>=Arthur Flatau
 > (setq *random-state* (make-random-state t))

You might want to consider binding *random-state* (eg with let) instead of 
setqing it.

 > There is no way to provide some other number to initialize the random state.

True, but it may be sufficient to "customize" your numbers based on some 
additional local information.

For example you might simply wrap the call to the random function with your 
own code that XORs the sequence with the machine's IP address, or some 
similar scheme.