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[DXimenes]

Hello, first topic here in TIG.
I wasn't sure if I should post this on "Game Design" or "Technical" (it's GD, but very math-ey), so I'm sorry if I made the wrong choice.

I'm currently working on a pet project that is an RPG system - I intend to use it on a PC game, but for now I'm worried about making it work analogically.
I've always been an RPG player, but was never satisfied with any failure/success systems. I started digging through forums and google until I finally stumbled at this particular piece.

I had already devised the graphs for DnD, WoD and FATE systems by myself before I found this article, but the "ideal" curve it describes just seemed more smooth for a game system, and I want to test it.
This is the curve - taken from the link I posted above:


I'm not interested in discussing whether this looks like an ideal system for skill conflict resolution or doesn't. It certainly doesn't seem worse than the others to me, so I intend to test it extensively.
Right now, I'm looking for a way to bring that graph's distribution to a tabletop system - by using dice or other analog mechanics -, but since I'm my knowledge of mathematics is subpar, I don't even know where to start.

Is it possible to do it? Do you have any suggestions?

Thanks guys

[starsrift]

I've always been a fan of the oWoD / Shadowrun system.

I think when you talk about a graph of mathematical purity and degree of success, you first need to define what that success is. You need to build parameters to work your 'ideal graph' into. You may be running into quite a bit of complexity - like your link said, simplicity is a value as well.

[JWK5]

A quick and dirty setup I used for fast pace play between classes back in junior high was as follows:

Action Taker's Stat - Challenge Stat/Opponent Stat = Value
Value + 50 = Chance
If chance is over 95 chance equals 95, if chance is under 5 chance equals 5 (i.e. always a 5% chance to fail, 5% chance to succeed).

So if my ability to shoot a gun is 15 and my opponent's ability to evade it is 8 then the remaining 7 is added to 50 giving a 57% chance to succeed, which I must roll a d100 equal to or under. A roll over 95 always fails, a roll under 5 always succeeds. If you wanted to get a quick idea of how well the action succeeded just base it off how close to the target value the roll was.

If I needed 57% and I rolled 50% that is pretty close to the mark so it can be assumed the shot was a good one, if I succeeded with a roll of 12% that is pretty far from the mark so it can be assumed my shot was sloppy.

If you want a quick and dirty damage application, you can assume that all characters (etc.) have an HP range of 0 to 100. On a successful attack you take the successful roll (let's say it was the 12%) and add to it a second d100 roll. Let's say my second roll was 25, I add that to the 12 and get 37 and that is how much damage is taken away from the target.

If they have armor, a quick and dirty setup is to assume full armor reduces damage to 1/4 and partial armor reduces damage to 1/2. So if I have a bullet proof vest (partial armor) I might get half as much damage from bullets.

It is not fool proof, but for gaming on the go with the only resources being some dice, a pen, and paper it worked (especially when playing with a fairly big group on a short time frame).

I figured I might as well drop the idea here for you as you might (or might not) be able to build off of it or get ideas from it. Anyways, I hope it helps.

[DXimenes]

@starsrift I love the oWoD system, but I've been playing it for years and it is very easy to get positively wild results now and then that can completely ruin a session.

I'm not really worried about mathematical purity, but I'd like to get as close as possible from the "Ideal DoS Distribution" graph in a conflict resolution system - making it as easy to use as possible, of course.
About the definitions, I'll quote the ones from the article:

Definition: Success
If the outcome is near enough to the goal, we say that the action is a success.

Success would be to roll a value that fulfils the "success condition". It can be rolling above a determined X (Difficulty) by adding N dice and static values (like DnD and FUDGE), or getting at least 1 die to roll above a determined Y (like WoD).

Definition: Degree of Success
The degree to which an action can be said to have obtained the goal. Abbrevated DoS, the higher the DoS, the better the result.

The DoS would be, then, how far above the X value did you go (DnD, Fudge) or how many successes did you get above the required 1 (WoD).
This determines how well/fast/awesome the action was carried to success.

