I know we've been down this "road" before... But I've changed how the dice are used and I'd like to have some "computation" done with regards to the probability.

So here is my problem that I need solved:

Roll 3d6 (White) + 1d6 (Black) = Compute ALL possible outcomes.

I don't want a listing, just the total number of possible outcomes. Where I am stuck is with the "Black" (1d6).

For that die, can replace any of the other "White (3d6)... If so desired. Usually you would do this to replace one of the lower dice. But at the same time IF you can drop one point and gain a better formula, you might also consider dropping to a lower value.

Anyone have the time to give me the details - would be much appreciated.

Before I was using 1d6 (Blue), 1d6 (Red), 1d6 (Green) and 1d6 (Black). And the values were fixed with the exception that the "Black" die could replace one of the other dice.

But instead of FIXING the dice colors and values, I figured I'd make them all "White" and one "Black" die. This gives players MORE "Outcomes" and possible "plays" (which is what I need help calculating...)

Many thanks!

Since there are THREE (3) White (3d6), and order is important (because each die matches a "resource"), we have:

6 x 6 x 6 = 216 possible outcomes (not too bad!)

Now where I have no clue... Is how to introduce the ONE (1) Black (1d6)...

It's always rolled and then the players decide IF they want to SWAP.

Need HELP --> Here <-- !!!