So the first one i will make will be a turn based multiplayer game. a real-time multiplayer game is a very complicated task
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In a turn-based MP game, you send data at the end of the turn. In a realtime MP, you send data when something occurs (a bullet is flying to its target, a monster is hit and dies, a character moves, a gate opens, etc.). In both cases, these data contain all changes since the last state and, when the other player receives them, the game is updated accordingly. Nothing technically difficult.
The major difficulty for the real-time MP is to synchronize events (when the game needs synchronization, which is not the case for all real-time MP games) because you have to deal with latency, and this problem increases with the number of players. But this problem has solutions since long so you will find easily tons of books and sites on the subject to solve it without a big headache.
On the other hand, you have problems specific to turn-based MP (data storage as matches can last a long time, simultaneous matches with different players, detection of the game status because inactivity doesn't mean that someone stopped playing, etc.) and if your game includes an AI, it will be more difficult to implement a good AI for a turn-based MP than for real-time MP.
After implementing both modes in real games with the Google Play Services library, I'm not convinced there's a huge technical difference.
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