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Author Topic: In Search of a Fortune Mechanic  (Read 9291 times)
JMendes
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« on: February 17, 2003, 07:24:58 AM »

Hey, all, :)

Lately, I have found myself questing for a mechanic that would comply with a series of design specs, and I thought I'd put those specs to consideration by this group.

I'll start by laying out these specs and then summarizing how a number of already existing mechanics follow or break the specs. The mechanics I'll be using will be d20, shadowrun and simmetry.

The specs:

1) The mechanic should be simmetrical. In other words, the effect of applying a bonus should be of exact same magnitude and opposite sign as that of applying a penalty.

2) The mechanic should display exponential decay. In other words, compounding bonuses or penalties should have a progressively smaller effect.

3) The mechanic should yield a level of effect. In other words, it should not be all-or-nothing success or failure.

4) The level of effect should also display exponential decay. In other words, higher levels of effect should be progressively difficult to achieve.

5) The level of granularity should be high (i.e. fine) with respect to both bonuses/penalties and levels of effect. In other words, very coarse mechanics or curves that decay too fast are a no-no.

6) Ideally, the mechanic should be highly open-ended, both with regards to bonuses/penalties and to levels of effect. However, this particular point might be sacrificeable.

7) The mechanic should apply equally well to multi-part conflict as it does to one-on-one conflict. By multi-part, I do not mean us three against the five of you, but rather, one against two (or more) that are also against each other.

Note: At this time, I am not particularly concerned with search time or handling time. As I progress, I am likely to want to minimise one of those (and not necessarily the other), but this is definitely not a priority right now.

Also note: The relationship between specs 2 and 4 above is undecided. That is, assuming success, it is not clear to me whether it should be harder to generate a high level of effect on a difficult test than on an easy one.

Ok, enough of that. Let's take a look at what's out there:
Code:

Spec    d20       SR       Simmetry
1       Yes       No       Yes
2       No        Partly   Yes
3       Yes       Yes      No
4       No        Yes      No
5       Yes       No       Yes
6       No        Partly   Yes
7       Yes       Yes      No

The reason for the 'Partly' bit is that SR exhibits the required behaviour on the positive side of the scale (bonuses) but not on the negative (penalties).

So, that's that. I hope I made sense. Ideas, comments, anyone?

Cheers,

J.

P.S. I'll follow up my own post with an idea that I and a friend came up with, that has its own obvious limitations, but that might serve as a starting point.
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Ron Edwards
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« Reply #1 on: February 17, 2003, 07:30:21 AM »

Hi Jeff,

Are you familiar with the Sorcerer mechanic? It seems to fit the bill ...

Best,
Ron
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JMendes
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« Reply #2 on: February 17, 2003, 07:37:33 AM »

Hi, again, :)

To follow up from the above, here's what we came up with:

A) Start with Simmetry. However, figure out your total bonuses and penalties, as they apply to you only and not your opponent(s). (Yes, this goes against Mike's rant about opposed/unopposed die rolls...;)

B) Everyone involved rolls. For each roll:
B1) If the first roll succeeded, you will be generating positive (0+) effect numbers. Otherwise, you will be generating negative (<0) effect numbers.
B2) If you succeded the first roll, subtract one from your total bonus/penalty and roll again. If you succeed, add one to your effect number. Repeat until you fail.
B3) If you failed the first roll, add one to your total bonus/penalty and roll again. If you fail, subtract one from your effect number. Repeat until you succeed.

C) Everyone allocates the generated effect number (whether positive or negative) at will to each antagonist party.

There is an obvious and a not-so-obvious shortcoming to this approach:

Obvious - Can you say klunky? :) In a limit case, you might get stuck rolling some seven dice about four or six times, having to be careful to track your results. Then again, this mechanic is not intended for detailed action resolution, so that might not be so bad.

Not-so-obvious - The level of effect curve decays too fast. For a 50/50 test, the chance of generating a mere +1 effect is very close to 25%. In other words, the granularity of the level of effect is too coarse.

Comments, anyone? Please? ;)

Cheers,

J.
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JMendes
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« Reply #3 on: February 17, 2003, 07:40:43 AM »

Hey, Ron, :)

Whoa, that was a fast reply. :)

Quote from: Ron Edwards
Hi Jeff,


Erm... It's Joao. ;)

Quote
Are you familiar with the Sorcerer mechanic? It seems to fit the bill ...


