You can also use any fair dN as a fair dN+X, by rolling ceil(log_N(N+X)) times and interpreting the result as a base-N number. (This is commonly done in D&D: in

You can also use any fair dN as a fair dN+X, by rolling ceil(log_N(N+X)) times and interpreting the result as a base-N number. (This is commonly done in D&D: instead of rolling a d100, you roll two d10s.) For example, say you want to roll a d20, but all you have is a coin. Flip the coin five times, producing a 5-bit integer (again discarding if the sum is not an exact multiple of N+X). A weirder example would be using a d6 to simulate a d100: ceil(log6(100)) = 3, so roll 3 times, then compute 36*r0 + 6*r1 + r2. Edit: Even more generally, you can use any set of fair dice. Imagine you have a d2, d4, and d6, and you want to simulate a d40. Roll the d6 and multiply by 4*2; roll the d4 and multiply by 2; then roll (flip) the d2. The resulting sum is a fair roll in the range (0, 48]. This is a significant improvement over rolling a d6 three times: you can roll all of the dice together, and you're much less likely to need a reroll.