Blurb from the Box-On randomness: how random is random?

Today’s post will be a bit math heavy, but I promise to make it fun along the way!

 

Let’s say you and I decide to make an awesome new game.  We’ve decided to make “Fall of the 11th Age”, because 13 is too many ages for you.  A major part of the game is number 11.  We’re going to base the main dice mechanic on its so important.  You’ve had an awesome idea to make a cool new die called a d11 that will go from number 2 to 12, and you excitedly start making the game.  I say that we don’t have the kickstarter money to custom make d11s, so I start working on my version that uses 2 regular six-sided dice (2d6).  Since we both cover basically the same numbers (2 to 12), out systems look close enough to one another. So, we merge my and your ideas and start to really make some headway in the play testing.  But, some strange things begin to happen.  When we use my 2d6 system, things are pretty predictable.  The fighter almost always hits the goblins.   But, when we use the d11, the fighter misses the goblins ~50% of the time, and the wizard pulls of some hits that we didn’t think were possible.  What’s going on?

The answer lies in the math behind the game or, more specifically, the statistics of the dice.  Below I have two graphs.  The first is a graph showing how random each result is on the d11.  Statisticians love them some dice problems, so lots of work has gone into the dice.  On a fair die, every side has equal probability of occurring.  For our die d11, that means every side has a ~9% chance of being rolled.  This makes the behind-the-scenes math of “Fall of the 11th Age” pretty easy to figure out.  Here’s a quick example:  to hit the goblin, a fighter needs to roll a seven or better.  So the fighter can roll a 7, 8, 9, 10, 11, or 12.  That’s 6 numbers.  To find that probability of that occurring you multiply 6 by the probability of each event (6 x 1/11).  So the end result is 6/11 or ~55% chance of success on any roll.  I’ve put in a handy chart to show what I mean.

 

 

 

But things are not that simple when it comes to the 2d6 system.  Above, I mentioned how statisticians love them the dice, well a major part of that is how fair dice are and independent.  When you roll a d6, every die face has an equal probability of occurring.  When you roll two, each side has an equal probability of occurring AND what occurs on one die face does not affect the result of another.  There are a few assumptions that go with this and I don’t want to get crazy with physics of rolling dice together, so we’re going to keep this simple.  PLEASE!  It gets weird from here if we go deeper!  So dice are random and separate.  So when we want a result, to figure out the probability of that result we have to count the number of ways to make that result.  I’ve included a table to help with this.  A really important thing to note on this chart is how multiple dice roles make the same number.  For a simple example, look at the 3.  A 1 on the first die and a 2 on the second makes a 3 while a 2 on the first die and a 1 on the second also makes a three.  This is part of the independent results thing above.   So if we use the same “Fall of the 11th Age” math we used above with the d11 to hit the goblin, we need at least a 7 on 2d6.  There are multiple ways to make a seven.  For this, the best way to find the likely hood of this event is to ADD the percentage likelihood of each individual event.  So for a 7 to occur we add 16.67+13.89+11.11+8.33+5.56+2.78 which equals 58.34%.  This may not be a massive change from the d11 system, but it’s also not the whole story.

 

 

 

Besides just finding the likelihood of hitting the goblin, there is a few more statistics “things” at play.  These are the mean, median, mode, and standard deviation.  Let’s look at the first three.  A mean is the average that we all know and love.  For “Fall of the 11th Age,” we just add up the dice results of 2 to 12 and divide by the total number of events (11) which is 7.  The median is the middle value; think of the median as a balance on a teeter-totter on a play ground.  If we moved the middle of the wooden beam around a bit, where would both sides balance one another.  Again this is 7.  2 3 4 5 6-7-8 9 10 11 12  There are five numbers to 7’s left and five numbers to 7’s right.  Where things really get interesting is with the mode.  The mode is the most likely to occur event in our group of events, or another way to think about it is, the event with the most number of ways it can happen.  For “Fall of the 11th Age,” in the 2d6 approach 7 can occur the most often since six different dice rolls can make a seven.  But, in the d11 approach, there is NO MODE!  Every number can occur equally.  (Again, we can get all math argue-y with if there is no mode you take an average bla bla bla, but this is my article and I want to make a point, so NO MODE!).

