Sorry, follow up to my post.. Let me give you an example scenario about what I'm talking about using your deterministic RNG.. Assume very simple 1 x 1 MP..
Init: P1 and P2 RNG seed=1
Time 0: P1 execute action 1.1, RNG seed now at 1
Time 1: P1 -> send sync action 1.1 to P2, waiting for ACK from P2
Time 2: P2 execute action 2.1, RNG seed now at 1
Time 3: P2 -> send sync action 2.1 to P1, waiting for ACK from P1
Time 4: P2 recieve action 1.1 from P1, send ACK to P1
Time 5: P2 execute action 1.1, but RNG seed now at 2
Time 6: P1 recieve action 2.1 from P2, send ACK to P2
Time 7: P1 execute action 2.1, but RNG seed now at 2
Time 8: P2 recieve ACK fom P1
Time 9: P1 recieve ACK from P2
Although it may seem that both P1 and P2 are in sync, isn't it true that action 1.1 was executed with RNG=1 on P1, but P2 had RNG=2 when it executed 1.1? Same with action 2.1 but reversed. I don't know if this sort of scenario applies to Sins, so I'm just asking..
EDIT: when I say "RNG seed", I really mean the position in the RNG sequence. I assume the real RNG seed is identical across P1 and P2, and yes, as Blair said, RNGs are not "really" random, they follow a mathematically known sequence..