Construct a dice simulator?

Hello
My goal is to evaluate the user-friendliness of the Wolfram language by “translating” a dice rolling Excel simulator into an interactive, visually attractive application.
In the original Excel very manual and cumbersome application I am playing with the following parameters

  • Number of dice: D

  • For each individual die, the die identifier: Dd

  • For each individual die, the number of faces: F(Dd)

  • For each individual face of any given die, the face identifier: Ff(Dd)

  • For each individual face of any given die, the quantity attached to it : Q(Ff(Dd))

  • For each individual face of any given die, the probability of occurrence attached to it: P(Ff(Dd))
    My first question is HOW TO PRESENT NICELY the theoritical possible combinations WHEN D , Dd , F(Dd) , Ff(Dd) are modified. In the attached illustration, I am rolling 2, then 3 then 4 dice, each of them with 4 faces, each face identified by a number 1,2,3,4. The visual is fractal like. With mathematica i have been as far as

    Grid[Table[f[2].f[1], {f[2], 4}, {f[1], 6}]]

Best regards
JP

Hi Have you seen this thread on SE?

Nice formatting for the results of a dice game simulation