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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:

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.

Hi Jeff,

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

Best,
Ron

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.

Hey, Ron, :)

Whoa, that was a fast reply. :)

Quote from: Ron EdwardsHi Jeff,

Erm... It's Joao. ;)

QuoteAre 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.

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.

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%?

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 EdwardsThroughout 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.

Quote from: JMendesRon, 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 EdwardsThroughout 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.

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

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

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).

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.

Quote from: Joao Mendes1) 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

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

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

Hey, guys, :)

Yes! Good stuff. Hmm... I'm gonna be taking all of these in order.

Quote from: M. J. YoungI 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.

Your interpretation of #1 is almost correct and your interpretation of #2 is also approximate. The problem only became clear to me upon reading Walt's followup. The corrected statements should be:

Quote#1. If I have a chance of success of X=50%, the value of {(X+1)-X} should be identical in probability to the value of {X-(X-1)}. But, for any X other than 50%, +1 and -1 would not be the same offset in probability.

#2. If I have a chance of success of X>50%, the value of {(X+1)-X} should be lower in probability than the value of {X-(X-1)}. That is, for any X>50%, -1 should be a larger step than +1 in terms of offset in probability. Conversely, for any X<50%, -1 would be a smaller step than +1.

Or at any rate, this is what I originally meant, though I readily admit I stated it badly. See my response to Walt below for possible further insight.

Quote from: ThreeGeeThe 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.

Actually, with a skill of 10, the +5 bonus is utterly meaningless, whereas with a skill of 1, that same bonus is going to multiply your chance of success by 6. Under a good decay behaviour, the same +5 bonus should have smallest effect at the extremes (i.e. skill=1 or skill=10 in your example) and greatest effect near the mid-range (i.e skill=5 or skill=6 in your example).

I might also point out that skill (and attribute and whatnot) is really just another type of bonus and does not necessarily have to be treated differently. This in itself is not a requirement, and if a solution presents itself that treats the skill value and the pluses/minuses in wildly different fashions, great. However, given the original specs, intuitively, I find that unlikely.

Quote from: wfreitagI 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.

You are correct. My original statement of spec #1 was ambiguous at best and it took several people pointing out various inconsistencies for me to realize it. Your restatement accurately depicts my original intent.

Quote from: wfreitag alsoWhat 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. [...] But without the ability to say "my penalty is exactly equivalent to the other guy's bonus," [...] this property seems to lose a lot of its singificance.

This, however, I disagree with. I'll restate it as 'this property would have a very different significance'. :) The main point behind this requirement is precisely that I can cancel out bonuses and penalties as they apply to me at will, and (as combined with spec #2) stack them at will, without regard to which point in the distribution I start with. I'll also note that, if the mechanic works as specified, then, in the particular case of a two-way contest, addind a penalty to me will be the same as adding a bonus to my opponent.

Quote from: Lastly, wfreitagSince that limitation exists anyway, you might drop requirement #1 and instead use a well-behaved dice pool mechanism [...] 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.

This one, however, is not consistent to your reiteration of Jack's point that at its simplest, a penalty should simply cancel out a bonus. I think that the basis of the Simmetry mechanic is that everything is a bonus/penalty. Thus, the beauty in its simplicity. If I take this route, this particular aspect is lost. I mean, you have to start the minimum pool at some value. :)

I hope I have shed further light into my devious inner mind. :) I know that I am gaining understanding of what my intent is. I don't think I'll be remiss in thanking you guys yet again for the continuing debate. :)

Cheers,

J.

Hey J,

Oh! That's completely different. You want a bell curve, not a straight line. No wonder you threw out the d20 mechanic. I had started along those lines, ala GURPS, but realized it violated my interpretation of #1 rather badly.

Let's see, skills between 3 and 30, centered around 16-17, roll 3d10, roll equal or under skill, apply bonuses and penalties directly, divide the successful roll by some arbitrary constant (2 or 3, probably), compare successes all around. There you go. Raise the number of dice to lower the standard-deviation of the curve (increase the funkiness of the decay), and raise the die-sides to increase the width of the curve (increase the fineness of the granularity).

