feat: sistema de 2 rondas con puntos dobles

Ronda 1: 5 categorías con puntos normales (100-500)
Ronda 2: 5 categorías diferentes con puntos x2 (200-1000)

Backend:
- question_service: soporta excluir categorías y multiplicador de puntos
- game_manager: trackea current_round, start_round_2() carga nuevo tablero
- game_events: emite round_started al completar ronda 1

Frontend:
- useSocket: escucha evento round_started
- Game.tsx: muestra indicador de ronda actual
- types: GameRoom incluye current_round

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/services/game_manager.py

@@ -37,6 +37,8 @@ class GameManager:
         room["current_player_index"] = {"A": 0, "B": 0}
         room["board"] = board
         room["scores"] = {"A": 0, "B": 0}
+        room["current_round"] = 1
+        room["round1_categories"] = [int(cat_id) for cat_id in board.keys()]
 
         await room_manager.update_room(room_code, room)
         return room
@@ -153,14 +155,20 @@ class GameManager:
                 # Switch to other team for potential steal
                 room["current_team"] = "B" if failed_team == "A" else "A"
 
-        # Check if game is over (all questions answered)
+        # Check if round is over (all questions answered)
         all_answered = all(
             q["answered"]
             for questions in room["board"].values()
             for q in questions
         )
         if all_answered:
-            room["status"] = "finished"
+            current_round = room.get("current_round", 1)
+            if current_round == 1:
+                # Round 1 finished - need to start round 2
+                room["round_finished"] = True
+            else:
+                # Round 2 finished - game over
+                room["status"] = "finished"
 
         await room_manager.update_room(room_code, room)
 
@@ -189,6 +197,19 @@ class GameManager:
         room["current_question"] = None
         room["can_steal"] = False
 
+        # Check if round is over
+        all_answered = all(
+            q["answered"]
+            for questions in room["board"].values()
+            for q in questions
+        )
+        if all_answered:
+            current_round = room.get("current_round", 1)
+            if current_round == 1:
+                room["round_finished"] = True
+            else:
+                room["status"] = "finished"
+
         await room_manager.update_room(room_code, room)
         return room
 
@@ -205,6 +226,45 @@ class GameManager:
         index = room["current_player_index"][team]
         return players[index % len(players)]
 
+    async def start_round_2(
+        self,
+        db: AsyncSession,
+        room_code: str
+    ) -> Optional[dict]:
+        """
+        Start round 2 with different categories and double points.
+        """
+        room = await room_manager.get_room(room_code)
+        if not room:
+            return None
+
+        # Get categories used in round 1
+        round1_categories = room.get("round1_categories", [])
+
+        # Get new board excluding round 1 categories, with 2x points
+        new_board = await question_service.get_board_for_game(
+            db,
+            exclude_categories=round1_categories,
+            point_multiplier=2
+        )
+
+        if not new_board:
+            # Not enough categories for round 2 - end game
+            room["status"] = "finished"
+            await room_manager.update_room(room_code, room)
+            return room
+
+        # Update room for round 2
+        room["board"] = new_board
+        room["current_round"] = 2
+        room["round_finished"] = False
+        room["current_question"] = None
+        room["can_steal"] = False
+        # Keep current_team - winner of last question picks first
+
+        await room_manager.update_room(room_code, room)
+        return room
+
     def calculate_timer_end(self, time_seconds: int, is_steal: bool = False) -> datetime:
         """Calculate when the timer should end."""
         if is_steal: