feat: add full Backgammon game — bot AI, multiplayer, tournament rules
Complete backgammon (طاولة) implementation:
- 24-point board with bar, bearing off, doubling cube
- Bot AI: easy (random), medium (heuristic), hard (positional eval)
- Local pass-and-play + VS bot + online matchmaking + private rooms
- Server-side move validation, opening roll, gammon/backgammon detection
- Supabase Realtime WebSocket for multiplayer
- Responsive CSS with wood-grain board, triangle points, stacking checkers
Co-Authored-By:
Claude Opus 4.6 <noreply@anthropic.com>
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