Arithmetic Complexity in TTRPGs | Design Discussion

#ttrpg #dnd #gamedev
Let's talk about mathematics in tabletop roleplaying games like D&D, Pathfinder, and Blades in the Dark! This video is not so much about how to calculate the math or what sort of dice systems you should use, but rather how the mathematical steps influence the type of game you're building.

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** Chapters **
00:00 Intro
00:37 Definitions
01:38 How much burden to use?
01:56 Case Study: D&D 5e
03:25 Case Study: Pathfinder 2e
04:24 Case Study: Rules-lite/Narrative Games
05:08 Where should your game sit?
05:35 Stacking burden
06:40 Tales from Elsewhere's approach
10:16 Outro

Written and presented by Peter Lange
Logo, graphic design, and animated characters provided by Maribel Navarro
Music by @RyanikeAudio and @piercemartinmusic
Edited by @TimothyWeinell

[TTRPGeniuses]

Fun fact, if I counted right, you say Math 20 times in the video! That's almost 2 maths a minute! Talk about Arithmetic Complexity in just the transcript!

[Trekiros]

This is a thing I constantly have my eye on. I have a companion web app so I don't do a lot of the math myself, but I want my game to be playable with pure pen and paper. And because I'm used to doing so little math, any amount of it that I can see in my game feels like too much :'D

[consoya]

Some ttrpg and wargame systems use a dice pool and don't add the numbers but count how many dice are over a certain value (hits).
It relieves the math burden of adding numbers, but when the dice pool is numerous it ads the burden of counting results 😅

[mkklassicmk]

I stopped using things that give you +# bonuses. Instead you take something that says "makes a climb check easier" which just means the difficulty is lowered by one whole stage, i.e. very hard checks become hard checks. Also, no extra rolling to calculate damage, its just part of the attack roll. I managed to lower the math that was necessary but without losing the tactical play or the character building options that a crunchier game offers.

[AdamPerry-yisz]

Diegetic math would be in-game, in character: "Eight orcs attacked you, and you've killed three. How many are left?"

[sethofalltrades]

Once again! Incredibly interesting, thoughtful discussion on the ins and outs of TTRPGs and game design. Love it!

[monkeymule]

Dude. brilliant! I find the crunch heavy/lite comparison fairly crude, crunch appropriate being where the juice is. Some of the games in the 90's when i was growing up certainly were heavy without much pay dirt. On the other side, the only game that feels well matched to PbtA has been Kult, IMHO, where it really shines.

Side note: I always appreciate when a game has the designers intent openly stated through out the game. When a reader comes across and unfamiliar mechanic and has that instinctual friction, having the authors note there explaining the intent is underutilized. Nights Black Agents does a superb job of this, and made me miss it in other rulesets.

[emilfischer]

Damn, I'm so glad I found this channel! this is twice in a row you just happened to have a very articulate video on a topic I was clumsily discussing in a recent conversation. Nothing to add this time. I just appreciate the well thought out conversation!

[aaronabel]

I do not mind crunch as long as it pays off in increased detail. In Mythras and Runequest it pays off, in Pathfinder it does not.
Also I really enjoy that you don't use a script, I can get a real feel for your depth of knowledge and passion.

[gmikese]

I think this video is useful not just for a game designer but for a DM/Group to think about when selecting the game they want to play. My group is using Pathfinder 2e Revised right now partly because I know my players wanted a game where hitting things with spells and swords felt good and had numbers that went up in ways they found exciting as they gain levels. Pathfinder does that well.

So when it comes to the amount of burden to use I Like that there's a wide variance in games. Different groups want different levels. My player who's a sorcerer loves rolling a bunch of D6 for her fireballs right now. But I've also had games where it's nice to have things fast to keep the action going (like Outgunned which doesn't even use the values, it's counting sets of dice).

I suspect and wonder if it's true that higher hit point games will in general have higher burden for the math as well. Though I think that may just be two different things that are aspects of another... the real metric might be more about how often the party is getting into combat and how many times they take damage. A game with players who need to take damage more often in a fight and expects at least one fight per session may need higher hit point totals and damage numbers to make the combat feel different and exciting round to round.

[SplotchyInk]

You kind of also missed a point. There's rules heavy, there's rules light, but something people don't realize that there's also "Rules Efficient".

There's a difference between say, Lasers and Feelings where its a single D6 roll over/under a certain number to see if you "Do a lasers thing" or "Do a Feelings thing" and thats about all. Its another thing when you use the same mechanic in a variety of different ways to simulate different aspects of a game like combat, leveling up, different types of contests, and so on.

Take say, the new RPG hotness currently, "Everything must explode" I think its called (though if you wanna get nitpicky, the Monty Python RPG kind of did a very very similar mechanic first." First, its your classic Dice ladder system, something very easy where you can say "Alright Bill, the bigger your dice, the better you are at doing that thing. And if you roll the highest number on that die, you get to increase it AND roll again." Alright, So you have a simple "roll over system", but that system is not ONLY your skill check resolution system, but it is NOW a RNG based leveling up system AND critical hit system. A single mechanic, just from its mechanics is now doing 3 different things.

So now you only need to teach someone one thing to do multiple aspects of the game.

And with this, you can reduce the burden of Arithmetic Complexity without actually 'reducing the complexity' of the game.

