Critical GLOG: Base Resolution Mechanics

It has not escaped my notice that GLOGhacks are sort of a thing.

There's even a subreddit with a list of GLOG resources. (And a lot of them are actually quite good.  At some point I intend to sift through them all and showcase all of their innovations.)

Usurpers, know that your challenge has been heard.  I am Very Advanced at the GLOG.  I, Arnold, will knock you all down!

I'm going to write ~5 GLOGs to demonstrate this, but not before philosophizing for a few blog posts first.

Anyway

The GLOG is a philosophy, not a specific ruleset, much less a specific rule.  (Although, yes, the magic dice are very nice, but they are not essential.)

To restate the central thesis of the GLOG:

It is folly to think that there is one true rule system. 

It is folly to think that one ruleset is superior to another in every way. 

Even the shittiest rulesets have something to teach us. 

The best game at your table will not be the best game at my table.  Our groups need different things--they are full of different people. 

Your job (as DM, but also as player) is to run the best game for your table. 

The best game for your table does not exist in one book.  It exists in several.  Your salvation requires you to steal.   

The best game for your table will also probably require some things that are not written down in any book.  Your salvation may also require you to invent.  

You have been lied to.  The only difference between rulings and rules is that one is written down slightly earlier. 

Steal, invent, remix, destroy, and recreate.  Sharpen your ruleset.  It will never be sharp enough, but it will be better, and it will be yours. 

There is a huge fallacy that tabletop rulesets are something that must be crafted by masters and carefully balanced.  I remember watching this internet woman talking about she was ready to play a custom class that had been made for her, especially now that she had paid to have it professionally balanced.  

It shouldn't be like that.  You should be authors of your own game, not renters of someone else's.

Anyway, the first step in making your own game is learning not to suck at game design.

Considerations

When you are considering a Base Resolution Mechanic, there are some things you need to ask yourself first.

There are also nine characteristics of a base resolution system, which I'll elaborate on below.

Why Have a Resolution Mechanic?

Why do we even need dice at all?

Weirdly enough, I've run excellent sessions where the dice hardly touched the table.  The gameplay was driven by player actions, and all of their choices had immediate, interesting consequences that didn't require any random chance.

Lots of point and click video games get along fine without any sort of RNG.  I'll fight you if you say that Secret of Monkey Island wasn't fucking great.

In tabletop, we use dice because:

• some actions don't have obvious results (e.g. does my arrow hit?)
• broadly, to have more unexpected things happen (especially for the DM)
• specifically, to insert more dynamism into combat
• it's just fun to roll dice and say "yay" or "boo"

Even shitty games are fun if you add dice.  Snakes and Ladders.  Monopoly.  They become fun because the dice add just a little bit of chaos into the mix, especially when you can alloy it to how much fun it is to compete against friends.

Bottom line, you don't.  You can just Monkey Island it.  But if you're reading this, you're probably already pretty committed to using dice, so I'll press on.

Why Have a Base Resolution Mechanic?

Why have just one resolution mechanic when you could have several?

This is a non-trivial question.  I've definitely played games that had too many resolution mechanics.  

But I think the opposite problem is more common--I've definitely played a lot of games that have relied too heavily on d20+number vs DC.  The D&D diaspora has turned d20 into sort of a lingua franca, and now it's essentially the evolutionary trunk of this tree, for better or worse.

Systems that want to differentiate themselves usually make a big deal of their core mechanics.  This my thing, my gimmick, and it's superior to everyone else's.

It's one of the big ways that game can distinguish itself from it's competitors.  VtM uses dice pools.  Dungeon World uses that 2d6 thing.  West End Games had a d6 thing.  BitD has a different d6 thing.  The frothing carcass-lineage of 3rd edition continually spawns d20 systems, and we will eventually drown beneath them.

So, a Universal Resolution Mechanic is often tied to a system's identity.  They rarely change.  Call of Cthulhu has always been d100 roll-under, even though you could convert it to d20 roll under relatively easily.  The central dice mechanics are the parts among the most resistant to change within a system, because they are the Most Sacred Cow.

Having fewer resolution mechanics is nice because players have fewer things to learn.

Having more resolution mechanics is nice because you can tailor the dice roll to what you want.  (Lots of people like using 2d6 for reaction rolls because it clusters in the middle--that sort of thing.)