Later,
Grant

Quote from: JMendesThis one, however, is not consistent to your reiteration of Jack's point that at its simplest, a penalty should simply cancel out a bonus. I think that the basis of the Simmetry mechanic is that everything is a bonus/penalty. Thus, the beauty in its simplicity. If I take this route, this particular aspect is lost. I mean, you have to start the minimum pool at some value. :)

But this method is much simpler, actually. Instead of subtracting penalties from bonuses, you just add dice to the appropriate pool. This serves to perform the subtraction for you in rolling. Let's look at Synthesis, with the adding, and a simple combat example.

I could take a 6 die pool, and subtract 2 dice for slippery and roll against my two opponents each with a 6 die pool. What's the net effect? An average drop from zero successes against each to them each scoring one success. What happens if I add 2 dice to each of their pools? The exact same effect. The only difference is that they now have a larger range of possible successes. Which, given that they're fighting against a disadvantaged opponent makes sense. In fact, this is how the system allows players to exceed their normal limits when attempting something easy. Either it's a bonus for the PC, or it's a penalty for the target. In either case, the game effect is the same, a higher average roll, and a higher max roll.

Or, IOW, what Walt said.

If you use Synthesis with only adding bonuses, there may be no problems at all. Looking back at #2 I forgot that the odds on a result do shift on a curve (expected value is not odds). I think that adding a bonus to yourself versus adding a bonus to your opponent might have not quite equivalent effects, and therefore fail #1 technically, OTOH. But the effects are, in fact, naturalistic which is what the goal is about, I'm betting. That is, it seems that the only reason that you wanted to have them be symetrical is that you could then have them cancel. Since this is simpler, that's no longer neccessary.

I think I have a winner (or very close). No surprise since I was using pretty similar criteria when I adapted the Story Engine mechanic.

The only downside is potentially large dice pools to cover the fine granularity, and all bonuses thrown in. But again, I'm all for that, and you did say that low handling time wasn't important. ;-)

Also, keep in mind that there are options to the multi-player problem. It's not very realistic to have a character roll his entire pool separately against all comers simultaneously (as in my little example). In TROS, the player has to split his pool between opponents. This is visciously real. A more "heroic" option (but less so than rolling evenly against all comers) is to have characters only be fighting one opponent aided by his allies. In this case, there is only one addition to the opposing pool for penalties (or, possibly, with aiding rolls required, the bonus might be added to the aiding roll). Yet another functional model is to have multiple attackers recieve a bonus for superior numbers. The last is my least favorite as it's pretty arbitrary. Anyway, which of these models are you using, as it will affect which system is superior?

BTW, your definition of open-ended needs to be stated as clearly as your clarification above. For many people saying open-ended means that any number (from negative infinity to positive infinity) of successes is possible with any roll. Most exploding die pools are an example of this.

Mike

Hey, :)

Quote from: Mike HolmesI could take a 6 die pool, and subtract 2 dice for slippery and roll against my two opponents each with a 6 die pool.

Hmm... What if I am subtracting 2 dice for slippery but adding 1 for supperior equipment? Am I gonna roll 6 dice against 7 or 7 against 8? If the latter, the penalties and bonuses aren't cancelling. Assuming the former, where does the 6 come from?

About the multiple opponent thing. Things keep getting boggled down, here. I don't mean A and B against C, I mean A against B against C. There is no bonus for multiple attackers, there's a three-way there-can-be-only-one all-out shootout. Hmm.. Ok, I'm gonna come out and say it. :) Spec #7 also means that the mechanic should also work in the limiting case of a one-sided conflict. (This is the part that I said earlier would go against your opposed/unopposed roll...)

Ok, now, to clarify open-ended: open-ended pluses/minuses means a task can get arbitrarily easier without ever actually getting to 100% probability and can get arbitrarily harder without ever getting to 0%. Open-ended effect numbers means a character can generate an arbitrarily large positive result as well as an arbitrarily large negative result. Keep in mind that these are not absolute requisites and spec #6 will be the first to be tossed out if the whole spce set becomes unwieldy.

