There are six standard polyhedral dice: d4, d6, d8, d10, d12 and d20. When using these we assume that the dice are fair - each side is equally likely to come up. If we were to create or simulate a die with X sides it would be best if it were fair. We cannot simulate a d11 using 2d6 directly - we get a range of 11 possible values, but there are different probabilities for each value. The simulated die would not be fair.
We can simulate a few dice with the six standard polyhedral dice through either re-rolling on the high value, or by "halving the die". It is not too difficult to introduce simple notation to account for both of these actions.
d6/2 gives a d3. We let d6r stand for the situation where we reroll the 6. We only want values 1-5 so d6r results in a fair d5. However, d10/2 also gives d5, and without the reroll. From the standard polyhedral dice we can simulate the following dice easily:
|d2 = d4/2, d6/3, etc.
d3 = d6/2, d12/4.
d5 = d10/2, d20/4.
d7 = d8r.
|d9 = d10r.
d11 = d12r.
d19 = d20r.
We could also simulate a fair d9 by rolling two d3s; these act as indexing nine entries in a table. We could denote this with d3 x d3 or (d3)^2.
|d3 x d3||1||2||3|
These various actions - re-rolling, halving and dividing across tables - allow us to build up a greater number of simulated fair dice. I'll go into more detail in future posts, and see if I can start to make sense about how we might simulate a dX for any positive integer X.