ABS12: The anatomy of the combat numbers

All the changes from this page will be added to the complete master game page at A Basic System 12 (ABS12).

For this post, I wanted to look into what exactly the numbers in the formula mean. This is important to help determine how to describe actions.

Minor change

One other change I'm making is removing the PL from PL damage roll, PL Live, and PL defense, which don't seem to make sense anymore.

Verb Skill formula portions

1. Situation roll portion

The first roll 1d12, in every type of roll means the situation roll. Situations can vary from good to bad. The first random roll tells you how good current situation about the skill or combat.

Player should describe exactly how the character does something, not just what a character does. 

If a character uses a description verb to look for clues, then the player should explain exactly how the player will search for clues. Will they look through all the drawers and cupboards? Having explained how the character will search, the roll can then be performed to describe how lucky fate is with the character in performing the task.

Interpreting the numbers

A 1 is so bad that it's a fumble. A 12 is so good that it's a automatic success.

Describing the situation depends upon what type of action is being performed. Once you have that action in mind, you can describe the situation surrounding the action using adverbs and adjectives in similar degree to the the result rolled. The situation may be environmental. It may include actions of opposing characters. It may include the conditions of the character performing the action.

Above six becomes more positive.

Below six becomes more negative.

Here is a general adjective scale denoting quality and degree for the situation surrounding the how the action is performed.

If as in the prior example, if the character is looking through all the drawers and cupboards looking for clues, and the player roll a three - what does that mean?. A three is very bad. What could a very bad situation mean or look like when searching through cupboards and drawers? It might mean that the character rushes through the search doing a poor job of searching. It might also mean that despite ones great skill, something happens to be covering the thing that the character is trying to find. The first explanation is a more method based or quality of performance rational. Whereas the second one is luck based or quality of the environment. Either way, they both explain and describe a the situation that is very bad.

2. Learned description level and power level experience portion

Both the PL and DL portions are fixed. 

The PL represents experience as the character acquires more real world experience. Characters recognize patterns and appropriate methods just by watching life around them. The learn little tricks to help live even doing unskilled and untrained actions easier. They have life knowledge.

The DL represents learned skill. It represents actual study, practice, exploration, teachings, and education. They receive education formally or on the job.

The next portion of the formula appears in combat. It is a special kind of roll called the damage roll.

Offensive roll 1d12 + PL + DL + Damage roll

3. Why is the damage roll added to the offensive roll?

The damage roll represents how viscous and potentially damaging the attack, blow, or strike is. The damage roll is potential damage, rather than actual damage.It represents how deadly the strike could be - how much force and accurate the blow may be. Even with a little lesser luck, a very powerful attack my still do damage if the attack is powerful. Too much of a bad situation will make even a powerful attack miss. Yet a great situation might help a weak attack still hit and do damage depending on the defender's situation.

The lowest damage possible is 1. Even variable damage weapon will at least do 1 point of damage

In damages where even a roll of 1 is made out of 1d12/6, = is all one or the other. There is no fumble or automatic success from the damage roll. Your only trying to find the amount, in this case 1 or 2. It's either one or the 

Damage roll is countered with the armor value portion of the defense. The defender offsets the damage roll with their fixed defense which is made up of skill (DL) and experience(PL) plus any armor.

Damage Table

A Basic System 12 (ABS12)
Index of my blog

Dice, Cards, and Probability part 4 More than one dice

In this Dice, Cards, and Probability Series

In Part 1, I looked at probability, notation, number of occurrences.

In Part 2, I looked at linear die/dice (single) results

In Part 3, I looked at the d12, rolling over, rolling under, modifiers, target numbers, difficulty, proficiency, and values

More than one dice

Comparing the 1d12 flat probability to multiple dice, a dramatic shift in shape and probability results from adding more dice.

Looking at max 12 combinations

Following along my own interest, I will consider three dice combinations that can fit in with the 1d12 for comparison. These are 2d6, 3d4, and 4d3. I do this for comparison purpose. In a similar manner, other dice combinations can be looked at with the same principles and influence of using multiple number of a certain dice.

2d6

2d6 is an extremely popular system at the moment.

Its results form a pyramid shaped probability.

3d4

This probability is more round.

4d3

This is the basis for Fate and Fudge dice systems. This is a steep bell shape.

Fate/Fudge

This is a popular cinematic system, the current edition is the third edition. It is based on 4dF dice which have a -, +, and 0 sides meaning -1, +1, and 0. Because of rolling four dice, the results are a curved probability of -4 to +4 with the center 0 being the most frequent result.

Comparing the four dice that max at 12 result

1d12 is very flat.
2d6 is a sharp pyramid shape
3d4 is rounded
4d3 is a steep bell curve shape

Of course, the more the dice the higher the initial number, effectively squeezing the available results narrower.

