Ideally, we want to:
- use the standard polyhedral dice: d4, d6, d8, d10, d12, d20;
- minimise re-rolling dice as much as possible;
- not have any more dice involved than necessary.
The first insight which was really helped is the idea that indexing X elements in tables is the same as rolling a dX, where X is any positive integer. Imagine that you take X square pieces of paper, write the numbers from 1 up to X on them, and paste them to a board. Throw a dart blindly at the board and you randomly select a number - which, for all intents and purposes is the same as rolling a dX.
Take the numbers down off a board now and try to arrange them into a table, or into a series of tables. Here comes the IF:
If we can arrange the X squares into a series of good* tables, then we can index X elements easily.A consequence of all of this is that those good tables could just as easily contain the numbers from 1 to X written on them. So rolling a dX and rolling to get one of those X elements add up to the same thing, more or less (in maths terms, I think we could safely say that the two things were homomorphic).
And this was my big thought on the topic so far (well, one of them at least): it makes as much sense to see how we can simulate a dX using the standard polyhedral dice as it does to think about organising X elements into tables.
In future posts, simulating dX with the standard polyhedral dice! And how this ties in to random tables.
*in the sense of the three criteria from earlier in the post