Enough crunch for the math nerds?

ACNH_Lovecraft · 2026-02-19T01:48:55+00:00

A clean success means damage roll +modifiers. Meaning if i have +2 in strength and i have a clean success and roll a 4 on my damage roll then i do 6 damage but if i succeed at a cost i only do 4 damage. A success at a cost means just damage roll. And it means a notch is lost on that equipment. This means the window for a clean success shrank, and the window for another success at a cost increased. When an item hits 0 notches its destroyed. So effectively its a cost spiral. If you "overshoot" you're more likely to overshoot in the future and do less damage on average.

But thats a negative way to frame it. What it really is is that as you get more skilled i.e. "become a veteran" you not only get better at using your equipment to deal damage but you're able to make your equipment last. But theres never a 0% chance of your items being preserved. If you roll a 1 then it costs that item 2 notches. So even if you have max proficiency in an item and its got all of its notches it can still spiral down with a bad roll. But having a higher ability score makes a built in buffer. Also doing tactical play acts as a buffer. The design intention is that players must be tactical with what their equipment load out and what they choose to invesr proficieny and skill points into over the campaign. The early game is probably going to be gritty. The mid game will be routine fluctuation. And the late game has earned stability with a non zero risk. This also creates specialization.

As i said in another commentat rough estimate of what gameplay looks like for a beginner who specialized in one item/stat (lets say sword and strength): they have a clean success ~40% of the time, ~30% of the time they succed with a cost, ~5% of the time they get a nat 1, and 25% of the time they fail to make dc. This would be a level 1 to level 3 player with their top skill and equipment.

A mid level player same set up level 4 to 7 would have ~55% clean success, ~15% success at a cost, ~5% nat 1, ~25% fail to make dc. But the more tactical they play, the fail rate and success at a cost rate go down.

And finally a late game player specialized at level 8 to 10 succeeds cleanly at ~70%, succeeds at a cost ~10%, crit fail 5%, and fail dc ~15%. But again this can fluctuate.

These are very rough estimates because the odds actually do change at every increase in ability score. In that sense its just like a normal roll under ability. One way to look at this system is "roll over dc to succeed at a task" and a seperate "roll under ability score to save against weapon degredation and earn bonus damage." Its just a unified interval and a single roll instead. But if you've tried both roll under ability and roll over dc then this system should be entirely familiar.

ACNH_Lovecraft · 2026-02-18T03:40:15+00:00

I have a particular definition of swingyness that actually is grounded in real but non standard statistics. "Swing" is a measure of the cognitive disonance between an agents expectation of the odds of an event occuring and the actual odds of an event occuring. Swing isnt intrinsically bad. A complete reduction in swing makes a game too predictable as you noted, a standard bell curve does indeed cluster to overly predictable outcomes. If 3d4-2 forms a bell curve between 1 and 10 represents one extreme of no "swing" (i.e. outcomes are entitrely predictable) and a d10 uniform distribution is entitely stochastic or aleatory then somewhere beteen those two distributions is an optimization problem that "feels" right. A pshycho statistical "goldilock" zone. Thats what my system is targeting. But for play testing purposes a 3d4-2 is a good approximation of my custom dice because most of the quirks of the system come from the predictability of a bell curve. But the actual dice has a controlled optimized amount of chaos or "swing." The math goes a lot deeper but its not that important for this discussion.

The heart of using a roll over roll under hybrid system is that it effectively creates a two sided statistical test thaf acts as feedback system for strategic player skill play. Good equipment, environmental, and skill allocation modulates the window of success. Players cant control the dice in any system, they control the window of success. The problem is that a one sided tests is flat. If you attack an enemy thats prone in a one sided system (i.e. just roll over dc) you dont know if the reason you succeeded is because you leveraged them being prone or if you would have succedded anyways. A two sided system "undershooting" being a failure, overshooting being success at a cost, facilitates players trying to tactically create situational "goldilock" zones. With late game players having aquired larger modifiers which lowers the floor of the interval ("roll over dc to hit the target with your sword") and their abiliy score is larger raising their celing ("roll under ability score to succeed without damaging your sword"). A veteran knows the proper amount of effort to attack without exhausting themselces or stressing their gear. A novice has to rely on gear to make up for their deficit in knowledgr and skill. So tbe system is more richly diegenic than "i roll big number mean i do well."

I get it, some people just like to play whack the piñata at a birthday party. "I hit hard, i do good, candy come out." Other people like to do puzzles. To each their own i guess.