At the ends, the probability goes down from 8.33, to 2.78, to 1.56, to 1.23.
In the middle, the probability goes up from 8.33, to 16.67, to 18.75, to 23.46.

Summary

A linear system is fine with a plain 1d12 and 2d6.
Curvilinear systems may want distributed results that 3d4 and 4d3 (4dF) gives a game.

Dice, Cards, and Probability part 3 The d12

In this Dice, Cards, and Probability Series
In Part 1, I looked at probability, notation, number of occurrences.
In Part 2, I looked at linear die/dice (single) results

Having seen what a single die/dice of can role and compared them to each other in the prior post, I wanted to spend this post looking at specifically the d12 and a potential framework for using it. In a similar manner it and any other based dice can construct similar mechanics.

Mechanics

To compare mechanics, I will either use open source or unrestricted single systems by name, or mention summaries of copyright systems only by reference to a created summary name, not their proper names.

The first mechanical difference seen between systems is that many are roll-over systems. However, there are a few roll-under systems. After that, I focus on the core mechanics of modifiers (bonuses and penalties), proficiency/skills, and then the difficulty ladders.

Rolling over or rolling under

Systems are either of two types. Rolling over and rolling under a certain value. Also the system must address what rolling equal to that certain value means.

The roll over system either compares against another character's roll or a target number based on difficulty. The roll under system normally uses the base state + skill as the number to roll under. Both types are modified with bonuses and penalties.

We will look at two roll over systems (a converted d20 and a full d12) and then a d12 roll under system.

Modifiers

Modifiers for abilities, skills, proficiency, and situations can be also applied either to a roll or a target number.

Target/difficulty number in both systems

In a roll over system, a chart of standard target numbers by difficulty must be created. This is used to figure out what number must be rolled over when tasks must be accomplished when not competing against another sentient being. In those competing tasks, the target number is rolling against the other being.

In a roll under system, difficulty is normally a modifier to the stat + skill basis.

Breaking it apart

Systems normally have besides the dice roll adjusting modifiers based on attributes, stats, skills, abilities, magic bonus, equipment bonus, talents, gifts, species bonus, and such. We will analyze a few popular open license game content to help us see different perspectives.

1d12 Probability Graph

A summary of the linear graph can be shown in this image. We can compare this probability chart of rolling 1d12 to other types of rolls.

image made at anydice.com

1.) d20 5e converted system ¹

Starting with the latest of the d20 systems, 5th edition is the newest incarnation. It is based on a d20 as mentioned. The main modifier is the Ability Modifier, based on an ability score that is normally from -5 to +5 but sometimes is up to +10. That modifier is added to the roll and compared to a target number. Proficiency bonus from +2 to +6 is given for select skills. For skill checks, the target number is in increments of 5 up to 30, for a total of 6 degrees of difficulty. 5e (fifth edition) is a modified roll equal to or over the target number to succeed type system. For contest checks, each side rolls and modifies. The higher number wins, and ties means the situation remains the same. For combat, armor type bonus called armor class, Dexterity bonus, and a few other defensive bonuses determines the basic target number that the players need to roll equal to or greater to cause damage. Spells are automatic as long as conditions are met, except for some that require attack rolls and resistance rolls, which are also based on  the ability modifier.

Bonus and Proficiency conversion
Bonuses -5 to +5 (+10)
Proficiency Bonus +2 to +6
Bonus Percentage of dice= -25% to +25 (to +50%) of d20

d12 Bonuses - based on d20
d20	-5	-4	-3	-2	-1	0	+1	+2	+3	+4	+5	+6	+7	+8	+9	+10
d12	-3	-2		-1		0	+1		+2		+3		+4		+5

Difficulty conversion
Difficulty 25% to + 150% of d20

d12 Difficulty numbers
d20 Difficulty Adjective	Very Easy	Easy	Medium	Hard	Very Hard	Nearly Impossible
d12	3	6	9	12	15	18

This is a conversion of to parts of the mechanics that go with the dice rolls. The bonuses are added to the rolls based on what activity or skill designates the ability bonus (str, dex, con, int, wis, cha). Unlike the d20 previous versions, 5e doesn't have individual skill bonuses added on top of that, but rather uses a proficiency bonus for certain proficient skills. The bonus conversion chart can also be used to find the proficiency bonus.

Advantages and Disadvantages: 2d12

Earlier versions of d20 provide additional bonuses or penalties for situation, special abilities, traits, and environmental factors. Edition 5 now uses advantage and disadvantage rolls instead of adding and subtracting bonuses and penalties.

Advantage

 If an advantage is judged to be in effect, the higher of 2d12 results is used. As you can see, the probability is no longer flat. Instead it leans more towards the upper numbers.

