[RPG] Help Calculating Dice Odds for a Unique d6 Dice Pool

anydicedice

I'm attempting to design a unique d6 dice pool system, and I want to try programming the probabilities in AnyDice but I'm not sure how. Here's how the system works:

  • Dice pools are between 2 and 10 dice
  • A roll of 5 or 6 is a success
  • Any dice that sum to 5 or higher also count as successes

For example, a roll of (6,3,2,3,5,4,3,1) would be 5 successes (1 from 6, 1 from 5, 1 from 3+2, 1 from 4+1, and 1 from 3+3).

What kind of program in AnyDice or Excel would I use to calculate average odds for each dice pool up to 10 dice?

Best Answer

An exhaustive generation of the possibilities can be done.

It is not 100% clear what you mean by "dice totalling at least 5", I've chosen to interpret this as "sum up to 5 dice" and that means one would have at least one success with a pool of 5 or more dice (and at least 2 successes with a pool of 10 dice).

In principle, the algorithm is simple:

# interpret "roll a die" as "loop from 1 to 6 and for each..."
declare a tabulation function
declare a "generate all rolls" function, taking dice to roll and rolls so far
  if we should roll only one more dice:
    roll it, add it to the rolls so far, pass that to the tabulator
  otherwise:
    roll a die, add it to the rolls so far and call ourselves, generating one less roll

Then you can tabulate all the number of different successes. So far, I have the results for pools of size 2-9 in and can edit the entry with the results.

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