In light of these clarifications, your solution fails to meet spec #6, but if nothing better comes along, I might just have to take it, or some combination of it and other possibilities pointed out in the thread, as a final solution.

The only viable alternative I've come up with on my own so far revolves around players using some sort of log table (necessarily not open-ended) or log calculator (ugly) to figure out the bonuses, then rolling one die at a time in a slow decay fashion to figure out the effect number.

Cheers,

J.

Hey J,

I am fairly certain your definition of 'open-ended' is impossible. In order to allow for an infinite number of modifiers, an infinitely finely-grained system is required. Otherwise, at some point, the output falls below the granularity threshold and that is the end of it.

I really wish I could draw you a picture, but try to imagine a bell curve drawn on graph paper. At some point on both tails, the curve drops below the last horizontal line above zero. Even using a logarithmic conversion on the bonuses, you run into the same problem, just at a different step.

Can anyone provide a counter-example? It has been a while since I have done any real math, so I could easily be overlooking something.

Later,
Grant

Hrm.  It's less mathematically elegant, but since you specifically don't care about how ugly the system is, how feasible would a percentile-step (choose an arbitrary center point, and give each "step" a diminishing value, either arbitrarily or by a formula) be?

Say the steps are 10/10/5/5/5/3/3/2/2/1/1/1....... from a 50% center, we end up with a chart that looks like:

1%... (-14+)
1%   (-13)
2%   (-12)
3%   (-11)
4%   (-10)
5%   (-9)
7%   (-8)
9%   (-7)
12% (-6)
15% (-5)
20% (-4)
25% (-3)
30% (-2)
40% (-1)
50% (0)
60% (+1)
70% (+2)
75% (+3)
80% (+4)
85% (+5)
88% (+6)
91% (+7)
93% (+8)
95% (+9)
96% (+10)
97% (+11)
98% (+12)
99% (+13)
99% (+14...)

Apply bonuses and penalties as steps rather than percentile changes, and in the extreme (trans-14 cases) differences become apparent with the successive application of penalties or bonuses (thus, suppose the rank equates to skill: the best swordsman in the world (Rank 17) has almost no difference (under controlled circumstances) from the second best (rank 14), but in an extended contest where both accumulate penalties, the 3 rank difference becomes more pronounced.

Margin of Success calculations are easily derived from the chart to whatever degree the user wants, with the simplest method being the gap between the effective rank and the rank acheived by the roll (which also helps out with our sample swordsmen)

How effective it will prove in a multi-element conflict is pretty subjective - I'm comfortable with the combination of ranks to represent combined effort, but I'm not certain that would suit everyone's needs.

Anyway, It's something of a brute force attempt at a solution (when I use somethign similar, it tends to be rather simpler) but I'm curious where it's flawed. :)

-Rob D.

Hey, :)

Rob, yes, your solution falls in line with what I was envisioning, and is of course a direct illustration of Grant's point that infinite open-endedness is a problem.

Grant, I just wanted to note that ultimate open-endedness is not entirely impossible. For instance, my own klunky approach is completely open-ended at all steps:

a) T = (sum of all bonuses)-(sum of all penalties)
b) I = sign(T) * log( |T| ) (where sgn(0)=0)
c) roll d6: 4-6 means R=I and increases, 1-3 means R=I-1 and decreases
d) roll d6: 6 means you are done. stop rolling. R is your final result
e) R=R+1 if increasing, R=R-1 if decreasing
f) repeat from step d

There is no limit to the input into the log function, so there is no limit to the open-endedness of how hard/easy a task can get. There is also no theoretical limit on how many times you can roll a d6 and not come up 6, so there is no limit to how high or low an effect number can be generated.

Of course, you could use a table instead of step b. It makes it easier on the players, but now the open-endedness is limited to how big a table you want to make. You can also use a single linear roll against a table, like Rob suggested, in which case, you are correct, the open-endedness is limited by the granularity of the roll. It is, however, humongously easy on the players.

By the way, Rob, I did not find your solution to be at all inelegant, as you claim. Quite the contrary, in fact. I'd be interested to know why you said that. Oh, and I am also comfortable in combining ranks to show cooperative effort.

