in reply to Rolling a biased die

Say you have n values with probabilities d_1, ..., d_n. Normalize your values so that all d_i's are at least 1. Then you can do with O(sum(d_i)) storage and O(1) time. For each integer l less than sum(d_i) there is at most one transition from one d_i to the next one between l and l+1. For each l, just store either the outcome which covers all the l-th unit interval or the two outcomes and the transition point.
It's not the most elegant solution and in case you have very small values you may think of some variation, but in your case it should work quite well.
Best regards