Develop a real-time Multiplayer Trivia Game using React, Node.js, Socket.io, and Tailwind CSS. The application must allow game hosts to create public or private trivia rooms with custom category selections, question counts, and round durations. Players join rooms using a simple 6-digit access code, entering a display nickname and picking a custom player avatar. Implement a strictly server-authoritative game state engine where the backend server broadcasts questions, manages a precise 15-second countdown timer per question, and computes player scores dynamically based on both correctness and answer speed. Build smooth, animated round transitions displaying a real-time leaderboard showing player rank movements, streaks, and cumulative points. Store master trivia question banks in MongoDB and cache active game session state in Redis for low-latency operations. Handle client socket disconnections and rapid reconnects gracefully without losing player state.