[House Rules] Rolling for Fog of War with special dice

[Shad]

Been thinking about custom dice this morning!

The probability of Fog of War (3d6 >=16) is 4.6296(repeating)%.

I was wondering if you made custom dice with the following specs:

1. 6 sides
   
2. only 2 faces (FoW, continue)
   

would there be an arrangement of face counts such that rolling exactly three FoW would have the same probability as 3d6 >= 16...

The following arrangement works:

Die 1: 5 FoW, 1 Continue
Die 2: 2 FoW, 4 Continues
Die 3: 1 FoW, 5 Continues

Probablistically, your odds of rolling FoW are:

Die 1: 83.3%
Die 2: 33.3%
Die 3: 16.6%

and your odds of all three coming up FoW at the same time, and therefore ending your turn, are:

4.6296296%

EDIT - turns out the site I consulted was rounding their results without saying so. That arrangement works perfectly.

Anyone else have an opinion?

(of course some scenarios modify the FoW roll, you're shit out of luck for those! )

[Shad]

Ok, with:

Die 1: 5 FoW
Die 2: 2 FoW
Die 3: 2 FoW

you can get the proper probability for 3d6 >=15. Which means if you had a set of four FoW dice: 1, 2 x 2, and 5, you'd be able to roll for both >=16 and the >=15 which is found occasionally.

[Matt W]

Note that at night you would need to use the dice to get to 15 anyhow as you add 1 to the roll during night turns.