Yet again, cumulative thanks for all the input.

Cheers,

J.

Quote from: JMendes

By the way, Rob, I did not find your solution to be at all inelegant, as you claim. Quite the contrary, in fact. I'd be interested to know why you said that. Oh, and I am also comfortable in combining ranks to show cooperative effort.

That was probably more reflective of a personal bias than anything else.  I tend to use a system like that to reflect the ease of learning the basics of a skill but the difficulty of mastering it, (so the progression tends to look like 40/60/75/85/90/93/95/96/97/98/99/99....)  so switching it over to a more balaced curve felt like I was complicating something simple. :)

Mostly though, it's because  while for the table based (rather than formula based) solution pays of in ease of use, the curve is definately mathematically inelegant, which was my main reason for choosing that particular turn of a phrase.

- Rob D.

PS - I'm actually fine with infinitely extending 99%'s.  Einstein isn't going to be able to answer a basic physics problem beter than j. Random Doctor of Physics, so having them operate ona  similar percentile level for 0 difficulty tasks is cool with me, since when a very difficulty task comes along and drops them both 7 ranks or so, Einstein is still in the high 90s, while the doctor is now somewhare around 60%.  (or at least, that's my thinking in using the model - really, it was designed to allow for lots of very good duellists whose differences in skill only really showed itself in the face of adversity)

PPS - I should also note, I got the idea originally from a game revolving around Art Auctions that I cannot remember the name of. They used Log formulas, and I remembered liking the reasoning but being paralyzed by the prose, so I simplified it to a table.

[Edited because I type with flippers ]

It looks to me like a table will suit you just fine, and it does not limit the granularity if you allow rerolls. Here's one system:

percentile   25  30  35  42  50  59  71  84  100
score       8+r   7   6   5   4   3   2   1    0


Roll percentile dice, reading 00 as 100. Find the lowest (leftmost) percentile in the table that's greater than or equal to the number rolled. The score in that column is the magnitude of the result. (So, for example, the result is 5 if you roll 36, 37, 38, 39, 40, 41, or 42 on the percentiles.) Simultaneously roll any 50-50 chance to decide the sign of the result, positive or negative.

On a throw of 25 or less, the result is "8+r" meaning reroll and add 8 to the result (but do not reroll the sign). Multiple rerolls (adding 8 each time) are possible.

The result for a character's action is the score from the die roll (positive or negative) plus and minus any modifiers for skill, conditions, etc. Degree of success (or failure, if it comes out negative) is the result minus the difficulty (if unopposed) or minus the opponent's result.

In the case of ties (degree of success 0), a positive sign roll (even if the magnitude was zero) breaks the tie and succeeds against a static difficulty score or against an opposing roll whose sign roll was negative. Similarly, in a tie a negative sign roll represents failure against a static difficulty score or against an opposing roll whose sign roll was positive. In all other cases for ties, a partial success occurs or the tie must be broken with another roll.

At the cost of greater relative rounding error in the probability curve, you can widen the table somewhat to reduce the number of rerolls needed:

percentile   12  14  17  21  25  30  35  42  50  59  71  84  100
score      12+r  11  10   9   8   7   6   5   4   3   2   1    0


I believe this meets all your specifications. One caution, though: the distribution of degrees of success/failure decays exponentially, but not always so as to make results of lower magnitude the most probable. For degree of success when the odds were against success, and for degree of failure when the odds were in favor of success, the exponential decay is perfect and the results of lower magnitude are the most probable. But for degree of failure when the odds are against success, and degree of success when the odds are in favor of success, the behavior is different. The most likely outcome is a degree of success or failure equal to the overall numerical advantage or disadvantage in modifiers the character had going in, with the probability of other degrees of success or failure decaying from that maximum in both directions.

Makes some intuitive sense. If you have a 20 point advantage in modifiers, and you get very unlucky and fail despite your advantage, you're most likely to have a degree of failure of 1. Only half the time will the degree of failure exceed -3; only one fourth of the time would it exceed -7, and so forth in the normal exponential pattern. But when you succeed, you're most likely to succeed with a degree of success of 20 and very unlikely to succeed with a degree of success of 1 or 2 (just as unlikely as to succeed with a degree of success of 39 or 38).