No, I am not. Could you post a quick primer or point me to it? (Alas, much as I would like to, I do not have the possibility of purchasing it at this point...)

Thanks. Cheers,

J.
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Ron Edwards
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« Reply #4 on: February 17, 2003, 08:07:35 AM »

Hi Joao (sorry, was thinking of another poster who uses "J"),

Sorcerer goes like this:

Roll dice = score that's relevant. Other guy (or whatever, could be the fence you're jumping over) does the same thing.

No target numbers are involved at all, ever. Just compare the rolls; whoever's higher, that says failure or success. If you need some degree of effect, then look for however many dice are higher than the loser's highest value. This obviously gives degree of failure as well; that's just a matter of POV.

Try it yourself a few times with a handful of dice. It doesn't really matter what type of dice you use, as long as they're all the same.*

Bob's character (six dice) is trying to get the attic window unstuck as the demon (eight dice) batters down the door. Bob rolls six d6, getting 1, 1, 3, 3, 4, 5. Biff, the GM, rolls four d6, getting 6, 4, 4, 3, 2, 2, 2, 1. The demon wins, his 6 beating Bob's 5.

Degree of effect = 1, because only one die of Biff's was higher than Bob's highest value.

Ties are handled through elimination - ignore them and proceed to the next dice.

Do not pair up dice as in Risk. That is not correct.

Throughout play, 1 die = 1 score point = 1 bonus = 1 penalty. There are no "pip" penalties/bonuses (e.g. "subtract 1 from highest value" or anything like that). This principle is the core of the damage system, the demon-Binding rules, and everything else concerning ongoing effects of rolls.

Now, for involved situations (fights, debates, ten guys with ten different and semi-incompatible goals in mind, etc), it goes like this.

1. Everyone announces their intent first. The order of announcement is meaningless; this phase is not over until everyone is exactly satisfied with what the characters are trying to do. Please notice that order of character action is not established at this time and cannot be relied upon to occur as any one person hopes.

2. Everyone rolls. The order of the attempts is set by the high values. Please note that none of these rolls are defensive.* At this point, we know nothing about "what happens" except for the order of events. Do not pick up the dice at this time. Leave them there.

3. Whoever would defend against the first guy who goes, if any, has a choice: abort your current action to defend with full dice, or defend with one die in order to (if you live) carry out your previously-stated action.

4. If the second guy hasn't aborted, repeat #3 with his attempted action. Carry on through all actions. All effects of actions occur immediately upon their completion (not waiting for the end).

Note that everyone can see everyone else's "offensive" dice at all times. All defensive rolls are made with other dice. I'm not explaining the within-round effects of damage because (a) they're not special and (b) it would impede the point at hand rather than clarify anything.

This system works very, very well for the Woo/Tarantino situation of five guys all pointing guns at one another simultaneously, or with people all shouting at their demons or pulling weapons or jumping over catwalks in a confused flurry of choreography and differing agendas.

Best,
Ron

* This point has one or two exceptions or ramifications that I'm not explaining in the interests of space and clarity.
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Walt Freitag
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« Reply #5 on: February 17, 2003, 08:22:32 AM »

Hi Joao,

Do you want the distribution of levels of success to be the same for tasks of different difficulties? In other words, if I succeed in a difficult task, should I then have the same chance of any given level of success than if I succeeded at an easy task? In other words, should the decay rate on the levels-of-success curve be the same regardless of the original bonus/penalty for the roll?

Can you tell me the decay rate you want for levels of success (perhaps, what numerical gradation of success or under should be achieved 50% of the time, assuming success in the first place), either as a constant (if the answer to the above question is yes) or as a function of the overall chance of success?

- Walt

Edit to say: oops, you already answered the first question in a way; you said it was undecided. Sorry I missed that. With that in mind, can you give me the decay rate for levels of success that you'd want to see given an overall chance of success of 50%?
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JMendes
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« Reply #6 on: February 17, 2003, 10:37:47 AM »

Hey, guys, :)

First off, thanks for taking the time to stab at this rather convoluted problem of mine. :)

Ron, I like Sorcerer's mechanic, and I can see it working in a number of situations. However, it fails to meet the specs here:
Quote from: Ron Edwards
Throughout play, 1 die = 1 score point = 1 bonus = 1 penalty.

This is highly non-simmetrical, as adding a die and subtracting a die have wildly different effects.