@JWK5 This system looks A LOT like the brazilian Daemon system. Don't know if you have heard of it since, I believe, it wasn't published outside of Brasil. The problem with this is that the numbers start to get kind of high, and this kind of puts a hill between the system and people who can't make fast calculations.

I got the damage systems working quite well, right now I just took the oWoD system and tweaked it just a little bit to account for different body parts and combat circumstances. The combats get a little longer, but a lot more exciting

[starsrift]

I'm not really worried about mathematical purity, but I'd like to get as close as possible from the "Ideal DoS Distribution" graph in a conflict resolution system - making it as easy to use as possible, of course.
About the definitions, I'll quote the ones from the article:

Uhhh, yeah, but like the article says, it depends on how you attribute success - which is why the oWoD system has the strange falloff. If you don't define your result parameters in a specific way, you can't start to construct a die system.

[DXimenes]

I know, but the way you decide how success is met will influence the way the graph behaves, and may get me further away from the curve. I need help deciding which will be the success criteria if I want to get closer to it, get it?

[DanglinBob]

Always remember that in a tabletop RPG dice rolling is a SUGGESTION OF WHAT MIGHT HAPPEN. That is to say, most DMs cheat in favor of their players (It isn't really cheating, but lets call it that).

This means the mathy greatness of that graph is really a fuzzy edged sword. Fail by 1 and maybe you don't fail at all given the circumstances. Fail by a lot and  you really will fail.. unless it will kill the whole party, then maybe you won't even though you failed.

I guess my point here is you don't need to be a math wiz to calculate the best possible set of curves - though frankly there's so many examples of dice games out there you can copy it shouldn't be hard to find one... What is important is you get a decent level of granularity and then leave it up to the DM to decide how far your success or failure really "moves the needle" - because in the end tabletop RPGs are about storytelling, not about dice rolling... despite what some players think :D

PS: To those players, GET OUT OF MY GAMING GROUP ALREADY I DON'T CARE HOW HIGH YOUR WIZARDS INTELLIGENCE IS IF YOU KEEP PLAYING HIM LIKE AN IDIOT.

PPS: Sorry, that felt good to vent incognito :D

[DXimenes]

Thanks for your input, Bob.
I agree with everything you said, but as I stated in the original post:

I'm not interested in discussing whether this looks like an ideal system for skill conflict resolution or doesn't. It certainly doesn't seem worse than the others to me, so I intend to test it extensively.

The validity of the curve is not an issue, neither is mathematic "purity".
I am merely trying to come up with a valid tabletop approximation of the curve I presented so that I can test it.
Having a good system to support the story efforts and the fun helps the GM a lot.

How well balanced the system feels also affects the player's perception of the game's results A LOT, and this is exactly my concern.

[starsrift]

In the absence of any parameters given, you can easily replicate your desired curvature with the sine function.

Sorry, that's a dick statement.
I just mean that seriously, all you're looking at is a parabola. y = Ax^2 + Bx + C. y = Ax^3 + Bx^2 + Cx + D for x = M < x < N, even. Yes, of course we can find a function to fit the curvature. What do you want the numbers to mean or be?

[DXimenes]

I can oddly understand the operations you just put there o.o Guess I'm not as rusty as I thought I was at math after all.
 But the thing is that I don't need a function to fit the curvature, because I'm not developing this mathematically and running it on computers.
What I want is to devise a playable tabletob conflict resolution system with dice/cards/wtv that, when reverse-engineered to a probability graph (like the author did with the other RPG systems) it looks something like the "Ideal" model he described.

If finding a function helps me do that as a starting point, it certainly doesn't need to be perfectly the same as the one in the graph. I just need the "saddle point" to dislocate right and get higher as the character's "Skill" rises.

[DanglinBob]

I see what you're driving at now.

Without spending TOO much time at it: The goal is that increased skill != decreased variance - or something along those lines.

I'd use some kind of bonus system to achieve this.

Lets take a simple method, roll to succeed, add skill.

Then based on the level of your personal skill for that task, add in special dice. They can easily come in two flavors ala WoDs -1, 0, 1 dice. Make 3/6 facings +1. 1/6 -1, 2/6 0 (or something like that, im not doing math I am just guessing).

