallet is global,
+  `game.state`/`game.hint` carry it as a separate `wallet_balance` field beside the combined
+  `hints_remaining`, so the client derives the per-game allowance (`hints_remaining -
+  wallet_balance`, which it may cache per game) and reads the wallet **live** from the
+  profile — otherwise a wallet hint spent in one game would leave a stale, too-high count
+  cached on every other game.
 - **Word-check tool**: unlimited dictionary lookups against the game's pinned
   dictionary; each result offers a **complaint** (complainant, game, variant,
   dict_version, word, the disputed result, an optional note) that lands in the admin
@@ -568,7 +575,8 @@ disguised robot stays indistinguishable from a person.
   the `kind` admitting `robot`),
   `sessions` (revoke-only opaque-token hashes), the game tables
   `games` (carrying the `dropout_tiles` disposition column), `game_players`,
-  `game_moves` (the move journal), `complaints` and `account_stats`, and the
+  `game_moves` (the move journal), `complaints`, `account_stats` and
+  `account_best_move`, and the
   social/lobby tables `friendships` (the request/accept graph, its status admitting
   `declined`), `blocks`
   (per-user blocks), `chat_messages` (per-game chat and nudges, carrying the per-message
@@ -596,8 +604,21 @@ disguised robot stays indistinguishable from a person.
   non-guest accounts only — the finish-time recompute skips any `is_guest`
   seat): wins, losses, **draws**, max points in a game, and
   max points for a single **move** (which already folds in every word the move
-  formed plus the all-tiles bonus). A tie increments draws only; a resignation or
-  timeout is a loss for the acting player.
+  formed plus the all-tiles bonus); plus two summed counters — `moves` (the player's
+  plays, i.e. tile placements; passes and exchanges do not count) and `hints_used`
+  (every hint taken, allowance + wallet) — from which the screen derives the **hint
+  share** = hints_used / moves. A tie increments draws only; a resignation or
+  timeout is a loss for the acting player. A companion table **`account_best_move`**
+  (keyed by account **and variant**) keeps the highest-scoring single play **per
+  variant** with the word itself: its main word as an ordered JSON array of tiles
+  (letter, tile value, blank flag — value 0 for a blank), so the statistics screen
+  renders it as game tiles without the variant's alphabet table. Blank flags are
+  taken from every blank ever placed in the game (equivalent to reading the final
+  board, since a placed tile never moves). It is replaced only by a strictly
+  higher-scoring play, written in the same finish transaction, and skipped for
+  guest/honest-AI games exactly like `account_stats`. It is filled forward only —
+  plays finished before the table existed are not back-populated (the aggregate
+  `max_word_points` still covers them numerically).
 
 ### 9.1 History invariant (must hold forever)
 

docs/FUNCTIONAL.md

@@ -229,7 +229,12 @@ honest-AI practice game (a live game's export would leak the move journal; an AI
 game is throwaway). The client shares the `.gcg` file where the platform supports
 it, otherwise downloads it. Statistics (durable accounts only):
 wins, losses, draws, max points in a game, and max points for a single move (the
-best play, which already includes every word it formed plus the all-tiles bonus).
+best play, which already includes every word it formed plus the all-tiles bonus). It
+also shows the player's **move count** (their plays — passes and exchanges do not
+count) and their **hint share** (the percentage of those plays where a hint was taken).
+The best move is also broken down **per game variant**, showing the **word itself**
+drawn as game tiles (a wildcard shows its letter but no value) — one row per variant
+the player has played, omitting variants with no plays.
 A game that can no longer be continued — because a rule changed and an earlier
 move would now be illegal — is closed as a **draw** the moment someone opens it,
 never left stuck on an error: the move history shows an impersonal organizer note

docs/FUNCTIONAL_ru.md

@@ -233,7 +233,12 @@ UTC), суточного окна отсутствия (away; сетка по 10
 с ИИ одноразовая). Клиент делится файлом `.gcg` там, где платформа это поддерживает,
 иначе скачивает его. Статистика (только у постоянных аккаунтов):
 победы, поражения, ничьи, макс. очков за партию и макс. очков за один ход (лучший
-ход, уже включающий все образованные им слова и бонус за все фишки).
+ход, уже включающий все образованные им слова и бонус за все фишки). Также
+показываются **число ходов** игрока (его выкладки — пасы и обмены не считаются) и
+**доля подсказок** (процент таких ходов, на которых бралась подсказка).
+Лучший ход также даётся **с разбивкой по вариантам игры** — **само слово**,
+нарисованное игровыми фишками (wildcard показывает свою букву без очков), по одной
+строке на каждый сыгранный вариант; варианты без ходов не выводятся.
 Партия, которую больше нельзя продолжить — из-за изменения правил более ранний ход
 стал бы недопустимым, — закрывается **ничьёй** в момент открытия её игроком, а не
 остаётся висеть с ошибкой: в конце истории ходов показывается обезличенная заметка

docs/UI_DESIGN.md

@@ -279,9 +279,16 @@ enabled on the first, uncached load) and flip in place when an event refreshes t
   and the "searching" hint is hidden; the game starts already seated, the opponent shows as **🤖**
   everywhere (score card, lobby row, turn line), the add-friend 🤝 is never drawn, and the chat's
   send field and 🛎️ nudge stay **disabled** while the 🔎 dictionary word-check keeps working.
-- **Statistics** (`screens/Stats.svelte`, the lobby 📊 tab): a 2-column grid of stat
-  cards (wins / losses / draws / games / win-rate / best game / best move) — pure
-  numbers, no charts.
+- **Statistics** (`screens/Stats.svelte`, the lobby ✏️ tab): a 2-column grid of stat
+  cards (games / wins / draws / losses / moves / hint-share / best game / win-rate) —
+  pure numbers, no charts; hint-share is a one-decimal percentage in the active locale's
+  notation (e.g. "4.8%" / "4,8%") — followed by a **full-width "best move" card** that
+  breaks the best move
+  down per variant: one row per played variant (catalogue order, empty variants
+  omitted) with the variant name on the left, the **word drawn as game tiles**
+  (`components/WordTiles.svelte`, the board's placed-tile look at a small fixed size;
+  a wildcard shows its letter but no value) right-aligned to a shared edge, and the
+  score right-aligned in its own column.
 - **Profile editing** (`screens/Profile.svelte`): an inline form — display name, a
   **UTC-offset** timezone dropdown (defaulting to the browser's offset), the away
   window as hour + 10-minute dropdowns (24-hour, ≤ 12 h), and block toggles — plus an