Walt, your question gives me pause for thought:
Quote from: wfreitag
[Assuming success,] can you give me the decay rate for levels of success that you'd want to see given an overall chance of success of 50%?

Unfortunately, I don't have a well-informed answer, as this falls into about the same category as the relationship between specs 2 and 4, and as such, is also largely undecided. I do know that a 50% decay rate (where each level of effect is half as likely as the previous one) is definitely waaaay too steep. Intuitively, I'd say that an 80%-90% decay rate would feel about right. Anything higher than that is likely to lead to unwieldy results.

Hmm... Yeah, I notice that a decay rate of 84% leads to a 'half-life' of 4 levels of effect (i.e. the 5th extra level is half as likely as the 1st), which is rather close to the original simmetry, so I'd aim for that.

Again, folks, thanks for devoting your neurons to this stuff. :)

Cheers,

J.
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Jack Spencer Jr
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« Reply #7 on: February 17, 2003, 11:59:18 AM »

Quote from: JMendes
Ron, I like Sorcerer's mechanic, and I can see it working in a number of situations. However, it fails to meet the specs here:
Quote from: Ron Edwards
Throughout play, 1 die = 1 score point = 1 bonus = 1 penalty.

This is highly non-simmetrical, as adding a die and subtracting a die have wildly different effects.

I don't get how you could say that it seems to be very symetrical to me.
1 bonus = rolling 1 extra die
1 penalty = 1 rolling 1 less die

It is simply one more or less chance to roll a success. I don't see how they differ wildly.

But it might be more to your liking if you apply a bit of theory Ron had on penalties where it's best to not bother with them. I can't find the thread, but basically it went something like The player will keep a sharp eye on any bonuses they may get, because it does offer them an advantage but will sorta "forget" about any penalties for the exact opposite reason. Not that said player may be actively trying to cheat. It's just human nature. Which means it's up to the GM to make sure the player is applying any penalties to their dice roll. After a while, the GM gets tired of this and stops doing it. So then the player only has their bonus, which they kept a sharp eye on, but no penalties.

How I took this is that you can have bonus dice, like in Sorcerer and the players will keep an eye on that. Then any penalties are better applied in an opposite manner, either being added to the taget number or, in the case of Sorcerer, to the opposing roll.

There's my two cents.
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Mike Holmes
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« Reply #8 on: February 17, 2003, 12:53:54 PM »

Quote from: JMendes
(Yes, this goes against Mike's rant about opposed/unopposed die rolls...;)
Not really. You use the same system for everything, right? Then it follows the advice of the rant perfectly.

You can "fix" the Sorcerer mechanic to suit your needs by simply saying that penalties do not subtract from your pool, but instead add to your opposition's. OTOH, the Sorcerer mechanic is a bit ideosyncratic. Meaning that rarely do you have more than a 90% chance of success. The underdog always has a decent chance of success. This would dissappear somewhat in a game that used more dice for finer granularity as diparities would be larger. But still, it takes a lot of dice in your favor to get a very relieable result. This is cool for Sorcerer, but you should consider it if you go with it.

Also, Sorcerer probably does not suit #5 well, in that it decays very rapidly (1 is by far the most likely roll). For a method that "fixes" this, however, see Donjon.

Synthesis, one of my sysetems, uses a the simplified version of the Symmetry system with none of the small dice. In case you've not seen it, here it is (it's based off Story Engine if that helps):

You roll a dice pool, versus an opponent pool. As per the Sorcerer "fix", bonuses are added to your pool, and penalties to the opponent's. Ironically in this system that's unneccessary to keep things symetrical, but neccessary to prevent pools from bottoming out. Evens are successes, and you subtract your successes from the opponents. The high roller gets that difference in levels of success. So, I roll 8d and get 4 evens, and you roll 7d and get 5 evens, that means you have 1 net success level.

This works for whatever level of granularity you want assuming you don't mind rolling heaps of dice (which I don't personally). For multiple people fighting, basically a success by my character helping yours out becomes one more die for you to roll. So, two against one, I help Bob, and he attacks you with my bonus. For a less heroic version where everyone is accounted for, the solo defender decides which of his opponent's successes to cancel, and the rest come through. So it works in whatever sort of groups you like. In fact, you can just pile up one side's dice in one pile against all the opposing side's and let the GM dole out the results.

The Synthesis system fails critera number 2, I think, in that each die results in the average result being .5 higher on average with no decay. The return curve, however decays quite naturally (#4/5).

