Just a thought: a FPS multiplayer game could use the proof of work generated by the Bitcoin mining network (e.g. a pool share 1/20th the difficulty of a block hash, which would be generated on average once every 30 seconds) as the seed for the RNG. This would be:
* unpredictable in practice (theoretically a player could reliably predict the hash, but only if they overpower the entire Bitcoin mining network, at a cost of billions of dollars in mining hardware)
The only drawback would be that the time between proof of work shares meeting a particular difficulty target is somewhat random, in being a Poisson distribution that only averages to a particular value.
I'm not sure if it solves any problems, but I think it might, for a couple of reasons:
* it's provably fair, with no reliance on a trusted third party to provide a fair random number, with fair being defined as a random number that none of the participants can predict / obtain foreknowledge of.
* propagation might be faster than what can be achieved through the internet, because dedicated broadcast channels are being created for Bitcoin blockchain data, like the BitSat program, which will broadcast Bitcoin blocks to the entire planet via a cluster of 24 nanosatellites, or the Kryptoradio project, which broadcast the data over radio in Finland.
I very much doubt you could synchronize with the bitcoin consensus faster than synchronizing with the other players. If you're willing to communicate with each other then you can generate a random number in a consensus way easily (e.g. everyone generates their own and XOR them all).
* unpredictable in practice (theoretically a player could reliably predict the hash, but only if they overpower the entire Bitcoin mining network, at a cost of billions of dollars in mining hardware)
* globally verifiable, allowing reliable synchronization
The only drawback would be that the time between proof of work shares meeting a particular difficulty target is somewhat random, in being a Poisson distribution that only averages to a particular value.