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# Gaming Discussion

For all things gaming related.

# Formalizing and Rationalizing GURPS

Serpent of the Tree of Knowledge

Formalizing and Rationalizing GURPS

Hello MW.

I have been learning GURPS over the past couple of weeks and have found myself a little overwhelmed at the task. While there are many a good primer and introduction out there, I feel that they do not address the more formal aspect of GURPS, which I believe is the very essence of its versatility. As a didactic method and also a mental exercise, I was wondering if any of you fellow Weavers would be interested in constructing a formal 'derivation' of the GURPS rules and put together a mathematical primer with me.

Perhaps 'formal' is not the best word, as I don't see the necessity of decades of pages devoted to proofs, but 'rational' at the very least, in the sense of giving the reason as to why GURPS rules has us do one thing over the other. One example is the success roll that seems counterintuitive to most. Given a value S in order to succeed, most games require a roll R such that RS, whereas GURPS has RS. This can be explained (though in a roundabout and not necessarily all that rigorous way) by a single-tailed test. Assuming the value of each roll is a test statistic,
 To be truly rigorous, each roll is technically an event, but that is why we roll three independent die. Given our sample size n=3, our test statistic is thus the sum of each independent value, although many statisticians would frown on the power of such a shoddy statistic. Furthermore, one can even argue that each roll is pretty much a generated statistic of the event itself--we blackbox the actual event and simulate the statistic itself!
(caveat) S serves as a rejection criterion. Given a normal distribution of R values, we succeed iff RS. Failure, then, is a 'statistically significant' event (as per the language of the single-tailed test), meaning that for GURPS, the null hypothesis is success, whereas for other systems, the null hypothesis is failure.

I admit firsthand that I haven't made the argument above sufficiently rigorous enough, but this is the sort of level of discussion I would like to build on for the primer. I would like to take this kind of analysis and apply it to the game mechanics--starting from the point system, give quantitative reasons as to why each attribute credits or debits the character point pool (and by how much!), extending to describing the algorithm of combat and character interaction, including a discussion on the general mathematical structure of modifiers, possible meditations on the economies in the gameworld, and, most importantly, the modularization of such rules so we can define a scalability (i.e. how the general rules that act on the individual character level can also extend/be modified for groups, societies, worlds, etc.) A lot of my thoughts on this focused on finding a more unified way to address the Mass Combat supplement, and I think it would be interesting to see if there is any rational structure that we can tease out of the rulebooks.

Ultimately, the purpose of such a primer is two-fold: (1) provide a rigorous treatment of the GURPS rules that shows the derivation of each action and result, so newcomers to the system are given a graded introduction to the system, and (2) specify the rational design of GURPS which allows GMs to easily tweak the system to create a consistent 'homebrew' structure as needed.

Of course, many out there understand the rules quite easily without such pedantry, and I suggest this not to knock anyone down. In fact, many would argue that such pedantry is what overwhelms neophytes to GURPS in the first place. I feel, however, that it would be a useful resource to those like me, who learn best through formal rules and are fascinated by the mathematical structure of the system (it's why I was attracted to GURPS in the first place!)

I would love to talk with anyone who is intimately familiar with the GURPS rules, and also those who are interested in/have exposure to formal mathematics. I think this would be a frightfully fun little project to embark on, and anyone interested, please pitch their ideas!

I afraid that there's no rationality behind GURPS. Most of the rules evolved through trial and error. If you want to bring mathematics into it, you will also have to bring in physiology and sociology. That is, you can only explain the rules in terms of how people think and how they interact.

Serpent of the Tree of Knowledge

Quote:
 Originally Posted by shawnhcorey I afraid that there's no rationality behind GURPS. Most of the rules evolved through trial and error.
Hmm, could you expand more on that? While I agree it would be futile to completely axiomatize the system (which I admit I did not make clear in my post), at the same time, the mere fact that it's not an ad-hoc game and has clear rules (at least in the sense of having a core set of rules) means that there is some formal structure. Otherwise, you wouldn't be able to strategize (think 'power players') or even play the same game common across all players.

