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I request a random number generator based on a cryptographic hash function, for example SHA-1, using the ready-made PHP-function sha1().
Every game is assigned a secret key. The key is concatenated with the move number and input to the hash function. The dice rolls are determined from the hash.
The advantages: 1. this will create random numbers with very good statistical properties, practically as good as real random numbers. 2. Predicting the dice rolls is infeasible when the key is secret, even if the algorithm is published. 3. After the end of the game the key can be revealed, so that everyone (or at least programmers) can check if the dice have been rolled correctly. The players need no longer be sucpicious if the random number generator is bad or buggy.
Thom27: that would imply that separate random number context is saved for every game, but that should be doable, after all, it's just two more fields at the game. This can be even realized without implementing any new algorithm - the current algorithm could be published and the seed number stored in that way. Publishing the algorithm would be a good idea in itself, so anyone could verify that it is good (or not good), and stop whining (Yes, there are people who would still whine because they don't understand math, but we could just ignore those)