Conversely with low skill you end up with 3 -1s, 1 +1, 2 0s. The number of "bonus" dice is simply based on the skill (or simply distance from the difficulty you're attempting, I dont know which makes more sense from the speed / planning perspective).

This would mean that your first roll would be randomly modified, skewing better as opposed to D&Ds guaranteed bonus. Then if you feel crazy, add in some kind of manual override system (fate points or whatever you want to call them) for re-rolls, dice nudges, etc to ensure you have a stop-gap for failing a critical roll due to shoddy luck despite huge skill.

That could be a terrible solution btw :D It's just the first one that popped into my head.

[DXimenes]

Fuck yeah! I cracked the matrix :3
Thanks for the input, guys!

@danglinbob, definetely worth trying it out, specially if you're into using multiple dice types. My group would probably scorn it though. They're very lazy. I'll be lucky if I get them to test this system without cringing.

Here it goes!

• System similar to oWoD where you sum Attribute [1-5] + Skill [0-5] to determine your total Proficiency for that test;
• The DM determines the Base Difficulty of the test - I came up, comparing difficulties from the WoD system - with Hard: 25; Medium: 15; Easy: 10;
• Subtract your Proficiency from the Base Difficulty to determine the Final Difficulty of the test;
• Roll 3d20. Each die that beat Final Difficulty (TD - [# Rolled] < 0) counts as a success. If you get at least 1 success, you passed the test;
• Exception 1: If you roll a 20, you get to roll another d20. 20s from extra d20s gotten this way don't add another d20;
  
• - Exception 2: If your Final Difficulty is above 20, you count it as 20, but take away one die from your dice pool. You have only 2d20 to roll, git gud;
• Exception 3: If your character's contested skill is 4, he get's a Specialty. If the test is related to that specialty, he gets an extra dice, rolling 4d20;
• Exception 4: If you roll no Successes and at least one 1, your roll counts as a botch and you must face the consequences.
• Alternative Botch Rule: (Wasn't accounted for in the calculations, but will be tested on the table. Shouldn't be too bad.) A die that rolls a 1 counts as a botch, and subtracts from your Successes. If you end a roll with -1 Successes, you botched the roll and must face the consequences.

Here's are my premises to settle for this model (until I test it further):
- My group plays an overly house-ruled oWoD system. I wanted to make something that wasn't too far off from the system, so I opted for the "throw dice, count successes, profit" approach. It has the added bonus of requiring minimal math on the table;
- I wanted that the rise in chances from one point in Proficiency to the other (say, 4 to 5) to be a little smaller than the oWoD. I got the numbers and compared them to set the guiding difficulties (Hard, Medium and Easy) that I mentioned above and they matched pretty well;
- The CURVES. Oh, gosh, once I made it in Excel, the Prob. Graph looked beautiful. Here it is:

(Not accounting for botches. Their chances are part of the "0 Successes" anyway.)
If you're a complete moron, you will consistently fail. As you get better at it, you start to have a larger spread of successes, not being consistent ("insecure") but getting better. As you get more and more pro, you get an increasingly higher number of successes, being more consistent.

[valrus]

I don't know much about the different RPG systems, but you should be able to get taller and narrower curves for higher skills by increasing dice thrown without increasing dice counted.  So your skill is represented by the number of dice you throw, but the number of dice you count always remains the same.  Say, you go from throwing three dice to throwing seven, representing increasing levels of skill, and maybe even fewer than three if you're clumsy or completely inept.  But you still always count the top three dice. 

The curve won't look quite the same, I think, but it I think it might have the property you're looking for, and it's conceptually very simple. 

[DXimenes]

Thanks for the suggestion, Valrus. That was my starting point when I was developing the above solution.

I experimented with adding numerous dice in a "Count the three highest" manner, but the progression curve got too steep - with 1 point in skill giving a practically definite advantage -, and to fix that I would need to adjust the "Difficulty" of the tests and either add more dice or use dice with bigger numbers to raise the "range" between failure and success - from a d20, that goes from 1-20 to, say, a d100. When it started to get complicated, I stopped.