Digression: What is not a Base Resolution Mechanic

Dice mechanics like GLOG magic dice, or Black Hack usage dice, are depletion mechanics, are so they are out of the scope of this post.  (Numenera's thing has a form of depletion baked into its primary resolution mechanic, so it can stay.)

I also won't touch the many, many types of rolls that get folded into subsystems, like combat.  Maybe in a later post.

Digression: You're Not Special

I'm going to be cynical and say that most of these dice mechanics don't matter very much.  At the end of the day, it's mostly just a % chance that you'll do the thing.  It doesn't matter what sort of tortuous route you took to get there--it's still just a % chance.

Advantage/Disadvantage is shockingly similar to +4/-4.  The two methods only differ at the extreme ends of the range.  I don't often use advantage/disadvantage for this reason.

Dungeon World's system (roll 2d6, 2-6 = fail, 7-9 = mixed success, 10-12 full success) is very close to: roll a d20: DC 8 = mixed success, DC 16 = full success.  Double the bonuses (+1 with 2d6 = +2 with d20) and you're pretty close--only a few percentage points off, in most cases.  And do those percentage points even matter?  Why is 41.67% superior to 45%?  It's not, but it sorta feels that way sometimes.  (But see also: Scaling, below)

Opposed Progress Clocks (in Blades in the Dark) are identical to skill challenges from 4e but no one talks about that.  You've been bamboozled just because it's round like a boob.  Wake up, sheeple!

I'm pretty cynical here.  Base resolution mechanics tend to feel very different but be very similar once you crunch the numbers.

Yes, there are significant differences in resolution mechanics.  But often these differences aren't drastic, and often a system will lean very heavily on a specific resolution mechanic (it's their identity!) without actually considering what that resolution mechanic is good or bad at.

Our resolution mechanic is a simple d20 + modifier!  Let's stop examining it and use it for everything!

Our resolution mechanic generates a bell curve!  Let's stop examining it and use it for everything!

Our resolution mechanic generates partial successes!  Let's stop examining it and use it for everything!

Our resolution mechanic uses special dice (FATE, Fantasy Flight)!  Let's stop examining it and use it for everything!

Anyway

Most games work best when players don't have to learn a bunch of subsystems all at once.  

It's okay to put extra mechanics on in places where the complexity can be built up gradually (wizards) or for players that intend to have a more complex class (modron mathmaticians).  But be cautious of mismatches between complexity and expectation, such as a brand new player who wants to play a wizard and doesn't like all the of the complexities.

So what are the characteristics of a resolution mechanic?  How do we compare them?

1. Law vs Chaos

How reliably can a strong character break down the door?

Let's look at a Str 16 barbarian.

In (one example of) a roll under system, that barbarian has an 80% chance of kicking down the door.

In a d20 + stat bonus system, let's assume that an average character (Str 10) has a 50% chance to kick down the door.  The door is DC 11, then, and our same barbarian (+3 Str bonus) has a 65% chance to kick down the door.

This is the difference between failing once very 3 attempts, versus failing once every 5 attempts.

The difference is even more drastic for a Str 18 Barbarian.

Roll Under = 90% success (fails once every 10 attempts)

d20 + Bonus = 70% success (fails once every 3 attempts)

Now the difference is getting more significant.  Failing once every 10 times is pretty rare.  Failing once every 3 attempts is pretty common.  This is pretty subtle, but those two barbarians will feel very different in play, even though they have the same character sheet, with the roll-under barbarian feeling much more competent.

Digression: Versimilitude

Versimilitude is what makes the game feel like it's an actual place, instead of a bunch of numbers on paper.  It requires the game to feel (a) internally consistent and (b) fair.

The DM is free to make up any rules and rulings that they want but good rules preserve the versimilitude of the game world.  If some quirk of the rule gives the barbarian a 30% chance to punch through stone and a 40% chance to punch through stone, it feels like a glitch.  Like a shitty computer game instead of a living, breathing world.

Similarly, lots of videogame-style exploits also destroy versimiltude.  Like the peasant railgun--since a peasant can pass an object to another peasant as a free action, and a party that has a lot of peasants acting in a single turn, a potato can be accelerated to frightful speeds, and one-shot a dragon.  (Although I would rule that since we are doing rules as RAW, the final peasant would have to throw an improvised weapon for 1d4 potato damage.)

