Fudging Fudge dice

[punkbohemian]

I know what the probability curve looks like for 4dF, but I'm wondering how it would change if the fudge dice were modified. For example, let's say it's 2dF with another die thrown it that has -2, -1, 0, 0, +1, and +2 for sides. Or maybe if it was just two of these modified dice. Obviously, the range would be the same, and the curve would have a weaker central tendency, but more than that I can't really figure out offhand. I mean, figuring out curves for ordinary dice is pretty easy, but it gets wonky when you used modified dice. Like with Fudge Dice, the fact that there are two sides with the same value (0) changes probability in a way that normal dice equations won't fit.

Are there any shortcuts people can share? Thanks.

[J. Scott Timmerman]

With two of the modified dice (-2,-1,0,0,1,2), the curve ends up like this:

-4:  1 in 36
-3:  1 in 18
-2:  5 in 36
-1:  1 in 6
0:   2 in 9
1:   1 in 6
2:   5 in 36
3:   1 in 18
4:   1 in 36

And for 2dF+1dModified:

-4:  1 in 54
-3:  1 in 18
-2:  7 in 54
-1:  5 in 27
0:   2 in 9
1:   5 in 27
2:   7 in 54
3:   1 in 18
4:   1 in 54

I just use OpenOffice Calc (a spreadsheet program like MS Excel) to model the statistics.  I also used the same method in order to determine a dice mechanic that approximates a logarithmic curve, which I use for my games.

-Jason T.

[Monkeys]

A Fudge dice is the same as (d3-1).

[J. Scott Timmerman]

A Fudge dice is the same as (d3-1).

Actually, 1dF = (1d3 - 2).

-Jason T.