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Abilities are expanded (meaning the definition of the ability is placed in the formula anywhere that ability appears).
Macros are expanded, including nested macros up to 99 levels deep.
Variables are substituted
Roll queries are executed (the player making the roll is asked to provide a value for each query, and that value is substituted in where the roll query appears in the formula)
All previous steps are repeated until there are no longer any unresolved abilities, macros, variables, or queries. This allows for nesting (e.g. putting an attribute in a macro).
Inline rolls are executed, starting with the most deeply nested inline roll working upward. The overall result of the inline roll is substituted in place where it appeared in the formula.
The remaining roll is executed: first, dice are rolled for any dice (e.g. "2d6" is rolled; including any special dice such as dropped or exploding), then the result of that roll is substituted into the formula. Next, floor() and ceil() functions are executed. Finally, the entire remaining formula is evaluated, including observing proper math order of operations (parentheses first, then multiplication/division, then addition/subtraction).
All Types Of Dice
Basic Roll of NdX
Fate/Fudge Roll NdF
Computed Dice Roll (N+Y)dX or Nd(X+Y)
All Roll Modifiers
Target Number / Successes (B,F) - CP
Failures (B,F) - fCP
Exploding Dice (B,F) !CP
Compounding Dice (B,F) !!CP
Penetrating Dice (B,F) !pCP
Dice Matching m and mt
Keep / Drop Dice (B,F) khN or klN or dhNdlN
Rerolling Dice (B,F) rCP
Sorting Dice (B,F) sa or sd
Order of Operations for Modifiers
Exploding, Compounding, Penetrating, Rerolls
These are applied while the dice are still rolling. imagine that you roll some exploding 6d6 on your table and the instant one of them settles as a 6 another die is rolled
Keep, Drop, Success, Failure, Sorting
These are applied after all of the dice have "settled" and all of the result values are known.
The code used by Roll20: https://ghostbin.com/paste/2n67m
Documentation: https://wiki.roll20.net/Dice_Reference
NdXNdF(N+Y)dXorNd(X+Y)mandmtkhNorklNordhNdlNrCPsaorsdkhNorklNordhNordlNCPfCP