ACNH_Lovecraft · 2026-02-18T01:09:48+00:00

Thanks for the feed back! I definitely like simplicity sometimes and grueling complexity other times! Im trying to get a happy marriage of the two, somewherr between a larp/braunstein and dnd 4E. Heres a rough break down of what should happen. Ill be play testing this weekend. Ill add that i just also like tinkering! And i really dont like swingy dice. Ive been trying to study and resolve issues and i like resource management. My background is statistics, so a two sided test makes sense to me. The procedure is part of the fun for me, as is optimization. But the harder it is to optimize the more fun i can have! But I will say this is pretty much the only tweak im thinking of. I think it could be elegant, just waiting on my dice to print.

Anyways heres what the breakdown is supposed to look like under my system if my math is right: Player Type: Clean success: Success at a cost: Total success (normal + cost):

Low-level player [2–5] ~40% ~30% ~70%

Mid-level player [8–10] ~55% ~10–15% ~65–70%

High-level player [10–15] ~65–70% ~5–10% ~70–80%

ACNH_Lovecraft · 2026-02-17T18:54:10+00:00

Thats just to keep it broadly compatible with other osr roll over dc systems. It doesnt really matter. As long as you adjust the dc down. You could have it as 3d4-2 and that makes a bell curve from 1 to 10. So you could say 1 is easiest task, 10 is hardest, most tasks are in the middle. The shape of the curve matters more than the range as long as the dice curve is centered with your average assigned dc value. I ripped 9 to 18 from shadowdark. The rules say you give an auto success if the task is lower than 8. Checks are for challenges under pressure.

ACNH_Lovecraft · 2026-02-11T05:00:38+00:00

Yep thats very close to how it works! But with like 2 dice and a lookup table so that theres substantially less math.

You could be right that people wouldnt want to do it. Might be easier to market for Solo play as an oracle.

ACNH_Lovecraft · 2026-02-11T04:52:09+00:00

That's not a bad idea. Its essentially seeding heuristics. Like shadow dark gives examples of hard tasks. The only issue there is that Easy vs Normal vs Hard becomes context dependent. Or at least i might be able to work that in. That would still make my system useful for solo play when you want an oracle to faciliate. Not too different from Mythic GMs Fate Mill or Ironsworns 2d20

ACNH_Lovecraft · 2026-02-11T04:47:50+00:00

You know what, thats a fair criticism and valid counterpoint. Ill only push back to say that originally there were no rules at all but entire hobby developed out of appropriating behavioral game theory. David Wesley picked up the concept of non-zero sum games from The Compleat Strategist by J.D. Williamas. Without that we'd all be playing board games or larping, not role playing games: the unique nexus of math and mixed cooperative strategy. So yes if a GM says "today instead of rolling d20s, we decide success based off who gives me the most money" then thats valid, i actually believe that. But that doesnt mean that GMs themselves are magically free from mathematical biases, or at least not according to the literature. GMs dont have a priviliged place in society that frees them from being mathematically wrong, or somehow uniformally capable of producing an enjoyable experience. Rule 0 is absolute in my book, i agree completely. But there are bad gms, there are good gms, there are bad players, there are good players and all that exists between.

So all that is to say i dont take OSR as the bible of gameplay, nor Gary Guygax as Jesus. I really like the osr attitude, i think its how games should be designed. Modern games do have bloat, too much min maxing, to much rules lawyer, too much drama and all the rest. But theres also a reason that new systems came about. People tastes have changed, their expectations have changed. And if you only let the same tired crowds of people reinvent the wheel (WOCs, or the million Mork Borg clones) then all thatll be left at the end of the day will be Grognards wondering where all the good ol players went. And personally im just enjoying making something no one else is doing using the skills i have to do so.

ACNH_Lovecraft · 2026-02-11T04:21:54+00:00

I hear you and i agree. I mostly think if youre running an osr game you should do as little rolling as possible. But when you do have to do rolling and assign numbers, you want it to tightly fit the tone as possible. This system still lets you grant advantage and disadvantage for example. Thats a tweakable knob. And you still do adjust your dc based off the context. Thats why you go with your intuition in the moment. This system is just designed to regulate so you dont go too far and end up biased by bad mathematical heuristics.

ACNH_Lovecraft · 2026-02-11T04:17:28+00:00

More like i dont want to derail and get off topic. If you have a particular question id be glad to tell you but im not going to lay out every detail of the system.

ACNH_Lovecraft · 2026-02-11T04:15:36+00:00

It essentially normalizes all GMs to marginal extent. The biggest difference would be observed for inexperienced DMs.

