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I've recently become fascinated by the idea of a role-playing game system that involves advanced math.

By advanced math (admittedly, a very vague description), I generally mean that it should involve mathematical concepts such as vectors, matrices, and integration. I don't necessarily mean it should be unreadable to anyone who isn't a mathematician.

Here are a few specific concepts that might feature in such a system:

  1. A system that defines damage as the integral of attack over time.
  2. A system in which chances of success are represented using concepts from probability theory (e.g. probability distributions)
  3. A system that defines mathematical, quasi-physical laws that determine how the world behaves.
  4. One where some outcomes and effects are resolved by the application of matrix multiplication.
  5. A magic system that is described using complex numbers, vectors, or similar.

To clarify, I'm looking for a system defined using these concepts, not one that can be analyzed and partially represented using these concepts. D&D for example can be analyzed, and this analysis may include terms such as 'probability distribution'. However, the game itself still involves rolling dice and adding modifiers.

I don't mean that the system should have a large amount of convoluted calculations, or very long numeric tables.

The game doesn't have to be playable in practice, though it would be nice if it is. I would also be interested in the system if it was designed to be implemented by computer.

I'm almost certain such systems exist, basically because I've seen similar treatments of fictional subjects and games on the internet (e.g. explicit details of the physics in a fantasy world, a proof that Magic: The Gathering is Turing complete).

Is anyone familiar with such a system?

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(2) is pretty easy, since many games use dice with a bell curve for determining success. The rest is the sort of thing you might find in '80s sci-fi RPG design, but has fallen out of favour in the past couple decades. –  SevenSidedDie Aug 18 '13 at 13:32
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I came to sci-fi RPGs long after the 80s, so I only know of a few, and only by reputation rather than experience. Other Suns was widely panned for its unnecessary math during character creation. Multiverser RPG is a 90s design that required math for (among other things) determining whether you fell over when walking under adverse conditions. Aftermath (a post-apocalypse RPG) was also widely panned/loved for its complexity. Actual players of that kind of design can probably help you more though. –  SevenSidedDie Aug 18 '13 at 13:54
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Query, would a game that used these concepts rather than the practice of these concepts be interesting? See: Dungeons and Discourse slatestarcodex.com/2013/02/22/… –  Brian Ballsun-Stanton Aug 18 '13 at 23:53
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@SevenSidedDie don't forget that one edition of GURPS Spaceships that required figuring area under the curve for volume calcs of a ship. –  Brian Ballsun-Stanton Aug 18 '13 at 23:54
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Games typically avoid mathematics more advanced than addition (and multiplication by certain, easy factors like 2, 3, 4, 5, and 10) for speed-of-play reasons. You're likely going to have a hard time finding such games since many (self included) would consider advanced math by itself as indicative of poor game design. (And I am a professional user of the mathematics you describe as advanced, so I am not shy about using them.) –  KRyan Aug 19 '13 at 1:58
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2 Answers

The only thing that rings through my brain for any of that is the old FASA company. Battletech/Aerotech tends to involve some pretty crunchy physics including things like skidding, falling, velocity, and line of sight. While it doesn't always force you to do complex equations, it's the most mathematically involved system I'm aware of at this time. Ironic due to SevenSidedDie's comment on the OP.

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I played a lot of Battletech in college, plus Mechwarrior, the tie-in RPG. We played around with the mech building rules, and developed a system for finding the optimal tonnage for a mechs at a give movement rating (4/6, 5/8, etc.) maximizing total tonnage available for weapons and armor slots after finding the engine and internal structure weight. It wasn't advanced math, just a series of charts. –  RobertF Mar 7 at 15:12
    
I just used the BattleMech Designer program for that. And those charts are usually derived from anything from algebra (for mech tonnage) to calculus (how tall your mech is, the angle of LoS and height of target or structures in between) –  CatLord Mar 7 at 17:38
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I wrote up something to model space movement with thrust application and vectors on a hexboard. Its fairly simple and generic, play tested once with some friends. Meant as a kind of 'movement engine' for space combat, it includes some very simple ship creation and combat rules, but you could do something like slap it into space borne Battletech mecha or the like. The advantage is that all units move simultaneously towards their new calculated destinations after applying turns and thrusters at the start of their turn vs the old Battletech movement method where everyone ran up behind the other guy and fired when it was their turn to move. We used a separate off board card for each ship and poker chips to keep track of the directional thrust vectors (disadvantage - probably impractical for large scale battles) Its not high order math by any means, but there are vectors and a little bit of f=ma built into it.

https://docs.google.com/file/d/0Bwf3bvFT3g7GbEFZWGZJa3VKcEE/edit?usp=sharing

(updated doc to .pdf format)

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Would you be able to host your writing on the internet somewhere where it will be relatively permanent (or as much as something can be on the web), e.g. on Google Docs? The problem with just dropping an email link is that this answer becomes not useful when you change email, miss an email, or stop responding to these requests with the Word document. It's a similar case to our aversion to link-only answers: once the link dies, the answer becomes crippled and useless. Please host your system somewhere people can freely access it on their own effort! –  Jonathan Hobbs Aug 19 '13 at 0:36
    
Hopefully you are able to get to the link now and the downloaded document has the graphics. Sorry for the size, I haven't used google docs before and am a bit of a Luddite. –  TysoThePirate Aug 19 '13 at 1:00
    
Updated doc to reasonably sized pdf format –  TysoThePirate Aug 19 '13 at 1:55
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