Standard Deviation is a bit more complicated, and I won’t go into it all.  For a great summary, go to http://www.mathsisfun.com/data/standard-deviation.html.  But, a real simple definition of standard deviation is a measurement of how much things very.  You use standard deviation to find out how random your stuff really is.  Let’s look at the 2d6.  The average result is 7, but over 60% of the time, you will role between a 5 to a 9.  When you roll a d11, the results get a little more varied.  Using standard deviation, 60% of the time you will roll between 4 and 11.  (If you check my math, I’ve simplified down the actual results.  It makes life a bit easier).  What this really means is you are more likely to be closer to the average in 2d6 then with d11.

Why does this matter?  Well it matters for how random you want your random to be.  For 2d6 vs d11, the difference between 55% and 58% doesn’t matter much, but what if we only needed a 6 instead of a 7?  Using what we went through above, the d11 likelihood is now a 64% while the 2d6 likelihood is now a 71%.  The difference is getting pretty substantial at this point.  Also, how random you want extreme events to be?  For the 2d6 system, 12 or crit will only be 2.78% which is pretty low.  But, for the d11 system, it’s 9%.  The d11 dice don’t really care what side comes up (dice, they are a cruel mistress….).  And since the math works the same in reverse, critical fumbles work exactly the same way (2.78% cs. 9%).  If we graphed the d11 results we would see a flat curve of probabilities.  When multiple ways to achieve the same value occur, interesting new things occur in the data and your game.

The example above is a pretty simple.  Let’s look at something a bit more extreme.  Let’s use Dungeons and Dragons d20 vs. Hero System’s 3d6.  (Yes, I know 3-18 is a smaller range then 1-20, but I want to use some real world example for the gamers).  A d20 is a single die, every side is equally likely, so every side has a 5% likelihood.  For Hero System, I’ve put another chart below to show all the results and likelihoods to make life easier.  For this one the “%=” column give the probability of a dice roll, and “%>” is the likelihood of this and all higher number dice rolls.  Let’s say you have to roll a 9 to hit a monster.  For a d20, you have a 60% chance to get that event.  But, for the Hero System, its 74%.  Again, this major difference has to deal with the mode and likelihood difference between each number in the two dice pools.  A d20 doesn’t really have a mode (See rant on mode averaging above), while a 3d6 pool has a mode at 10 or 11 and each number has a different probability of being rolled.  What if we need to crit to hit?  In DnD with a d20, its only a 5% chance, but in Hero System’s 3d6 dice pool, I’m looking at a 10-fold lower difference with a meager 0.463%.  When you look at the standard deviation, you are most likely to get between 8 to 13 on 3d6, while on a d20, for the same probability, you will most likely get between a 5 and 15.

 

 

 

What the crux of this argument boils down to is likelihood differences in getting different dice values.  How much random do you want in your games?  When I do something in the real world, is my life a full of extremes or is it pretty average?  How often do things get crazy vs. stay normal.  How often do the normal expected results occur when I do something?  On a d20, if a10 hits and a 14 hits, since each are equally likely, does a 14 really represent more skill or just another hit since both are equally likely?  For 3d6, I feel there is a palpable difference in likelihood and it affects the stories I tell.

What do you think?  Now, no system is “wrong”, but what does the math “say” to you?  What do you feel when you play these different games?  Do you feel a difference when a modes and different outcome likelihoods enter the game vs. when it’s just one die?  One of my favorite systems Arcanis uses 2d10 plus an attribute die for its d20 + attribute rolls.  I love that system because you get all the fun of a d20 game, but you also get the predictability of a smaller standard deviation.  While I enjoy the randomness, I feel that helps help keep the game from being overly swingy or random.  What do you want in a game?  How random do you want your random?

Daily Punch 7-11-17 Dinomen race for DnD 5e

DnD is going South, so why not have Dinomen to compliment the dinoriders!

 

 

Dinomen

Dinomen are a race of mystery and division.  Dinomen come from the southern jungles, living in isolated tribes of hunter gatherers.  They survive as a tribe through hard work with little contact with the outside world.  They are not know for their technology, but what they do have is  strong crafted stone tools.  Dinomen are not are not often found ranging from their homes, but when they do find society, they do fit in well to a new group.  Dinomen are know for quick growth, but their brains lag behind and even full grown dinomen standing over eight feet tall may only be as developed as a child.