It sorta fails #6 in that there is an upper limit on successes. But I find that realistic. The system allows you to roll from zero to your pool total in successes, but usually gives something much nearer zero. But you can always win against any opponent (they may roll a zero, and you might roll more). This means that getting anywhere near your upper limit is very rare, and represents the exceptional effort well. It depends on what you want the open-ended system to produce, open ended numbers, or just success at all possible levels? Synthesis does the latter while still limiting the resulting level, making the numbers easier to handle (Credit Story Engine).

BTW, I think that Wayfarer uses something like what you have above, where you roll untill you fail to determine number of successes.

Mike
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ThreeGee
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« Reply #9 on: February 17, 2003, 03:00:05 PM »

Hey J,

How about this: Skills have a window from 1 to 10 (i.e., 11-20 would be okay by subtracting 10, but more complex math yields more bang for the buck). Bonuses/penalties are percentile. Successive bonuses are one less, but never less than zero, r.r. for penalties (i.e., +5 and +5 is +9). Base chance of success is the skill^2 in percentiles, modified by the total bonus/penalty. Degree of success is the roll divided by an arbitrary constant (e.g., five), assuming the roll is equal to or less than the base chance of success. Compare the successes among all participants.

Weird? Certainly. Fits the criteria? If I understand you correctly, yes.

Later,
Grant
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Jason Lee
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« Reply #10 on: February 17, 2003, 04:05:01 PM »

Assuming I've wrapped my brain around his...

1) Use opposed rolls and only use penalties (penalize the opposed roll for a bonus).

2) Roll 1d12 + stat with exploding dice.  A penalty lowers the die type (d4, d6, d8, d10, d12).  I didn't check the math, but if I'm not mistaken the exploding dice effect should create a little decay.

3) Success based on how much the roll succeeded (or failed) by.

4) Should link to #2.

5) If you go with each point a roll beats another by as a success level I think it'd have a lot of variance (IMO).

6) Nope.  Success level is open ended, but penalties aren't.

7) For all rolls roll 1 defense die and 1 attack simultaneously (red and white maybe?).  Each opponent you have to attack or defend from simultaneously is a penalty to the appropriate die.  Just beat everyone elses attack/defense roll to dodge/hit them.  This doesn't have to be a combat system; you could manuever for politically power while defending your own (kind hafta).

Kind search heavy, and you need 10 dice (1 of each in 2 colors).
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- Cruciel
JMendes
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« Reply #11 on: February 17, 2003, 05:23:49 PM »

Hey, guys, :)

First off, good efforts all around. This is turning out to be a good brain jog and reading the suggestions is sending my mind along various tracks I'd never go down on my own. Hopefully, eventually, we'll come up with something perfect. :)

Now, to address specific replies:

Jack: Trust me, Sorcerer as is is not simmetrical. For instance, if I'm rolling one die, then adding a die will just about double my possibilities of a best result, whilst substracting a die will not halve it, but rather, will kill all my chances. Plus, while it decays nicely for bonuses, it behaves horribly for penalties, for much the same reason. Your suggestion to add penalties to the opponent's pool instead does fix both these problems. However, it breaks spec #7. To clarify, spec #7 is not about having more than one opponent, but about having more than one opposing side.

Mike: I am unfamiliar with Donjon and Wayfarer (yes, I know, I should at least find some way to do my research homework...:/ ) I would have to think harder as to whether synthesis displays an adequate decay or not. However, as it is, it doesn't work for multi-sided conflict. In fact, any system that 'adds penalty dice to the oppposing pool' is quite simply not going to fit spec #7. It does not break spec #6, however, as any die-by-die-success system that is open-ended in the number of dice is by definition open-ended in the number of sucesses.

Grant: At first, it also seemed odd that it would be impossible to generate a good level of success under adverse circumstances, but upon further consideration, this is beginning to sound more and more reasonable... However, your suggestion doesn't decay well. A +5 bonus is going to have wildly different results when your skill is, say, 2 or when it is 9.

cruciel: Your suggestion was rather intriguing and it got me thinking the most. It breaks spec #5, with a rather coarse limit of only 4 possible levels of penalty. At first glance, it seemed like it might also break #7, then I saw that you had it covered. Then again, it occurred to me that all that you are doing is reducing a multi-side conflict to a series of two-side conflicts, which means that a guy might succeed wildly against one oponent and fail miserably against the other. This is not exactly what I had in mind, but it may turn out to be the only feasible solution.

