I just noticed Joseph's comment in his question about Markov chains. My observations about the correctness of trying to use Markov chains to describe the rolling of a die, fair or unfair:
If by state in the Markov chains, you mean just the "face" it is currently on or the "face" which is lower-most in attitude at a particular point in time, then it is inappropriate to use Markov chains because the likelihood of transitioning from die face $F_i$ to die face $F_j$ is not purely dependent upon the current state. If $F_j$ and $F_k$ are two "faces" adjacent to face $F_i$, then the likelihoods of transitioning $F_i \to F_j$ vs. $F_i \to F_k$ is not just dependent on the "current state" being $F_i$, but also dependent upon the velocity, position, and orientation of the die. The "faces" are necessary but not sufficient to encode state in such a way for Markov chains to be applicable: that the Bayesian requirement that "current state" at time $t$ is all that is needed to be known in order to be able to predict the likelihood of the state at time $t+1$ (if you talk about discrete time) or time $t+\varepsilon$ if you talk about continous time.
If by "state", you try to get around this factor that only current state be considered and not the history of how you came to currently be in that state, then you could try to add the vectors of position, velocity, and orientation as extra "states", which is valid in numerical simulation, because ultimately all reals are still encoded into limited precision "floating point" representations of reals. However, the transition table would be huge if you allowed even for 16-bit floating point representation.
I do not think that history-less "Markov chains" can be applied in this situation.
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