The origin of the dinomen is a mystery.  Some speculate that their sentience was a gift from their mother goddess and the carnivores was a bane from their dark hunter god, while others point to wizards merging men and dinosaurs to create a stronger working stock.  In either case they have existed for centuries, and show no signs of going extinct any time soon.

An oddity among the dinomen is their complete lack of animal husbandry.  It is not known why their groups have not domesticated other, lesser dinosaurs or other creatures.  It is suspected that some dinomen might view this as slavery to their kin or that simple hunger may drive carnivores to eat all captures livestock.

Physical Description

The one commonality among all the dinomen is that they differ.  Dinomen very from depending on the stock they derived from.  Dinosaur men who were shaped from long necked, long bodied dinosaurs can stand over 10 feet tall.  Dinomen who derived from raptors might stand hunched and stand less then four feet tall at the highest point.  The all stand bipedal, but some have faces with too many teeth while others are slow herbivores who chew grasses constantly.

Society

The one truth about dinomen that is common among all the veried types is their tribal nature.  Each tribe of dinomen forges a close bond among all members of the troop.  These people work together in socialist, egalitarian groups.  However, trade between groups is looked up with suspicion as each group is unsure of the motives of the others.  Carnivores follow this as well, but their harvest tend to be more grizzly than their herbivore brothers.

Relations

Dinomen among other races are rare.  They function in society extremely well, but they tend to shun others as they are a naturally cautions race.  They tend to prefer open jungle, so dwarven ruins and other underground races see these people even less then the surface races.

Alignment and Religion

Dinomen tend to live simple lives where government is not an often considered problem.  Thus these people tend to be chaotic compared to other races.  They do follow traditions of their tribes, but they do not follow most laws seeing individual possession as asynchronous to survival of the tribe as a whole, thus they do not agree with most property laws.

For religion, they follow a polytheistic religion where two main gods view for dominion.  These two gods have different views depending on the nature of the dinomen.  Herbivors view the Grand Mother as a generator of all life and intelligence of their race, while they feel here opposite is the Dark Hunter stalking among the evil taking the good to be devoured in the dark.  Carnivores see the Dark Hunter as their noble progenitor teaching intelligence as a trick to harvest more prey, and the Grand Mother the simple behemoth who and whose children must be stalked as a necessary part of the circle of life.

Adventurers

Dinomen who do not want the simple tribe life are always free to leave the group.  This is a monumental step in an individual’s life as leaving is seen as suicide among the herbivores and being a traitor among the carnivores as they hunters now have a harder time surviving, but no one will stop this process.  Those who see a wider world leave often to find new hunting grounds or more interesting places to roam.

Male Names: Thark, Nurak, Berdic, Hiore, Mioric.

Female Names: S’ssars, Ppric, Weir, Quuica, Gricss.

 

Ability Score Increase: Your Strength score increases by 1, and your Constitution score increases by 1.

Age: Dinomen grow quick, but develop their intelligence slowly. They walk hours mier minutes after hatching, grow to the size of a man by age 2, but are not considered adult till then reach 20 winters.  They live to be around 70.

Alignment: Dinomen are creatures of instinct, and most tend to align more toward chaotic than lawful.  They can be both good and evil, but their tribal, family nature makes them much more likely to settle disputes through force then arbitration.

Size:  Dinomen stand taller then men, but vary depending on the type of dinosaure they came from.  Some dinosaurs are hunched and stand less then four feet tall, while long necked dinomen could easily stand taller then 10 feet tall with most of their height being their necks.  Your size is medium, and your base walking speed is 30 feet.

Dinosaur Toughness: Your family comes from dinosaur stock, and you evolved to survive hard attacks.  Increase your armor by +1 as your has a natural armor bonus from your hide.

Tooth and Claw: Whether from your spiked tail or large teeth and claws, you are a force to be reckoned with.  You are considered proficient with unarmed attacks, and your unarmed attacks do 1d4 piercing damage.

Darkvision and Colorblindness: Accustomed to running in the dark jungle, you have superior vision in dark and dim conditions. You can see in dim light within 60 feet of you as if it were bright light and darkness. You can’t discern color in any situation.

Dinosaur Heritage: Your ancient ancestors had to track game or find food in the wilderness, and this ability was passed to their young.  Gain proficiency in Wisdom(survival).

Languages: You can speak, read, and write Common and dinosaur. You can speak a rudimentary language that most dinosaurs speak.  It is a guttural language with clicks and sequels that most humans find almost impossible to speak.