Allows for what would be a 'lighter' game to feel more deep as a simple set of rules can do a lot of different things. While making a 'heavier' game feel more approachable as all the rules mesh together into a handful of cornerstone mechanics that get repeated and reiterated through out every aspect of the game.

Something that would be rules Inefficient would be 5e D&D, while it is considered 'medium weight', there's so much backlog information, so many disparate mechanics you need to keep track of (who uses the exhaustion mechanics?) that bloats it that makes it feel much heavier than a game should be (For example: every OSR (lets just say Knave 2e) that's come out over the past couple years does a most of what 5e does with a tiny fraction of the rules and mechanics).

So not only is 'what' your doing mathamatically kind of important, but do you use 'all of the Buffalo' when it comes to it. Do you actively make it to where everything you do surrounds that 'one or two' mechanics, or do you keep adding in more mini games for every new possibility. Even if they are all different variations of something 'relatively simple' as adding 2 dice together, that will feel more bloated and heavy, as opposed to a more complicated system that is used through out the entire game cause its learning 40 little mechanics as opposed to 2 big ones.

[bhuff]

In terms of lowering diagetic arithmetic burden, recently playing the marvel rpg I like the troubles and edges system. It’s got a lot of similarity to adv/disadv in 5e, but has more nuance with picking which die to reroll and stacking allowed. My first experience with an elegant solution to reducing diagetic burden was way back with alternate (the original in the 90’s). You had this nondiagetic burden of calculating your success thresholds for each skill which involved halving and halving again with rounding (it was d20 roll under system). But then during play you just added up positive and negative “step” bonuses based on range to target, their dodginess, etc which you could do on one hand. The final step bonus or penalty was then the die you added or subtracted from your base d20. A 1 step bonus was d4, 2 step, d6, etc. Combat rounds flowed very smoothly and quickly but still had a tactical feel.

[CalebWillden]

Delightful video! I love how well you explained the reason behind the simple d10 math (I hate the d10 shape but love how easy the math is) versus the dice pools math. A great demonstration of how to direct player focus and behavior through the mechanics.

I'm also surprised that you don't use a script given how eloquently you share your thoughts!

[BCMZeroZero]

I like games where there is a little math as possible. On the diagetic side, i want a game where the dice show up when they're needed and get out of the way the rest of the time. Let us tell a fun story, but consult the bones when something is dramatic and uncertain. I don't find it interesting to slow the game down so we can see if the fighter did 43 or 45 points of damage. I'd like to point to Chasing Adventure (a PbtA game that spun off of Dungeon World). Roll 7, do one point, roll 10, do 2 points, then move on. There is also the upcoming DC20, where you add 1 point of damage for every 5 you roll over the target number.

On the nondiagetic side, I don't want to give my players homework, and I don't want to have to audit character sheets. I gravitate toward games where a new player can sit down and and do something heroic in 10 or 15 minutes, not 2 hours. And between sessions you should be able to talk about how much fun you had and what you want to do next time, not open 4 splat books and grab a calculator to find the mathematically optimal feat to take with your skill points.

I'm not trying to yuck on anyone's yum. If that's fun for you, I'm glad! But those games aren't for me.

[SpydersWebbing]

My first project, Crescendo, is a really math-lite project, but very complex in ideas. So far I’ve found people can follow complex ideas without math surprisingly well. Something about numbers switches the brain off.

[jessewilliams]

Great videos! Found your channel this week and just finished watching all of your videos.

Something to consider that is parallel to arithmetic burden is Rules burden. For example, your damage mechanic sounds like it functions relatively similar to Blades in the Dark, in that you roll a pool and look at the highest. When someone asks me what 7 + 6 is, essentially what my brain does is consult a table I memorized in school (roughly 35 years ago) to give me the answer. That is roughly comparable to finding the lowest dice in a pool and then comparing that to a table (that you probably quickly memorize) to see what injury the number corresponds to.

Your's sounds pretty simple, it is just three different injuries, but it is something new for players to memorize so I think it would be pretty comparable to single digit arithmetic, in terms of player burden, though it would depend on the player. If you had 5+ categories of injury that an attack could result in I think that memorizing that would pose more of a burden on most players.

It's probably unavoidable to have some minimum amount of burden on the players, just something to consider. I've seen games that don't require math to figure out the result of an action but are still far slower than someone counting on their fingers because it required multiple table lookups.

I'm going with a step dice pool resolution for my WIP so I don't have a lot of arithmetic burden, but my players will have to figure out which dice to add to the pool, and be comfortable identifying the different polyhedral dice, so that is probably at least as much player burden as the math in some games.

Great videos and please keep them coming!

[jinxtheunluckypony]

I thought this video was going to be about the actual math of games and how to determine the rough probability that your players will succeed any given challenge. This is substantially less nerdy.

[StagRPG]

Today I was thinking about how a +1 or +2 in Traveller isn't the same percentage change since it's a 2d6 distribution. Don't know why, but that weirded me out. VS a d100 game where 15% change in chances equals 15% change in chances. 1:1 relationship makes the math pretty easy to understand in regards to how it affects the game.

Cool video talking about the hidden engine behind games!

[charlesgomes]

Great video! Completely different than I see anywhere else.

[sirguy]

Excellent video! As a thought exercise- why do people enjoying rolling dice? Is it the “gambling “ urge” of rolling high? Rolling low? Beating a set number? What if there are no dice rolling in the game?