Image made at anydice.com

Disadvantage

If a disadvantage is judged to be in effect, the lower of 2d12 results is used. As you can see, this is opposite of the Advantage roll. Now the results lean towards the lower numbers.

Image made at anydice.com

2.) A d12 system²

For this system, parts of it seem d20 related and part seems Fate related. First, comparison to the d20 conversion seems appropriate.

Instead of a d20-like attribute and proficiency system, it uses instead a +1 or +2 bonus very Fate-like. It does use however the advantage and disadvantage 5e roll system.

d20 conversion compared to a d12 system

The limit to normally +2 bonus and proficiency limits the 'impossible' skill level to 14 max (roll 12 + 2 bonus).

d12 Difficulty numbers
d20 Difficulty Adjective	Very Easy	Easy	Medium	Hard	Very Hard	Nearly Impossible
d12	3	6	9	12	15	18
A d12 system	Easy	Moderate	Hard	Very Hard	Impossible
d12	4	6	8	11	14

3.) Another d12 system³

Another d12 system uses the ability stats as a basis for a roll under system. Stats begin at 1 and can go above 12. Rolling a 12 however is automatic failure, so increasing above 11 only helps offset situation penalties.

Attributes in this game normally range from 1 to 4. In this other system they are permanent after initial character creation. Skills on the other hand can increase higher. Their chart goes up to skill level 12. They can be increased through spending points awarded from adventures.

Difficulty chart - modifiers

Although they do not have a comparable difficulty chart. A modifier chart can be constructed based on the samples of penalties.

Another d12 Difficulty modifier
Difficulty Adjective	Very Easy	Easy	Medium	Hard	Very Hard	Nearly Impossible
bonus/penalty	+4	+2	0	-2	-4 or -6	-7 to -12

Next Month

Probably will be Part 4 Rolling multiple dice probability

¹http://dnd.wizards.com/articles/features/systems-reference-document-srd
²https://d12rpg.com/
³http://www.dominiongames.com/download.html

Dice, Cards, and Probability part 2 Linear Results

In Part 1, I looked at probability, notation, number of occurrences 

Linear Die/Dice (single) Results

Looking at single die/dice rolls, which are linear in results. Linear means that there is a set incremental probability, which if graphed would form a straight line. Rolling a single die gives linear results. As opposed to rolling multiple dice which would create a curvilinear result, normally more triangular or in a bell curve shape.

Important probability increments

Fifty-fifty

The first natural probability divide is half. Fifty-fifty chances, much like the flip of the coin, is a common and popular. All of the dice except d3 can show fifty-fifty percent rolls, since the rest are multiples of two. These are d6, d8, d10, d12, and d20

Rule of thirds

Sometimes things aren't just "yes or no" or "black and white". Sometimes you need "maybe" and "gray/grey". Those dice divisible by three can show such results excactly. These are d3, d6, and d12.

Quarters

Another popular divisible chance is in quarters. Number of dice divisible by four can show such results exactly. These are d8, d12, and d20.

Dice Probability d3, d6, d8, d10, d12, and d20

# number, #% percentage of rolling that number, >% percentage of rolling greater than that number, >=% percentage of rolling greater or equal to that number.

d3
#	#%	>%	>=%
1	33%	67%	100%
2	33%	33%	67%
3	33%	0%	33%

d6
#	#%	>%	>=%
1	17%	83%	100%
2	17%	67%	83%
3	17%	50%	67%
4	17%	33%	50%
5	17%	17%	33%
6	17%	0%	17%

d8
#	#%	>%	>=%
1	13%	88%	100%
2	13%	75%	88%
3	13%	63%	75%
4	13%	50%	63%
5	13%	38%	50%
6	13%	25%	38%
7	13%	13%	25%
8	13%	0%	13%

d10
#	#%	>%	>=%
1	10%	90%	100%
2	10%	80%	90%
3	10%	70%	80%
4	10%	60%	70%
5	10%	50%	60%
6	10%	40%	50%
7	10%	30%	40%
8	10%	20%	30%
9	10%	10%	20%
10	10%	0%	10%

d12
#	#%	>%	>=%
1	8%	92%	100%
2	8%	83%	92%
3	8%	75%	83%
4	8%	67%	75%
5	8%	58%	67%
6	8%	50%	58%
7	8%	42%	50%
8	8%	33%	42%
9	8%	25%	33%
10	8%	16%	25%
11	8%	8%	16%
12	8%	0%	10%

d20
#	#%	>%	>=%
1	5%	95%	100%
2	5%	90%	95%
3	5%	85%	90%
4	5%	80%	85%
5	5%	75%	80%
6	5%	70%	75%
7	5%	65%	70%
8	5%	60%	65%
9	5%	55%	60%
10	5%	50%	55%
11	5%	45%	50%
12	5%	40%	45%
13	5%	35%	40%
14	5%	30%	35%
15	5%	25%	30%
16	5%	20%	25%
17	5%	15%	20%
18	5%	10%	15%
19	5%	5%	10%
20	5%	0%	5%

Deck of Cards

Also, I look at what a person can do with a standard 52 card deck when shuffled. A disadvantage of the card deck is that to retain the probability, one must reshuffle, or the probability changes each additional drawing of cards.