If you don't like that, and want the lower magnitude degrees of success and failure always to be the most probable, then make the degree of success or failure a separate roll on the same table (and it doesn't matter which side rolls).

- Walt

Hey, :)

Walt, your table hits the spot. I am left wondering why you decided to build it high-roll-low instead of the more intuitive high-roll-high, but other than that, the concept is very nice.

Now that the roll part has a satisfactory answer, I am pondering on the fixed part. I've been musing around the following formula:F = LOG   (0.1*|T| + 1) * SIGN(T)
      0.1rounded nearest, where T is the sum total of all bonuses and penalties including skills, attributes, equipment, conditions and whatnot. This yields a rather nice curve with F=T for -4<=T<=4, then having diminishing returns to the point where if T=30 then F=15.

My issues with it at the moment are:

a) Should I add the result of the roll (say from Walt's table) to T or to F for the final result? A good argument can be made for both cases.

b) What if there are two cooperating agents? Should I add their Ts together or their Fs? How many rolls should be made? Likewise for opposing agents. [Note that an opposing agent is not the same as an opponent side. The first is, say, an NPC that doesn't want you to succeed at what you are doing. The second is, say, someone who is attempting to do the same as you, only better (like in a race), or someone who is attempting to do to you what you are attempting to do to them (like in combat).] Again, good arguments for the various possible combinations can be built.

c) Is there any alternative to extending this table other than calculating its continuation?

Anyways, I think this thread has been yielding good results. Comments on the above points are now also most welcome, as well as any further alternative mechanics anyone comes up with. :) Again, thanks for all the participation.

Cheers,

J.

Maybe I'm mistaken, but it seems you want the curve of a 1d+/1d- system  (as per FUDGE) with the decay of a dice pool system (as per Sorcerer).

Would just slapping the two together yield the desired result?

For example (you may have a different scale in mind than the dice I picked):
Roll:  1d10-/1d10+ + pool:2d20 (take the highest)
A bonus would add an additional 1d20 to the pool.

Again, I didn't check the math, but the bonus dice should up the center point of your curve and decay while doing so.  Starting with a dice pool of two ensures you always have a curve on the bonus dice.  The dice aren't open-ended (which I think you were really going for), but you could perform some sort of trick on the bonus dice to make it open-ended.  For example, rolling doubles on the bonus dice allows you to add the appropriate bonus dice together.  You'd still need to stick with opposed rolls to get the uniform bonus/penalty effect.

J, I think you'd be getting into overkill territory by adding a complex procedure to modify the "fixed part." The exponential decay probability curves already implement diminishing returns, in that a point of advantage or distadvantage relative to the target number or opponent's ability becomes less likely to swing the outcome the farther away from an equal match (a 50% chance of success) you are to begin with.

Cooperating and interfering agents first need a model (even if only a general idea in mind) for the kinds of effects you want them to have. No resolution system including this one has such effects built into the math. Should someone who's cooperating be able, or likely, to decrease instead of increase the effectiveness of the one they're trying to help? Does it depend on the task? (Can one person help another to pick a lock?) You have to decide these issues first.

That said, the most conventional way to do it would not be to add the T's together beforehand, but rather resolve the helper vs. the task, determine the number of successes or failures, and add (or subtract) those from the other character's T.

- Walt

Hey, guys, :)

Wow. I've been away a couple of days and now spent all of four hours just catching up... Anyway, apologies on the late reply.

Walt, my musings for the past few days have led me to similar conclusions, i.e., that a general support/oppose mechanism probably needs more detailed considerations on what is actually being undertaken.

Since I don't have those considerations at hand, I guess we're done for now... :/

Anyway, again, to all you folks that jumped in, thanks for getting my brain strightened out.

Cheers,

J.

PS A friend and I got together and pondered on that table you posted. I'll be sharing what we came up with in a few, but that's for another thread. :)