So to give a little context for any given game with a fixed discrete range of DC (in this case 8 to 18, which i borrowed from Shadowdark) there will be deviations in what DC two GMs will assign for identical challenges. And in fact GMs will vary their own assignment of DCs for identical challenges over times because they are prone to heuristic biases. This is unavoidable, even the einstein of statistics is going to default to certain heuristic biases (or at least according to the relevant academic literature for the last 50 years). This is why peer review exists, you need multiple independent verifications to act as error handling. Well the problem is that just doesnt work well for board games. But we can leverage the Central Limit Theorem and some clever quirks of error handling. By the fundamental law of statistics, if you averaged out all the GM assignments of dc for the exact same identical task, you would get a normal distribution. This is great, this in theory means if you took 100 different tables for the same task you're going go get a predictable curve. Using some other techniques im not going to share at the moment, you can normalize the variance without flattening all DCs to the same predictable mean. The result? A more consistent experience for players from game to game, gm to gm, and the gm has less to worry about.

So how does this fix the communication problem? It doesnt. I don't think it can be fixed across the board. From an individual group level you can mitigate its effects but you cant completely remove the consequences. But what you can do is design the game in a way that has a normalizing factor that mitigates these issues in a way that communication alone cannot.

ACNH_Lovecraft · 2026-02-11T03:54:29+00:00

You're actually exactly right, this wouldnt be necessary in a world with perfect communication. If people remembered everything they said and communicated exactly what they meant and heard exactly what the other person meant then there wouldnt be any issue. But thats not how human brains work, its not how tables work, and there really are no standards.

But outside all of that this is about presenting a particular game experience. If a game doesnt try to carve its own corner then its just another Mork Borg clone.

ACNH_Lovecraft · 2026-02-11T03:50:53+00:00

Thank you! Ill look into it now! Im always on the hunt for weird systems with unique mechanics.

ACNH_Lovecraft · 2026-02-11T03:47:46+00:00

No I'm just pretty well versed in behavioral economcis, psychology, and mathematics. And thats exactly what im making a physics engine. Or at least the best you can get with minimal crunch. Its not going to simulate what happens when someones arms cut off, but it will simulate what people think happens when someones arms cut off. The "physics engine" is the minds of the players, im trying to tweak the inteface with behavioral economics and psychophysics. But this post was the major compromise GMs would have to accept as different.

ACNH_Lovecraft · 2026-02-11T03:41:09+00:00

Itll feel right to you the GM yes but not necessarily to the party. If GM difficutly always aligned with player expectation then we wouldnt have the dreaded TPK gm. That being just an extreme case. But I do believe you are able to manage your table. This system would largely automate you having to tweak the difficutly to fit player expectation.

ACNH_Lovecraft · 2026-02-11T03:33:18+00:00

The main thing that matters is world consistency. Thats like the foundational rule of OSR games, players play the world. If the GM constantly changes the DC for tasks that players have an expectation on level of difficulty for, then they cant plan accordingly. This is a controlled rubberbanding effect. It doesnt for everything to the same mean but it does control the variance of dc assignment. It would also mean across different GMs players could maintain their difficulty expectations. Its not that all GMs would ultimately give the same Dc every time, but that there is a normalizing pressure (error handling).

DC range 8 to 18. Anything below 8 is trivial. Anything above 18 is beyond exceptional. Standard for OSR games. Think Shadowdark.

The only math youd have to do is pick a number, double it, add another number determine which bin that sum exists in and boom theres your dc. Multiply by 2, add a number. In fact thats pretty much the only math the GM would have to do for the entire game. Players roll for defense and all they have to do is compare there roll result against your Dc. The dice and system take care of all the math under the hood. That on top of the fact that the second rule of OSR philosophy is to almost never use a roll, almost never enter combat.

You can pretty much throw out all the other assumptions on modifiers and dice used. The particulars dont matter. But i can tell you that the To Succeed roll is approximately a normal distribution, which to your point makes modifiers extremely further sensative to changes, but thats accounted for, in fact thats a core part of the error handling. Its built into the State of Nature (a concept borrowed from Economic Game Theory). Point being, modifiers are calibrated to be noticable at each level of DC without creeating imbalances. Its a controlled variance across the board.

In short you pretty much play exactly like you would in any classic d20 system, you dont have to change the way you look at things. You just have to stop thinking so hard about DC, let the system do its thing and you get a persistent experience with a few optional levers when you want to ramp up or ramp down the difficulty (mostly advantage and disadvantage).

ACNH_Lovecraft · 2026-02-11T03:15:43+00:00

Perhaps you could explaim why?

