refactor: use centralized ownership in RoomMemoryPairsProvider

Replace manual buildPlayerMetadata implementation with centralized utilities.

Changes:
- Import buildPlayerMetadataUtil and buildPlayerOwnershipFromRoomData
- Replace manual ownership map building (15 lines) with utility call (2 lines)
- Simplify buildPlayerMetadata: 33 lines → 8 lines
- Use shared utilities for consistency

Part of player ownership centralization plan (Phase 4/7).

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

apps/web/src/app/arcade/matching/context/RoomMemoryPairsProvider.tsx

@@ -5,6 +5,10 @@ import { useArcadeRedirect } from '@/hooks/useArcadeRedirect'
 import { useArcadeSession } from '@/hooks/useArcadeSession'
 import { useRoomData } from '@/hooks/useRoomData'
 import { useViewerId } from '@/hooks/useViewerId'
+import {
+  buildPlayerMetadata as buildPlayerMetadataUtil,
+  buildPlayerOwnershipFromRoomData,
+} from '@/lib/arcade/player-ownership'
 import type { GameMove } from '@/lib/arcade/validation'
 import { useGameMode } from '../../../../contexts/GameModeContext'
 import { generateGameCards } from '../utils/cardGeneration'
@@ -366,38 +370,14 @@ export function RoomMemoryPairsProvider({ children }: { children: ReactNode }) {
   }, [state.pausedGamePhase, state.pausedGameState, hasConfigChanged])
 
   // Helper to build player metadata with correct userId ownership
-  // This uses roomData.memberPlayers to determine which user owns which player
+  // Uses centralized ownership utilities
   const buildPlayerMetadata = useCallback(
     (playerIds: string[]) => {
-      const playerMetadata: { [playerId: string]: any } = {}
+      // Build ownership map from room data
+      const playerOwnership = buildPlayerOwnershipFromRoomData(roomData)
 
-      // Build reverse mapping: playerId -> userId from roomData.memberPlayers
-      const playerOwnership = new Map<string, string>()
-      if (roomData?.memberPlayers) {
-        for (const [userId, userPlayers] of Object.entries(roomData.memberPlayers)) {
-          for (const player of userPlayers) {
-            playerOwnership.set(player.id, userId)
-          }
-        }
-      }
-
-      for (const playerId of playerIds) {
-        const playerData = players.get(playerId)
-        if (playerData) {
-          // Get the actual owner userId from roomData, or use local viewerId as fallback
-          const ownerUserId = playerOwnership.get(playerId) || viewerId || ''
-
-          playerMetadata[playerId] = {
-            id: playerId,
-            name: playerData.name,
-            emoji: playerData.emoji,
-            userId: ownerUserId, // CORRECT: Use actual owner's userId
-            color: playerData.color,
-          }
-        }
-      }
-
-      return playerMetadata
+      // Use centralized utility to build metadata
+      return buildPlayerMetadataUtil(playerIds, playerOwnership, players, viewerId)
     },
     [players, roomData, viewerId]
   )