Subraces

Herbivore

You come from the dinosaurs who had to defend themselves to survive from the terrors of the dark.

Ability Score Increase: Your Wisdom score increases by 1.

Herd Tactics: Gain proficiency in Strength(athletics).

 

Carnivore

You derive from a long line of solitary hunters who stalked their prey through cunning and stealth.

Ability Score Increase: Your Intelligence score increases by 1.

Herd Tactics: Gain proficiency in Dexterity(stealth).

Daily Punch 7-10-17 Seelendieb sword for DCCRPG

My wife found a sword in DCC.  She loves it, but maybe she shouldn’t….

 

 
Seelendieb-this is a +1 longsword of impressive sharpness that also increases the wielders strength by +4.  It’s hilt is shaped like interconnected grasping hands of bone with the crossbar being a spine.  It was forged by a god of death and destruction and gifted to his chosen paladin to steal life in the multiverse.

INT: 18; PERS: 16; does not possess the wielder.  Wielder gains hit points equal to half damage dealt, and then the wielder then makes a Will saving throw, DC equal to hit points recovered.

Fail First Three-The sword now makes the hit point recovery feel amazing.  This process is almost addictive.

Fail Next Three-The wielders alignment shifts to chaotic.

Fail Final Three-The wielder becomes a soul wraith.  There is no physical change, but the character now eats souls instead of food.  This is done as an action over an intelligent creature that died less than 1 turn ago.  The character can also consume blood of intelligent creatures in place of souls.  The character heals damage as if they has used lay on hands on themselves using their own attributes if they drink blood.  The character can no longer heal hit points as normal, but may be healed by a cleric of a neutral or chaotic deity.  Healing from a Lawful cleric harms the character, but the character is allowed a Will save to prevent the healing, DC equal to amount that would the dealt as damage.  The character’s title shifts as follows depending on the level:

1-Thrall

2-Damphyr

3-Aufhocker

4-Vampire

5-Dracul

Daily Punch 7-6-17 Shadow Evocation for DnD 5e

I was about to convert shadow bolts for DnD 5e, but shadow evocation does not exist for DnD 5e!  Let’s fix that!

Shadow Evocation

5th-level illusion

Casting Time: 1 action
Range: see text
Components: see text
Duration: see text

You pull concentrated shadow from the plane of negative energy and throw it with your will as an imposter evocation spell.  When you cast this spell, choose an evocation spell of level 4 or lower.  This spell mimics that spell cast at the lowest level spell slot it is able, except the spell is now disbelieved with a Will saving throw instead of either a different saving throw or spell attack roll.  If the original spell required multiple attacks or saves such as magic  missile or scorching ray , each attack requires its own save.

At higher levels: When you cast this spell using a spell slot of 6th level or higher, you may choose to increase the effective level of the copied spell by one or choose to cast a one level higher evocation spell for each slot level above 5th.

Daily Punch 7-5-17 Shadow Bolt Spell for Pathfinder

What if Shadow Evocation and Magic Missile had a baby….

Shadow Bolts

School illusion (shadow) [shadow];   Level bloodrager 1, magus 1, sorcerer/wizard 1

CASTING

Casting Time 1 standard action
Components V, S

EFFECT

Range medium (100 ft. + 10 ft./level)
Duration instantaneous
Saving Throw Will disbelief ; Spell Resistance yes

DESCRIPTION

You tap energy from the Plane of Shadow to cast a quasi-real, illusory version of magic missile.  The spell functions exactly as magic missile casted by a character of your level for all effects and damage except all affected creature can attempt to disbelieve via success on a Will save. Each disbelieving creature takes no damage.  If the spell is  believed, then the target may react as if under magic missile attack, but effects such as the shield spell are expended without stopping the effect.

Daily Punch 7-4-17 Basic Errors negative quality for Shadowrun 5e

How about some shadowrun fun?

 

Basic Errors
Bonus: 5 Karma
Some people  are good at the hard stuff, but choke when they get simple.  A character with Basic Errors suffers no penalties to clutch actions, but attempting to do an action when unhurried such as driving on easy roads or doing a simple computer search for dinner must attempt an edge check.  If  if the character does not get three successes, then the character fails the simple action resulting in a critical glitch.  How often this occurs is up to the GM, but should not occur more than twice per session.

 

Thoughts?