Quote:
 Originally Posted by shawnhcorey If you want to bring mathematics into it, you will also have to bring in physiology and sociology. That is, you can only explain the rules in terms of how people think and how they interact.
Here I think I disagree. While physiology and sociology provide some 'laws' for our own universe (I use the term 'laws' heuristically, not to state any metaphysics), GURPS has its own 'laws' in terms of its core rules. While it's true that we can simulate many physical/social phenomena in the game, what matters in the reference of the game is the rules of the game, not of the reality it is purportedly simulating. That is, we are playing in the map of the terrain, not the terrain itself, so all that matters is the map. The mathematics I reference isn't the physical correspondence to reality, but the internal framework of the system, and seeing how each action follows from within the system.

Thank you for your counterpoints, as they definitely clear up some of my thinking.

I wasn't talking about any simulation of reality. I was talking about the designers and the players, especially during play-testing. It's their thinking and social interactions that have as much, if not more, influence on the design of the game than the mathematics.

Serpent of the Tree of Knowledge

Quote:
 Originally Posted by shawnhcorey I was talking about the designers and the players, especially during play-testing. It's their thinking and social interactions that have as much, if not more, influence on the design of the game than the mathematics.
Ah, I apologize for my misunderstanding. Thank you for the correction.

While I agree with you full-heartedly on the note of the actual players having (much) influence on game design, my purpose is to work specifically within the framework of rules. I do defer to you that rule revisions are based off of player feedback, but at the same time, I'm interested in analyzing the formal properties of the rules themselves.

To give an example, a game of Go will seriously depend on the skills and personalities of each player. However, there are fixed rules of Go (tweaked for handicaps--e.g. novice players will be given two initial stone placements) that gives rise to formal properties of strategy (e.g. opening strategies, josekis, captures, etc.)

I will further grant that RPGs are interaction-based, therefore less formal/fixed than Go and more psychological, like poker. Nonetheless, there are certain strategies and rules involved in poker, based both on hands (i.e. the probabilities of getting certain cards) and cold-reading of opponents. My goal is to work more with the former than the latter, and I believe even if it ignores the highly variable 'social' aspect of the game, it creates a more intimate familiarity with the rules of GURPS.

Alright, here we are and I'm going to bust this down pretty easy enough:

the 3d6 roll under success is used for a few reasons.

1) when it was invented getting a hold of dice at a local gaming store was near impossible. They didn't have many gaming stores outside of major cities (if at all) and the net didn't exist (virtual dice like on MW weren't even a thought back then), but everyone had at least 2d6 in their house monopoly or backgamon game. D6 where decided to be the only dice that would be used.

2) as such d6 has less possibilities than say, d100, but enough variance in outcome to comply with not making things too terribly math heavy while allowing for some realistic possibilities for failure and keeping combat and skills balanced and quasi-realistic when making characters at base point value. By altering the point value we then also adjust the style of campaign as well and make it more or less cinematic depending on which way we swing. This allows the GM have total control over how the setting plays out, not just the themes they introduce as the GM.

3) the reason for rolling under is because in GURPS as a point buy system you can raise a skill to level 24 or even higher if you so chose, and doing so even have in game consequences (such as extra range, reduced cost, or critical failures simply becoming failures, etc.). If you reversed the system you'd have to buy our skills down as well as your attributes, instead of up. Really what you're doing is more like a stat check in DnD, where you have an st of 17 and need to roll under it. Personally I think it makes a lot more sense once you get used to it, but probably not to you because you're accustom to something else, which is why so many games are built on that platform, because they are already used to using d20 and learning a new system is hard for players :/

If you want a condensed version of the rules, take a look at GURPS lite.

It's all very easy if you think of it like this:

Character generation takes a while (because it's so customizable), but once done, the rest of the game flows super easy without ever having to check back with books and charts again. After that just roll 3d6 to check something, anything, and see if it meets or goes lower than the target (contested rules are a bit more complex, but same idea). If you meet or go under, you succeed. Yay! No more pulling out the calculators to determine what happened and trying to determine how many success dice we have that explode to another die and failure dice and what happens when exploding dice fail and...

You see my point. It's simplified. 1 roll, that's it. There are a few exceptions like damage and contested rolls, but that's really the whole thing in a nutshell.

Granted the 3d6 thing is a bit dated as virtual dice eliminate the need for using a particular kind of die (or even a realistic one), but it also isn't broken, and would only imbalance and complicate the system unnecessarily if you tried to change it.

If there is any other questions I would love to help.

