Mon Apr 14 13:32:27 2014 by Daniel |

I'm so interested in this mechanic, and I'm curious about HOW the autor simplified the regular "d6-d6". It's possible to find the autor of "d6-d6, without math"? |

Mon Apr 14 18:05:49 2014 by Torben |

I can't find a user-contributed roll named "d6-d6 without math". I suspect you are thinking of a fairly well-known trick: You can get a probability distribution identical to d6-d6 by rolling two differently coloured d6s and selecting the lowest of these as the absolute value (0 if they are the same) and using the colour of this to find the sign (dark is negative, light is positive). It is debatable whether this is "without math", but it does replace subtraction by comparison, which many find easier (especially if you can get negative results). As for how you can see that this is true, a simple way is to use Troll to verify it: Compare the result of `d6-d6` to `A := d6; B := d6; if A<B then A else if B<A then -B else 0` . If you want to do the verification by hand, the simplest way is to write up all 36 possible pairs of two numbers from 1 to 6 (remembering that (1,2) is different from (2,1) and so on) and for each possible result (from -5 to +5) count how many pairs yield that result both using 6d-d6 and the comparison-based method. A more general method (that shows that the trick works for dX-dX regardless of X) is as follows:If both dice show the same, the result is 0 for both methods, so we need only look at non-zero results. To get a positive result R on dX-dX, the positive die must show A and the negative die must show B = A-R. This gives A-B = A-(A-R) = R. A can at most be X and B = A-R must be at least 1, so A can range from R+1 to X, both inclusive. For each such value of A, there is exactly one value of B that makes the difference equal to R. So there are X-(R+1)+1 = X-R ways of getting R. By symmetry, there are also X-R ways of getting the negative result -R. To get R with the comparison method, the positive dice must have the value R and the negative die must have a value greater than R. There are X-R values greater than R and no more than X, so we also here have that there are X-R ways of getting R. And, again, symmetry gives the same for the negative value -R. |

Tue Apr 22 22:49:14 2014 by Daniel |

Thanks for this explanation. |