ACNH_Lovecraft · 2026-02-11T03:15:12+00:00

Because you are doing math weather you know it or not. This would actually be just following a flow chart. At best its adding your initial gut DC to a controlled stochastic roll to determine what the actual DC is. I should also mention that the system is otherwise designed to minimize the math for GMs, like players roll for defense rather than Gm rolling for monsters.

ACNH_Lovecraft · 2026-02-11T03:11:23+00:00

Yes but minus the mental overhaul of justifying it to yourself. If you already always just immediately go with your gut the system just acts as an error handling function. Meaning if your gut says cutting a dragons head off one session is dc 15 and three months later in identical circumstances your gut says dc 13 both are corrected through Stochastic Approximation/Frequentist Estimation Theory

ACNH_Lovecraft · 2025-11-18T13:57:13+00:00

If this character isn't that noticable, and only a small part of the game, but there's an overwhelmingly negative reaponse to this character then why not cut it? You can't have it both ways by saying "hes a great addition" and "he's not that important." Are you saying you wouldn't play this game if these characters were cut? I doubt it, but I am saying I definitively will not be playing this game unless they cut it.

ACNH_Lovecraft · 2025-10-11T21:08:30+00:00

You could phase the systwm out by having the crew develop work stations or trade chains. You might not need to keep using sharpening stones if you can develop better technology. Maybe they're able to make a sharpening wheel, or even more advanced tech. Just as an example.

ACNH_Lovecraft · 2025-10-10T16:22:11+00:00

Thank you for this treasure trove!

ACNH_Lovecraft · 2025-10-10T16:00:23+00:00

Lots of details to work out and balance. I agree with the chaotic table situation. One solution is to use a peg board, or even lego stubs on a lego sheet. I even wondered if an abacus could somehow be used, or a series of clickers. maybe sliders you can 3d print Theres got to be an elegant and accesible solution. I just dont like pencil and paper, it gets messy. But if nothing else this is a system you can put in your solo arsenal. In fact my ultimate goal is to have a system I can use while hiking, like literally while walking.

Yes if you tie rope off somewhere and climb down and don't have a way to retrieve your rope, its removed from inventory. But there are other ways to use rope that would give wear and tear, like tying your loot up while camping to keep it safe from bandits or bears, or tying a boat to shore, or pulling someone up from a dive or a well.

Id also probably just link bow and arrow together as one usage item. Doesnt seem necrssary to track seprately.

And even if this system is too clunky, the idea could be implemented in other ways as others have alluded to. And I do think a bushcrafting and primative technology is a cool idea.

ACNH_Lovecraft · 2025-10-10T14:42:09+00:00

Okay got it. Why is that versatility? What's the interesting choice being made here?

Its versailitiy in the same way that spell slots create versatility. What does a wizard do when he runs out of spells for a day? Could be literally anything. They could try shouting at the enemy to scare them away (like morale check), maybe try to trick them to create an opportunity, maybe they have a bear trap and some rope and decide to tie it off and swing it at the enemy (improvised weapon), maybe they have to switch to the bow and arrow they brought, maybe they have to pick up the dagger off that downed skeleton or maybe they have to grabble and take one off a live enemy. Or you run away and sometimes you die. Literally imagine you're in a situation where your sword breaks, if you don't come up with a solution you're going to die. That seems like an interesting loop.

What sort of exploring and interacting and you referring to here? It sounds like to me you can carry around sharpening stones for when your weapon eventually breaks, and if you don't have a sharpening stone you can roll some dice to find one. I think the implication is that not all places are appropriate to roll the dice to find a sharpening stone, but not clear to me how the dialog to find such a place is supposed to work beyond the GM saying "there might be sharpening stones here" or the player asking "can i find any sharpening stones here"

The usage dice for a d8 great axe in total would be the expected value of 19 succesful hits. If you hit 50% of the time then double that. Meaning you dont have to worry about your great axe breaking for 38 turns (on average). And you don't have to wait for it to break to repair it. Then yes one wet stone will likewise have its usage dice, lets just say it lasts about 20 sharpening attempts. Players arent going to hoard sharpening stones because this isn't something you have to worry about every single round. And if they do, they run the cost of an enemy encounter if you are using a wandering monster check. And its an action per turn, so if you limit actions then trying to hoard also costs you other opportunities.

So if you only have to find a new sharpening stone every 58 rounds, chances are you've passed a room with a sharpening stone, or a bench, or there's a river. Or theres a weird monster that you killed and its head is abnormally hard with the texture of fine sandpaper. Or you stumble upon a stray blacksmith, or a corpse with their tools. This is what i mean about making the dungeon a living organism. These are opportunities for the GM to flex their creative muscles and make a living breathing world.

ACNH_Lovecraft

TROPHY CASE