Serpent of the Tree of Knowledge

Hahaha, World of L_Tiene, I simply bow to your enlightened post.

I do have a question regarding virtual dice--do most virtual die systems simulate the actual die cast or is it just a random number generator? Because the distribution of values are different--a random number generator for the possible values would be 1/18 (=1/(3*6)), whereas actually simulated die casts would have different probabilities due to degeneracies (any one particular roll with a value a for dice 1, b for 2, and c for 3 would be 1/216 = 1/(6^3)). Outside of that, I have no qualms about your explanation of dice rolls, and I will say that I have no trouble understanding the r ≤ s criterion, even if I understand it in a convoluted and 'wrong' way :P

Thank you for clarifying how simple the game gets once the characters are set up and the dice starts rolling. I now understand that on a practical level, gameplay becomes much simpler.

However, what I'm trying to do is find people interested in a more formal treatment of the rules. I don't mean to replace what is already out there. But more than GURPS Lite's condensed rules, I'm interested in how the rules interact with each other. As I said, it's a purely academic exercise, though for people like me, it will help reinforce how the game core is structured. I hope I don't ruffle anyone's feathers, but I do want to be clear about my purpose.

Thanks to everyone for the insightful responses so far!

I've never played GURPS before but the question about dice rolling programs I may be able to put something to.

I had to write a small dice rolling program while at college a while ago and the way we had to do it was treat each dice seperately and add 0.5. I don't know how this MW's (and others) have encoded there's but ours were simple RNGs.

Just to clarify what we were taught the dice roll would essentially be this:

(Rnum(5)+0.5)+(Rnum(5)+0.5)+(Rnum(5)+0.5)

The numbers would be held as a single integer therefore there would be no decimal places and it would be rounded up. Possible values would be 0.5 to 5.5 then they would be rounded so they would be 1 to 6. As far as I can remember I think the programming language we were using meant that the Rnum command would give values with 4 decimal places. Plus the number in the bracket after the Rnum command would give the maximum value. So Rnum(5) would give values from 0.0000 to 5.0000. If we wanted to make the rounding of the number more correct I guess we should have used a change of +0.4999 and place an if command that stated if the Rnum gave a value of 0.0000 then it should add 0.4999 and also add 0.0001, but for our purposes at college this level of accuracy wasn't needed.

P.S. I'm not a mathmetician at all, I just know some basic programming, so I know my mathmatical notations are probably all wrong.

Edit: P.S.S. I just thought of something, you could just ask a mod how the dice roller is encoded, they can probably find out somehow. Or make a thread in the Site Discussion forums.

When it comes to virtual dice rollers and math, MW is the only people I know of that actually did it right. I've seen other dice rollers but they were always horribly flawed.

As the for the exact math behind it, you would have to ask the administrator Michael, I believe he is responsible for that, but my guess is that they took a lot of things into account. Michael is a pretty smart guy and they've been banging away on this site for many years.

Now getting to your other "formal treatment of the rules" thing. That's really a matter of GM taste. Some GM's make you roll if you sneeze to determine color and consistency while others only make you roll during times when the outcome is cinematographicly questionable according to Hollywood standards, though most fall somewhere in between.

That's kind of the beauty of the system. It allows each GM to be as much or as little of a rules lawyer as they feel appropriate. This is where the house rules come in. I have a good one to do with this. If a player is unsure if they should roll, they should roll, and the GM is free to require a roll whenever they wish. This allows the players and GM to develop a flow appropriate to each game and scene, and in the case the GM wouldn't have required a roll but one was made anyway, then we now have additional information to help tell the story (IE, joe gets a critical success on his diplomacy roll, now allowing the GM to react accordingly with the NPC, even though he might have just rolled with it as he interpreted the text otherwise).

So that's the best way I've found to interpret those things.

If you have a specific question though, I might be able to address that.

Quote:
 Originally Posted by Aethya Just to clarify what we were taught the dice roll would essentially be this: (Rnum(5)+0.5)+(Rnum(5)+0.5)+(Rnum(5)+0.5)
I do know something about math and that is horribly wrong. Most random number generators create numbers between 0.0 and 0.999.... The formula would be:

int( rand() * 6 +1 ) + int( rand() * 6 + 1 ) + int( rand() * 6 + 1 )