Rules should generate outcomes that players think is mostly fair.  (Players don't mind the rare result--the natural 20 or the natural 1--since those are rare by definition.)  

But the barbarian should probably have a better than 55% chance of beating the wizard in an arm wrestling match.  95% is probably closer to an expected percentage.  So if you--as the DM--are ever called upon to come up to make a ruling on who wins the arm-wrestling match, please don't just have opposed Strength checks (d20+3 vs d20-1).  The wizard wins 30% of those matches, and it makes the game feel weird (unless that's what the players expect).

Lots of times, when people complain about realism in their tabletop games, this is what they're actually talking about.

"If I fall in lava, it shouldn't take me 18 seconds to die.  That's unrealistic."

What they're really saying is:

"The rules don't reinforce my vision of the game world."

That's why there's a risk to learning too much about medieval polearms and armor.  The next thing you know you'll be telling people that there's no such thing as studded leather armor and complicating everyone's day.

But here's the thing.  Those people have valid viewpoints, too.  Player A might not like it when the ranger falls off a 100' building and survives with most of their HP intact--they should be dead!  Player B might also dislike it for the opposite reason--they should be able to shrug that off!  This is high fantasy!  We're basically superheroes!

Those two players have different genre expectations.  This tension is at the root of a lot of perpetual attempts to fix the game.  It's also why people will never be satisfied with a single ruleset.  A group that includes both Player A and Player B will always have this internal tension.  There is no perfect ruleset for this group.  (Although there are certainly some rulesets that are less-perfect than others.)

2. Stat Spread

How much stronger is the strong character than the weak character?  

In a roll-under system, the Str 16 Barbarian has a 80% success chance, while the Str 8 Wizard has a 40% success chance.  That's a 40% spread.

In a traditional stat bonus system, against a DC of 11, the Barbarian with +3 to Strength has a 65% chance of success, while the Str 8 Wizard has a 45% chance of success.  That's a 20% spread.

I have a theory this is why older games used roll-under and newer games moved to stat bonuses.  Since everyone relied on the d20, as games inflated with more sources of bonuses to rolls (belts of giant strength, etc) the systems moved from a wider stat spread (roll-under) to a narrower stat spread (stat bonus vs DC).  More granular bonuses to rolls required the shift to d20 + stat bonus.

Digression: Bell Curves

A lot of people say that they like bell curves because they feel more realistic.

Sure.

But consider that anything that includes 3 or more dice rolls is going to generate a bell curve.  Even if everyone does a flat 5 damage on a hit, as soon as 3 attack rolls have been made against a dragon, probability graph of "damage done to dragon" is going to be a bell curve.  Keep making more attacks, you'll smooth out the bell curve even more.  If multiple rolls are involved, you can't stop it from being a bell curve.

Second, it's not the dice mechanic that matters at the end of the day.  It's the cold, hard percentage.  You can dress up your dice mechanic all you want, but a 40% chance is always a 40% chance.  So lets talk about bell curves.  We'll look at three of them.

First, the d20 flat.  This is no bell curve at all.  All probabilities are equally likely.

Next, the 3d20-keep-middlest.  You don't see this one too often, but it, too generates a bell curve of sorts.

Lastly, the 3d6. 

These three are easy to compare because they all have the same average.  If you told a player a player needed to roll an 11 or higher to succeed, they would have the same chance of success with all three methods: 50%

Average: Get an 11 or Higher
d20 flat	50%
3d20 middlest	50%
3d6	50%

But what happens when it gets a little harder?  The player needs to roll a 13 or higher?

Hard: Get an 13 or Higher
d20 flat	40%
3d20 middlest	35%
3d6	26%

Now the differences are becoming clearer.  Two points is only 10% on the d20 flat.  But on the 3d6, it's a whopping 24%.  +2 points on 3d6 is worth +5 points on a flat d20.  That's pretty big.  What if it was even harder?

Very Hard: Get a 16 or Higher
d20 flat	25%
3d20 middlest	16%
3d6	5%

Basically, it sucks to suck, but it sucks even more with 3d6 compared to d20 flat.  The underdogs are disadvantaged even more.

