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> Dice analysis paper, Is this overkill yet?
Ellery
post Apr 11 2005, 01:30 AM
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A friend of mine from my old gaming groups has demonstrated what happens when you put physicists around a new dice system. On this board, I think we've talked about almost everything that's in the PDF there, but someone besides me might also be interested in his fixed TN dice analysis.

There were a couple of surprises for me (if you can get past all the math). One is that our good old karmic reroll is really just a dice-heavy way of changing the target number; another is how hard it is to be assured of victory in an opposed test no matter how many or few dice you have, and whether or not the dice explode. There's also a graph showing how many times you have to roll the dice when you're using exploding dice, which I guess answers the question of how much rerolling there will be with exploding dice.

Also, the pictures on page 11 are really pretty, even if I don't quite understand what they mean.
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Kagetenshi
post Apr 11 2005, 01:46 AM
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Not overkill at all, why would it be?

Really, anything that changes the probability is equivalent to some degree of anything else that changes the probability, so the karma pool bit is no surprise.

~J
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Ellery
post Apr 11 2005, 01:57 AM
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I know--it's obvious in hindsight. I just wasn't used to thinking about it in those terms.
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Slash_Thompson
post Apr 11 2005, 01:58 AM
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didn't realize that this sort of general analysis (not the actual math, I'd never touch that without a trusty copy of Matlab) required a physics degree^^;

these sorts of mental calisthenics do prove rather well. that rerolling, changing numbers of dice, changing target number, changing success threshold, using a variable threshold (opposed test), exploding dice, are all just ways of manipulating percentages. i

n fact, using a lookup table. it would be possible (and by table, I mean like a 20 page manual; if not a program for calculation) to reduce every test in a game (opposed, open-opposed(very diff. to do without the aforementioned calculation program), fixed threshold success, single success at a known tn, etc etc) to a single throw of a few d10's (representing a percentile throw, to say... three decimal places of accuracy, so five dice) by one person.

would this be a fun system to play? I don't think so. part of the fun of a game is HOW it models chance, not just whether or not it is accurate.

it would even be possible, using the aforementioned above system, to do statistical analysis on the 'real-world' and generate direct 'success percentages' for certain common conditions. "%failure of a gun that has been maintained within the last month." "average number of hours a marathon runner can move at a known pace before they begin to show performance degredation over XX%" to add more 'realism' to your game.

I for one, don't want to play "Real-life" I want to play "Shadowrun".

that said, this is interesting stuff to read through, but it doesn't change my like or dislike of the old system.

but then, I'm one of those people who will still insist on real paper pages when the rest of the world has switched to electronic storage of books. I'm just a tactile person I guess.
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Penta
post Apr 11 2005, 01:59 AM
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Please sum it up for the math-impaired?
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Slash_Thompson
post Apr 11 2005, 02:05 AM
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@penta; there's a list of bullet points on the final page with the 'conclusions' of the analysis.

these are pretty much the 'ideas' that anyone might want to remember out of this paper, since they're very non-mathematic and quite simple to recall.
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Ellery
post Apr 11 2005, 03:47 AM
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I think the problem with a d%% system (4d10) is also that it's difficult to adjust percentages in a sensible way; you'd end up with a complicated formula for every adjustment.

What we would like to have is a system that gives reasonable results with simple modifications. I think SR3 actually performed that function rather well; what was lacking was a consistent way to apply all the bonuses and penalties. (The probability glitch between 5, 6, and 7 was annoying too, though.) SR4 has another chance to make things consistent again, but they're probably just winging it and going on gut instinct rather than doing much analysis, so even if the modifications are simple, I'm worried that the results will be unreasonable.

Incidentally, those color tables on p.11, if you zoom in, actually have a ton of information about what happens if you set people against each other with different numbers of dice and/or give them dice penalties and bonuses.

So on second thought, maybe all opposed tests should be resolved by looking up the color on a chart like that and rolling d%...that would certainly be fast and simple to roll (one roll of two or three dice!).
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Kagetenshi
post Apr 11 2005, 04:01 AM
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In my opinion, charts are bad. With the current rules it's reasonable to be able to run any given aspect of the game without consulting any reference material; charts of any meaningful size that cannot be trivially recreated destroy that ability.

~J
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Ellery
post Apr 11 2005, 04:10 AM
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I'm joking!

I've had enough table lookups from D&D to last three or four lifetimes (back when there was no logical progression to anything, and no two classes did anything the same way). But it could be given as an option to people who hate rolling dice; it would both work and be fast (with the aid of a chart).
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Critias
post Apr 11 2005, 04:17 AM
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Or you could just print up the probabilities as a pie graph, and toss darts at it.
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Wireknight
post Apr 11 2005, 04:21 AM
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QUOTE (Critias)
Or you could just print up the probabilities as a pie graph, and toss darts at it.

You assume the average gamer has enough hand-eye coordination to hit such a graph! Most stop developing that skill when they can reliably (95% of the time in a d20 system) reach their Mountain Dew, or snag a handful of Cheetos.
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hahnsoo
post Apr 11 2005, 06:04 AM
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But we're Shadowrunners ™! That means we have the hand-eye coordination (and the wrist fortitude) to toss dozens, even hundreds, of d6! Let the good times roll (literally)!
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Arethusa
post Apr 11 2005, 07:04 AM
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While this is really nothing new to me (though it's nice to see it formally organized and addressed), I do hope the people currently working on SR4 take note of this. SR3 was very obviously designed with almost no basic understanding of statistics and chance modelling, and with a complete revamp of the dice system, there's a very real potential for things to get a lot worse if the people designing it step in and don't have the shoes for it.
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Eyeless Blond
post Apr 11 2005, 09:21 AM
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Indeed, they really do need a mathematician somewhere on staff to help them out with stuff like this.
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SirBedevere
post Apr 11 2005, 10:42 AM
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I hope that the developers have compared the mathematical probabilities for the SR4 & SR3 systems!
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Tandem
post Apr 11 2005, 07:26 PM
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another interesting point is that if you want to improve your chances, you'll have to invest exceedingly more dice for each 1% you get. that means that gaining dice to your pool is less and less important against regular TNs.
the result is funky probability in high-level games, in which the mods on TNs matter more and the number of dice matter less.
this statistical issue has an impact on the game because lower-level games don't react like higher-level games, although the same rules apply on both.
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