Ive been musing around various rpg system for a long time. Though it might be good to post them.
RPG Stat and Random Functions
-Passive- also know as a "Static" modifier/number/value.
-Active- A modifier/number/value with an added chance via dice or card or other type of randomiser.
Active Attack : 5 + 1d20 ( 6-25 )
Games that use passive calculations rely more heavily on strategy, whereas games that use active randomisers are about mitigating risk and reward.
Dungeons and Dragons uses an Active vs Passive for most non-magical combat actions. A melee attack (active) vs the target defense (passive).
One thing to note about d&d’s system is the defensive base number is 10, which is half of the 20 sided dice ( a d20) . The static 10 and active d20 are interchangeable. Having both Attack and Defense be active (both rolling d20’s) adds more variability, but may increase the time it takes to play. Having both be a passive (static +10) removes the variables of chance and the game plays more automatic. The rule of the static number being half of the active dice size goes for many types of RPGs. ( A d10 based system would have a passive of 5, etc.)
Magic in D&d is operates in either Passive vs Active, or Active vs Passive, depending on the spell. The target defends itself as defined by the spell's description using either:
Willpower, Fortitude, or Reflexes ( active) or Armor Class(passive).
Card games more often use a Passive vs Passive system and the gameplay is more about strategy, building up better numbers, and finding better combinations of effects. The random variable is the shuffled deck which the player blindly draws from.
Dice act as a variable that adds chance to the game. A 6 sided dice has a 16.33% (⅙) chance of each number. A 20 sided dice has a 5% chance to land on each number. A 10 sided dice has a 10% chance. Two 10 sided dice can be rolled together, one as multiples of 10 between 0-90 and the other for between 1-10, giving a 1-100 percentile chance.
Nearly all roleplaying and many video games work with these types of calculations. Final Fantasy, Super Mario RPG, Ogre Battle, X-Com, Fallout, Elder Scrolls etc. If you can see the numbers in-game, you can usually figure out the formula.
Roll 1 dice (like a d20) and add any relevant numbers from a character's ability or stat. This is a very common and straightforward system. It's easy to adjust how much a random dice roll can be by using different dice sizes and character ability amounts. Higher dice = increased random. Larger static numbers= decreased random. These are the important variables to look at when balancing game mechanics.
Roll a number of dice based on skill. (higher skill = more dice).
Variant 1- Add dice together for final result. This is effective because a pool of dice has a greater likelihood of an average-range final result.
Variant 2- Final result is the highest two matching numbers.If you roll 4 dice and 2 dice land on a 3, then the result is 3. If all 4 dice land on 3, then it's still 3. Some game give a bonus if there is more dice match, such as adding +1 to the result for each extra matching number. In that case 4 dice all landed on 3 then the result is 5( 3+1 +1).
Variant 3- Result is amount of matching numbers. If you roll 6 dice and 4 of them land on 6, the result is 4. If only 2 of them land on 6, the result is 2.
Abilities use different dice based on skill. In Savage Worlds RPG, a low level skill uses a d4. Each increase of skill increases the dice size, i.e. d4 to d6, d8, d10, d12. This slightly increases the odds of rolling a higher number, but the minimum is the same. This keeps the challenges fairly balanced for various levels of characters.
A special mechanic used in some variable dice systems is the "Exploding Dice". When a dice lands on its highest number, the player can roll again and add the rolls together. The odds of a dice exploding is higher with smaller dice so it adds a level of chance for a small dice to beat a higher dice. This is comparable to a critical hit in d&d D20 systems.
Dungeons and Dragons uses a basic variable dice system for damage calculations.