Also, to get back to Walt: upon further thought, it seems that the more general case is to have the same distribution of effect numbers, assuming success, regardless of the original difficulty of the test. Let's call that the normalizd effect number. Then, if desired, one can do a simple arithmethic calculation with the normalized effect number and the original test difficulty to come up with the actual effect number. Or not. The point is that normalized effect numbers will be fine for the purpuose of this discussion.

Lastly, I would like to emphasize that all the suggestions given, even though not entirely suitable, were useful in that they got me to think and maybe even to challenge some of the assumptions behind the various specs. Ultimately, it may come down to the fact that my original spec are simply unattainable without massive buckets of dice and reams of spreadsheet calculations, but I sincerely hope that not to be the case. Thus, I would like to thank everyone so far, and please, keep'em coming. :)

Cheers,

J.
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M. J. Young
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« Reply #12 on: February 17, 2003, 06:57:16 PM »

Quote from: Joao Mendes
1) The mechanic should be simmetrical. In other words, the effect of applying a bonus should be of exact same magnitude and opposite sign as that of applying a penalty.

2) The mechanic should display exponential decay. In other words, compounding bonuses or penalties should have a progressively smaller effect.


These strike me as inherently incompatible objectives; since I can't imagine I'm the first to notice, I'm thinking that I've misunderstood something. So let me explain how I understand them, and you can tell me why I'm wrong.

I take #1 to mean this. If I have a chance of success of X, the value of {(X+1)-X} should be identical in probability to the value of {X-(X-1)}. That is, you're saying that for any X, +1 and -1 should be the same offset in probability.

I take #2 to mean this. If I have a chance of success of X, the value of {(X+1)-X} should be lower in probability than the value of {X-(X-1)}. That is, you're saying that for any X, -1 should be a larger step than +1 in terms of offset in probability.

I don't see how the bonus and penalty steps could be equal and the bonuses progressively less effective, save by specifically designing the penalties to match the bonuses, that is, to make a bonus of +5% and a penalty of -5% and calculate these (don't just count points).

What am I missing?

--M. J. Young
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ThreeGee
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« Reply #13 on: February 17, 2003, 07:28:26 PM »

Hey J,

I think we are misunderstanding each other. The bonuses/penalties are straight percentage. They do not modify the skill itself, but rather the converted skill level. In other words, a +5 bonus represents a +5% better chance to succeed, regardless of skill.

Or do you mean that a bonus/penalty should be fixed based on the raw skill? In other words, if a skill of X and a bonus of +5 means a +10% better chance to succeed, a skill of 1/2 X and a bonus of +5 means a +5% better chance to succeed.

Or do you mean something else entirely?

Anyway, it is great that all these ideas are getting you thinking.

Later,
Grant
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Walt Freitag
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« Reply #14 on: February 17, 2003, 09:10:09 PM »

Hi Joao,

It occurs to me that your criteria numbers 1 and 7 are incompatible with each other. What makes the symmetry in Symmetry actually useful is that the effect of a bonus is exactly the same as the effect of a penalty of equal magnitude applied to the opposition. D20 has the same sort of symmetry with a few more constraints (it can get distorted by edge effects).

But in a three-way contest, that can never be true. The bonus applied to me affects me vs. opponent A and me vs. opponent B, while the corresponding penalty applied to, say, opponent A affects me vs. opponent A (and B vs. A) but not me vs. opponent B.

I think your definition of symmetrical is being misinterpreted. As Jack pointed out, adding a modifier and taking the same modifier away again will always have equal and opposite effects. I think what you really mean is that the system has a center point and relative to that center point, the probability of success at a given positive modifier is the complement of the probability of success at negative modifier of equal magnitude (that is to say, they add up to 1.0) or equivalently, that the probability of success at a given relative modifier is equal to the probability of failure at the opposite relative modifier. But without the ability to say "my penalty is exactly equivalent to the other guy's bonus," which as I said doesn't appear possible in a three-way contest, this property seems to lose a lot of its singificance.

Since that limitation exists anyway, you might drop requirement #1 and instead use a well-behaved dice pool mechanism such as Sorcerer's, with the constraint that all modifiers add dice to pools. A penalty is applied by adding extra dice to all opponents, which will have equivalent effects as long as all rolls are opposed, and you won't have the granularity effects of removing dice from small pools.

- Walt
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