BUT take this with a grain of salt.  Remember what I said back in Consistency vs Chaos?  It's all about the ratio between random noise and +/- modifiers.  A d20 flat system might have stat ranges that go from -5 to +5.  A 3d6 roll-under system might have stat ranges that go from -2 to +2.  Those two systems are very comparable at that point (and you could even interconvert, if you wished).

What if things were easy, or very easy?

Easy: Get a 9 or Higher
d20 flat	60%
3d20 middlest	65%
3d6	74%

Very Easy: Get a 6 or Higher
d20 flat	75%
3d20 middlest	84%
3d6	95%

If you were good at something on a d20 system, you'll be even better on a 3d6 system.  (Or to rephrase, if your chances of succeeded were above 50% on a flat d20 roll, you'll do even better on a 3d6.)

Click to embiggen
Thank you anydice.com for crunching all the numbers.

So that's it in a nutshell.  If you swap a d20 for a 3d6 without any planning, the strong get stronger and the weak get weaker.  In a 5e game, the players are usually strongly favored to succeed on their rolls, so this makes players stronger (since players usually make rolls that they are good at, and try to avoid rolls that they are bad at).  Strong monsters get stronger, weak monsters get weaker (depending on, say, whether they were likely to hit players with an attack or not).

Dungeon World makes it work because there are such tight limits on the modifiers (typically -1 to +3) but it's very easy for a bell curve mechanic to fall sharply onto one side or the other, with players being either sure-to-fail or sure-to-succeed with little in between.

But this is also why I like the flat d20.  I like to cheer for the underdog.  I like more surprise upsets.  I want my players to have better chances against dragons, and worse odds against a goblin.

But that's me, and my tables.  Your group may be different.

3. Scaling

How do the probabilities change as a character gets really good at this task?

There are two basic types here:

With an unbounded system, you can get infinitely better at something.  Just keep adding +1 bonuses.  Soon you're getting 34s on your jump checks.

Even though 5th edition talks about bounded accuracy, this boundary isn't generated by the mechanic.  It's generated by the equipment and the classes.  There's nothing stopping a DM from tacking another +1 onto their monster's attack roll.

A truly bounded mechanic is one where you cannot get better forever.  At a certain point, you just get diminishing returns, or stop improving completely.  Blades in the Dark's d6 thing is bounded.  You can keep adding more d6s to your pool, but your chance of failure will never reach 0.  That mechanic is truly self-limiting.  

This is a gradient, since in some versions, the diminishing returns will diminish faster than others.

Like if you are doing d10*d10 roll-under, a stat of 24 gives you a 50% success rate.  A stat of 48 gives you a 78% success rate.

Dungeon World's mechanic has diminishing returns (since your chance of getting a critical success improves less and less with each +1 beyond the first) and is artificially bounded (since it is hard to get more than a couple of +1s).  It's not truly self-limiting, though, since you could theoretically just write down +7 next to your Coolness and God can't stop you.

When people talk about a dice mechanic being elegant, they're usually talking about diminishing returns, or how the mechanic is self-limiting.

4. Visibility

How clearly does the player know their actual odds of success?

The best mechanic for this is d100 roll-under.  

You're playing Call of Cthulhu and you need to drive a car really fast.  You look at your Drive Car ability and see that it's equal to 45%.  Quick, calculate what your odds are of success!  That's right!  45%!

d20 roll-under is slightly muddier.  A stat of 13 equals a 65%.

d20+stat is muddier still.  d20+1 vs 11 is not 50%, but 55%.  God help you if you're trying to figure out iterative attacks in 3rd edition (+17/+12+7 against AC 25).  I had a spreadsheet to help me figure out when to power attack (-1 to hit, +2 to damage, but you could later improve it to shit like -3 to hit, +6 to damage, etc).

This is another source of tension--in a game that supports min-maxing (e.g. Pathfinder, 5e) there are going to be players who want to min-max.  The players who will be best at this will be the ones who have taken stats classes and like to use spreadsheets.  Everyone else who wants to be good at the game will either have to copy homework from the nerds, or just resign themselves to being not quite as good.  Which kinda sucks, yeah?  In game, we're both bloodthirsty barbarian berzerkers, but I kill more troglodytes than you because I'm better at calculating when Power Attack was worthwhile.

