Ref: RuleSystems

Dice Roll And Differences

There is some games where dice are rolled and skills are added to the dice, or the dice have to be lower than the skill value. This page attempts to investigate the various models that are used and to explain how some systems are in fact equivalent.

Notations

For simplicity the following notations will be used.

RAND := The Dice Function

ie RAND = 2d6-7, d20, mid(3d20) or d100 etc

high(RAND) := The Dice Function is rolled and high is the good values.

low(RAND) := The Dice Function is rolled and low is the good values.

ie high(d20) is used in DnD35e and low(100) is used in RQ2

min(RAND) := The lowest value that the Dice Function will generate.

max(RAND) := The highest value that the Dice Function will generate.

ie if RAND = 2d6-7, d20, mid(3d20) or d100 then min(RAND) = -5, 1, 1, 1 and max(RAND) = 5, 20, 20, 100.

aver(RAND) := The mean value that the Dice Function will generate.

ie if RAND = 2d6-7, d20, mid(3d20) or d100 then min(RAND) = 0, 10.5, 10.5, 50.5

Theory

Standard Target Number Systems

In most standard Target Number Systems the objective is to add your skill value to a die roll and equal or beat a target number. Hence the player wants a high value from the die roll. So we can say:

Let DF be any Dice Function. (say d20)

Let TN be a Target Number. (say 15)

Let SK be a Skill Value. (say +4)

Target Number Test := high(DF) + SK >= TN

(TNT = high(d20) + 4 >= 15)

Standard Roll Under Systems

Notes

This is rubbish here for use whilst writing the doc - ignore it.

Skill_MCS := Skill_BCS + Professional_Bonus + Other_Bonuses

Skill_MCS + Situation_Modifiers >= (Low)d20