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Friday, November 10, 2017

The Anatomy of: AAIE Dice Mechanics.

Check out the rest of the  AAIE "Anatomy Of" series:
The series includes:
The Anatomy of Weapons.
AAIE "The town"
The anatomy of Balance.
The Anatomy of a Perk.
The Anatomy of an Ability
The Anatomy of AAIE Magic


Posting this to answer some questions that have come up lately , specifically about  what are the "standard" difficulties in AAIE, which was asked at Metatopia this year of our lord 2017.
I figured the best way to answer that question would be to  disgorge the die system in all it's fetid glory.

Try not to fall asleep this isn't the most exciting game stuff post ever..

AAIE is built around a concept of Bell Curves vs A straight distribution.
When I started this game I ripped the die mechanic form my table top skirmish game lovingly known as "The Block Game." Way back when I wrote the Block Game I decided that I didn't want a straight distribution of 5% per vlue that 1D20 provides. I wanted something that offered more options. More ways that the game could manipulate the chance of a characters attacks being successful. IN that effort I started looking at  the distributions of rolling more than one die with one being designated an "Effect Die" to  determine  attack damage. I figured the success chances back then, when AAIE came around I just used the same methods..

Hold your breath lets do this:

At its base  the game is this: For any normal action the player rolls 3D20 and looks at the  middle value versus a difficulty to  determine success.

For example:
If the player rolls three dice and they come up 12, 7, 16  the middle value is  12.
IF the  player has disadvantage on the task they look at the lowest value in our example 7.
If the player has advantage they look at the highest value in our example 16.

Typical difficulties look like this:
Very Easy: 6
Easy: 8
Average: 11
Difficult: 13
Very Difficult: 16

The  Game master lowers the  difficulty of a task based on the attribute (if any) the character can use during the task. If lifting a log's difficulty is 11 and the  players brawn is  4 the  final difficulty  will be 7. For the example character an average task is actually pretty easy.

Question: "Why does the  GM do subtraction? That seems strange and  kind of shitty."

Well yes it is.  That brings us to the straight distribution portion of this  dance.
The simple Answer is  if the  Difficulty falls to 1 or below  the  player doesn't have to roll to succeed they just do.

The complex answer involves the "Effect Die." The effect die is any one of your three D20 designated at the beginning of the game which determines how successful a successful roll is and how horrid a failed roll is.

Effect die:
Rolling a 16 or over on the  effect die during a successful roll means the  character can invoke perks, which are special effects that character skills or equipment can bring into the story.
Rolling low on the effect die during a success allows the GM (at their discretion) to interject complication into the character's success.
Rolling high on the  effect die during a failure allows for the Gm to  create partial success situations, where the character fails but still gets something done.
Rolling a 1 on the  effect die during a failure creates a critical fail situation which is about as bad as it gets.

Remember the question a paragraph or two above? 
If the difficulty is 1 or less the player only needs to roll the effect die. They automatically succeed but  they still need to determine how strong a success they have scored.

So they roll 1d20 giving them a 25% chance to score at east one perk by rolling a 16 or better.

Which as you will see below is a solid 5% better chance of scoring at least one perk then the best chance a  player can get on an average difficulty roll. In  fact it's .70 % chance better than  scoring a perk on a normal roll if the difficulty is only 2. Lastly it's still .02% better (WHOOPEE!) chance to score a perk even if the  player has advantage on the roll and the difficulty is only 2.

In other words in it's mathematically in the players best interest to get the  difficulty down to  or less if they can.




The maths:
Here are how the difficulties stack up with disadvantage versus Normal versus Advantage.
The chart also shows the % harder a disadvantaged roll is vs a normal roll, and the % easier easier an advantaged roll is vs a normal roll at each difficulty tier.



Here is any dice figuring the  Advantage  distribution:



Here is the  Normal roll distribution:


Here is the Disadvantage Roll Distribution. 

So Using the  same maths,  I can figure out the  chance to get a success vs a difficulty of 11 and roll over a 16 or better on one D20 to score a perk. ...

At the same time I'll look at what the chances of rolling a failure versus an 11 difficulty and also roll a 1 on a separate D20 (which is what is in effect happening when you designate one of the D20's as the "effect die."


What you want to look at here is the  bottom graph  which shows the  % chance of the statement being "true" as in "did I roll over 11  and also over 15 on the effect die"

This tells me that if I have Advantage I have a 20.84% chance to  be successful and score a perk.

On the  other side of the  scale if I have Disadvantage I have a 4.38% chance of  failing vs a difficulty of 11 and also  rolling a 1 on the effect die...probably causing my character to  explode in a mushroom cloud of  feathers and  bile.

To wrap this up nicely the game die mechanic can be said to revolve around the base chances and how the player's actions / characters attributes stack up against challenges in the narrative environment.

The middle ground ... those  base chances.
A  normal roll vs an 11 difficulty the player has 50% chance of success or failure, an 10.63% chance of success with a perk, lastly a 2.5% chance of a critical failure.

So that's that a look under to hood at how how the  dice in AAIE shake out. (HAr HAr)
I'm sure there have been some mistakes along the way.. I'm no statistician, Not even close. However if there are mistakes, I'm going to have to let them be because I built the mechanic on this foundation a long time ago.

WHEW .. That's a bunch.
Thank you for reading ..
-Mark

Check out the rest of the  AAIE "Anatomy Of" series:
The series includes:
The Anatomy of Weapons.
AAIE "The town"
The anatomy of Balance.
The Anatomy of a Perk.
The Anatomy of an Ability
The Anatomy of AAIE Magic


All calculations done with  "Any Dice" found here on the web. It's a great tool.