Unusual Dice Probablities

File: dice_probabilities_2.png (53KB, 1020x656px) Image search: [Google]

53KB, 1020x656px

I've recently been trying to come up with some sort of weird probabilities you roll a d2, d3, d4, d5, and d6 at the same time.

The reason for this is because you can use dice shaped like the platonic solids in order to roll this, just by rearranging the numbers on the races. Take a look:

>altered d4 = d{1,1,2,2} = d2
>altered d6 = d{1,1,2,2,3,3} = d3
>altered d8 = d{1,1,2,2,3,3,4,4} = d4
>altered d12 = d{1,1,2,2,3,3,4,4,5,5,6,6} = d6
>altered d20 = d{1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5} = d5

But even though this starts out promising, I haven't found any probabilities that seem very interesting yet.

>>8995075
>dice and the math behind them
The distribution of the sum of two or more independent die rolls is the convolution of the individual distributions.

That's about the only nontrivial bit of math you'll actually need.

>>8995087
Convolution?

>>8995093
http://lmgtfy.com/?q=convolution+of+distributions

File: dice_probabilities_3.png (37KB, 1070x550px) Image search: [Google]

37KB, 1070x550px

Here's a weird distribution you can get with just three d6s

What program is that OP? It looks like it'd be fun to fiddle around with.

>>8995198
www.anydice.com

File: 216.png (23KB, 1720x567px) Image search: [Google]

23KB, 1720x567px

Turns out that you can basically turn 3 six-sided dice into a "d216" just by relabeling the sides.

Hmm, this is somewhat interesting. You know I figured that you can use certain calculators in place of dice? All they need is a random generator function and you can emulate any dice, you just need to round the result.

>>8997060
Yes. Technically it won't ever be truly random, in order for that to happen you have to use some outside source (for instance, atmospheric disturbance or something). But the difference would be imperceptible when using a computerized random number generator

>>8997096
>implying the entire universe isn't deterministic