I also notice that one can use a 12 sided die/dice and nearly get the same probability, since the difference between 12 and 13 chances is very minimal.

Standard Playing Card 52 card deck (French suit)
Action		#%	>%	>=%
Picking one specific card	1/52	2%
Picking one number or face	1/13	8%
1 (ace)		8%	92%	100%
2		8%	85%	92%
3		8%	77%	85%
4		8%	69%	77%
5		8%	62%	69%
6		8%	54%	62%
7		8%	46%	54%
8		8%	38%	46%
9		8%	31%	38%
10		8%	23%	31%
jack		8%	15%	23%
queen		8%	8%	15%
king		8%	0%	8%
Picking a face [jack, king, queen]	12/52	23%
Picking one suit [spade, club, heart, diamond]	1/4	25%
Picking a red (or black)	1/2	50%
Picking a non-face	40/52	77%

Comparing Dice

Here is a linear version, rounded to multiples of 5, comparing all six dice.

Dice Comparison Probability
Die/Dice	5%	10%	15%	20%	25%	30%	35%	40%	45%	50%	55%	60%	65%	70%	75%	80%	85%	90%	95%	100%
d3	33%							67%						100%
d6	17%			33%				50%			67%			83%			100%
d8	13%			25%		38%			50%		63%			75%		88%			100%
d10	10%		20%		30%		40%		50%		60%		70%		80%		90%		100%
d12	8%		16%	25%		33%		42%	50%		58%		67%	75%		83%		92%	100%
d20	5%	10%	15%	20%	25%	30%	35%	40%	45%	50%	55%	60%	65%	70%	75%	80%	85%	90%	95%	100%

Thoughts on d100

I did consider d100 briefly, but then realized something. Looking over most of the bonuses of the d100 systems, they seem to change by +/-5. If most d100 systems ignore bonuses not multiple of 5, that tells me that going below 5 will not really affect the final result sufficiently. A +1 for a d100 isn't really much of a bonus to affect the outcome. In a sense, they seem like d100/5 systems - basically an exploded d20 systems.

Conclusion

I really like d12

Although d20 is the die/dice of the more popular games, I am seeing d12 as a very good one which can also do the rule of thirds type results, as well as quarters and halves. Using d12 also somewhat mimics a deck of cards.

I had never considered using a d12 as a main part of a system. However, looking over the probability, I may prefer d12 over d20. Doing so may also help to crush down the run-away bonus/penalties to more like +/-3 ranges much more like Fate/Fudge.

In the next dice post Curvilinear or Bell Curve Results. 

Dice, Cards, and Probability

Part 1 - Dice, Cards, and Probability - Foundation

This blog post is the first for a possible series of posts concerning dice and card probability. While I do not present any new information, I am posting this so that the basics will be covered.

I plan on looking at d20, d6, d100, and card decks in the future.

What is probability?

Probability is the chance or likelihood that an event or situation will happen or occur.

How do you simulate random occurrence in gaming?

In RPGs, probability and random occurrence is simulated through multiple means, methods, tool, or medium that a random probability is generated, called Random Number Generator (RNG) in computer science. Dice are the most commonly used tool to generate random numbers. Two other popular physical RNGs are a deck of cards and a computer program, app, or website. Coins, rock-paper-scissors, or guessing a number between _ and _ are other less popular methods.

Expressing the probability of single occurrence using notation.

In math, basic probability can be expressed in terms of "how many times occurrences" out of "how many times attempted".

let # = number
let O= # of occurrences
let T= total number of tries

successful O out of total T
"out of" keyword O out of T
Colon O:T
Division notation O/T or O÷T. It's best to simplify fractions.

Since probability can be expressed as a division, you can find a decimal between 0 and 1 by dividing the total number into the number of occurrences.

And that number can be converted into a percentage (%).

An example of expressing the probability of getting 'heads' on a coin flip.

For example: A coin flip is either heads or tails.
The chance of getting heads is one occurrence out of two: either heads or tails.
1 out of 2
1:2
1/2
To convert the chance of
1/2 or 1 ÷2 = 0.5
0.5=50% chance

Combinations Formula

! = factorial symbol
let n = number of items
let r = number of items being chosen at a time
nCr = n!/r! * (n-r)