And there is nothing wrong with min-maxing.  If the entire table loves that type of gameplay--do it!  Fuck OSR.  Play PF2 and revel in the dopamine that your diseased brains exude.

But, do recognize that visible mechanics makes it easier for everyone to min-max in a fun way.  If a mechanic is more visible, it makes it easier for everyone to see the effects it will have.

Pathfinder has a zillion feats, some of which were reviled as "trap options" since they look good to a new player but trap themselves in a sub-optimal build.  These feats don't have good visibility, since the math is pretty convoluted, and new players are unfamiliar with it.

So, there's an argument in favor of more visible mechanics on behalf on the min-maxers.

Here's another group of players who enjoy visible mechanics: OSR players.

OSR games have a lot of interesting, impactful, informed decisions.  Ideally, these moments are supported by the system, the adventure, and everyone at the table.

Now, inane life-or-death moments crop up fairly often in OSR games.  Do you attempt to throw the green slime into the summoned air elemental or light the goblin bomb?  If a decision like this is going to be informed, you need to know what your odds of success are.

Being informed means that you know what the stakes are.  It also means knowing the odds.

Which one of these scenarios sounds like a better game?

Scenario 1 (Least Informed)

Player: "Okay, I'll attempt the jump.  Hope I don't die." *rolls die*

DM: "Okay, make a Strength check."

Player: "Not a Movement check?"

DM: "No.  It's high-gravity here, so it's Strength."

Player: "I didn't know that".

Scenario 2 (mostly informed)

Player: "Okay, I'll attempt the jump.  Hope I don't die." 

DM: "Are you sure?  It's a hard Strength check, because the gravity is high."

Player: "Oh, wow.  If it's a hard Strength check I can . . . probably make it?  I think?"  *rolls die*

Scenario 3 (fully informed)

Player: "Okay, I'll attempt the jump.  Hope I don't die." 

DM: "Are you sure?  It's a hard Strength check, because the gravity is high."

Player: "Oh, wow.  If it's a hard Strength check I have a 60% chance to make it, which means I only have a 40% chance to die.  I'll take those odds."  *rolls die*

This dude understands dice mechanics.
If you recognize him, you're old.

If the player dies as a result of their decision, having more transparency in the decision gives them more ownership of the result.  In scenario 1, a dead character will probably result in a bitter player.  In scenario 3, the player is more likely to say "yeah, I guess I can see that".

And not just negative results.  Greater visibility in mechanics gives more ownership of all results, not just good ones.  

Imagine a game that never told you the rules, so you never knew what your chances of success were.  Your successes would feel just as unwarranted as your failures.

There is one group of players who don't need visible odds: storygamers.

Because storygamers are perhaps the most invested in the "play to find out" mindset, they are the group who benefit the least from knowing the odds.  The stakes are lower in most storygames, too, because the average story game is less focused on winning/losing and more on the emergent story.  (I've never heard of a TPK-go-roll-new-characters happening in Dungeon World.)  For most storygamers, the dice are oracular, not statistical.  Or to put it another way, the exact statistics are not as important as generating interesting story results.

5. Granularity

How significant is a +1?

Or to put it another way, how many fine graduations are there between strong and weak?

The standard "d20 + stat vs DC" has a good amount of granularity.  You can give out a lot of +1 bonuses if you want.  You can't hand out many +1 bonuses in Dungeon World, since the range is much smaller.

Conversely, you can hand out a shit-ton of +1 bonuses in a d100 system like Call of Cthulhu, since the range is huge compared to a +1.

To a certain point, the difference is trivial.  "Roll a 15 or less on a d20" is functionally identical to "Roll 75 or less on a d100".  

Do we want a granular system?

Granular systems are good for places where we have many small incremental improvements.  In Call of Cthulhu, you can improve each stat by +1, +2, +5, +8. . . whatever you want.  Granular systems are good for that.  

They're also help support min-maxing.  Part of the fun of Pathfinder is finding all the little ways to stack +1s onto your key abilities.  That's where the fun is!

Less granular systems are (supposedly) a little simpler, since you have smaller numbers on the page.  This is true, but only slightly.  "Roll 75 or less on a d100" is only slightly  more complicated than "Roll 5 or higher on a d6".

6. Multiple Outcomes

After you roll the dice, how many different outcomes are possible?

