Stage 5: robot opponent (pool, seed-derived strategy, move driver, matchmaker substitution)

- internal/robot: durable kind='robot' account pool (migration 00004); every
  per-game and per-turn choice derived deterministically from the game seed
  (restart-stable FNV mix); a background move driver; margin targeting (band
  1-30, closest-to-band); right-skewed [2,90]min delays (median ~10m);
  opponent-anchored sleep with +/-3h drift; daytime nudge reply + proactive
  12h nudge; friend/chat blocked via profile toggles.
- engine.Candidates (decoded ranked plays); game.Candidates + RobotTurns;
  social.LastNudgeAt.
- matchmaker: 10s wait then robot substitution (reaper) + Poll delivery seam.
- config (BACKEND_ROBOT_DRIVE_INTERVAL, BACKEND_LOBBY_ROBOT_WAIT,
  BACKEND_LOBBY_REAPER_INTERVAL); main wiring + boot-time pool provisioning.
- metrics: robot account_stats (authoritative balance) + robot_games_finished_total
  OTel counter + per-finish log.
- docs: PLAN, ARCHITECTURE, FUNCTIONAL(+ru), TESTING, README; account.go comment.
- tests: robot strategy units, matchmaker reaper/Poll, engine.Candidates; inttest
  robot full-game / substitution / proactive-nudge.

backend/internal/social/chat.go

@@ -103,6 +103,13 @@ func (svc *Service) Nudge(ctx context.Context, gameID, senderID uuid.UUID) (Mess
 	return svc.store.insertChatMessage(ctx, gameID, senderID, kindNudge, "", nil)
 }
 
+// LastNudgeAt returns the time of the most recent nudge senderID sent in the game
+// and true, or the zero time and false when there is none. The robot opponent
+// uses it to notice a human nudge on its turn and answer promptly.
+func (svc *Service) LastNudgeAt(ctx context.Context, gameID, senderID uuid.UUID) (time.Time, bool, error) {
+	return svc.store.lastNudgeAt(ctx, gameID, senderID)
+}
+
 // Messages returns the per-game chat visible to viewerID: the viewer must be a
 // seated player. Messages from a sender the viewer has a block with (either
 // direction) are dropped, and if the viewer has disabled chat only nudges remain.