The simplest resolution mechanics are like coinflips.  You either succeed or you don't.

An increasing number of games (mostly storygames) are developing resolution mechanics that have degrees of success, or "success with a cost", or "complications".

Even bog-standard D&D has a minimal form of this: crits and fumbles.  Four results are now possible: fail, succeed, crits, and fumbles.  The fact that crits and fumbles are generally pinned to be 5% each shouldn't be seen as a weakness.  (I actually think that that rarity is close to ideal for most of my games.)

Storygames enjoy variable successes the most, often because one of the big tools in their kits is improv.  You picked the lock but you rolled a complication!  I guess a guard heard you!  (Or your tool broke, etc.)

There's also games that have more concrete results from a mixed success.  You hit your enemy but your weapon starts to break.  Multiple outcomes doesn't always mean improv.  However, the systems that support multiple outcomes mechanically will always have that extra complexity from it.  Every roll can't just be a succeed/fail--it must also have some sort of mechanically-supported mixed result.

Lastly, I do want to say that multiple outcomes sometime artificially overload the die.  Consider the following:

Make a multiple-outcomes roll to see if you make the jump.  Fail = you fall.  Mixed success = you make the jump but you slip on the ice on the far side and take 1d4 damage.  Full success = you make the jump safely.

VERSUS

Make a roll to see if you make the jump.

If you make the jump, make another roll to see if you slip on the ice and take 1d4 damage.

If this was a movie, there would be no difference.  Different mechanic, same result.

It's also not too different from old-school D&D rules like "if you are surprised by monsters, you have a 2-in-6 chance to drop whatever you're holding".  

7. Speed of Resolution

How long does it take to resolve the mechanic at the table?

One of the most sacred cows is pretty slow.  The venerable "attack roll to see if you hit" followed by the "damage roll to see how much damage you do" is slower than it needs to be.  Sure, you can roll both dice at the same time, but it still takes a second.

From fastest to slowest:

1. Simple roll-under (or roll-over)
2. Dice pools, look for highest die
3. d20+stat vs DC
4. Summing multiple dice
5. Dice pools, look for highest
6. Complicated roll-under (either modified stat, or the blackjack thing from Whitehack/Errant)
7. THAC0
8. Anything with playing cards
9. Dice pools, look for matches and sets
10. Anything with a reference table (although the simplest tables are faster)

Or more simply:

1. Roll and compare
2. Roll and find highest
3. Roll, add, compare
4. Roll, subtract, compare
5. Roll and find matches
6. Roll, look up result on a table

Speed is important because (a) you can do more adventuring if you can get through content faster, and (b) it helps with player engagement.  The faster you resolve things, the faster you can get back to the interesting part of the gameplay loop.  Learn stuff, make decisions, repeat.

Speed of play is critical, unless you have highly invested players.  It creates cohesion and builds momentum.

8. Comprehensibility

How fast can your players learn this mechanic?  How often will they make errors when using it?

I won't spend too much time on this, but I will say that 

• there is a cost to having to teach your players a lot of rules.
• there is a cost to having to re-explain a rule if a player forgets it.
• there is a cost to a rolling something incorrectly, then getting and incorrect result.  
• Especially if they thing they succeeded, play proceeds, then someone points out that they actually failed.  This has happened to me.

9. Fun

But is it fun?

This one will also be pretty subjective.

Some players hate anything with roll-under, especially if they come from a 5e background.  ("It just feels weird to want low numbers, you know?  I want high numbers for all of my other rolls.")

Some players hate having to add more than one number.

I have a weird dislike for blackjack roll-under systems (roll-under your stat but above the difficulty) that is entirely undeserved.  It's a perfectly fine mechanic.

There is something hella fun about shit-slamming two fists full of d6s onto the table (fireball, your marines are shooting).

The traditional d20-flat isn't very fun, although crits and fumbles can spruce it up a bit.

"Fun" is nebulous, subjective, and is often in opposition to all of the other considerations I've mentioned.  It takes a while to count all those d6s, after all, while your other players are sitting there bored

Upcoming Sections

Part 2 - Reviews of all major core resolution mechanics.  (See diagram below.)

Part 3 - Application.  Deciding on the design goals for your system, then picking mechanics that support it.