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Mike's Standard Rant #5: The Myth of Opposed Rolls

When RPGs started resolution rolls were all of the "Roll vs. Target" type. Soon thereafter, however, somebody invented the idea of the "Opposed Roll". Where does this come from? As one moves from the early completely combat based resolution systems, and skills get introduced, you get situations occurring where characters are testing skills against each other in conflicts outside of combat. Well, with no target number, the obvious thing to do is to simply roll and see who gets the better result. Thus you get the dichotomy where skills used against things that are not rated via skills are rolled against a target number, and skills used against characters with similar skills are rolled using the "Contested Roll" method.

This all seems well and good until you consider that you've just created two entirely different resolutions systems for a single game. Now I can go on and on about the benefits of only having single systems for resolutions, but the advantages should be pretty obvious. The question becomes why do you need to have two systems? Bound by this particular tradition, most designers have to date continued to include dual systems for resolution. If you ask them how many resolution systems they have in the game, many will proudly claim one. But in fact, there are two similar systems. If you point this out the designer will say that it's just a modification of the single system for a certain type of circumstance, and an easy modification at that. The point still stands, however, that it's extra rules. Why is it needed?

The tradition hinges around that age-old dichotomy between active and passive opponents as mentioned above. Somehow, it seems intuitive that if you are playing chess against an opponent that both sides should get to roll. While if you are jumping a chasm, you out to only roll against a target. What is missing in the analysis is the fact these methods are, effectively, the same statistically. Neither method produces more information than the other, and neither can be claimed to have any more accuracy statistically a priori.

Let's look at an example. In a particular system you roll d10 + Skill to get over a target number to succeed, the level of success being the number by which you succeeded. The corresponding opposed mechanic is to have both sides roll d10 + Skill and subtract the lower from the higher, leaving the higher roller with the difference in levels of success. What's the difference between the two methods? At first glance there might seem to be a difference but consider this. What if the "opposed" system were to have one person roll Own Skill + d10 - d10 target is the Opponents Skill. This is the exact same system as the regular opposed system, statistically. What this points out is that it does not matter who rolls the die or dice, effectively the systems are the same. In the end there are randomizers, and you get an output number. All rolls in all systems are opposed by their difficulty. There are no "unopposed" rolls. The dichotomy is a myth.

What is different in the opposed system is the number of dice being rolled. What effect does this have? Well, the opposed roll, consisting of two dice gets you the pyramid curve (flat bell). As opposed to the unopposed roll which gets you the flat curve. Which means that the opposed roll is much more likely to come out with an "average" result than an unopposed roll. Yep, that's right, actively opposed conflicts are more predictable, than working against a stationary object. Counterintuitive, no?

On the other hand, this is just a contrived example, and you probably could find a way around this particular problem. But the point is that there are problems with such dichotomies. Which is silly when they can be eliminated simply be ignoring the dichotomy altogether. Yes, that's right, just ignore the whole passive/active thing altogether, and just use one system for all situations. At this point I won't even suggest that you go with a target system, or a both-roll system or anything in particular (despite having my own preferences), just that you have only one system for everything.

This seems at first glance to cause all sorts of problems. When I say this people inevitably point out certain things. Let's say we're talking specifically about going to an all-target-number system. The objection is usually, "What do I use for a character's target number?" Usually, in the example above, they'll point out that if I roll Own Skill +d10 to exceed Opposing skill, this gives the advantage to the roller. And they're right. What they should do is use that +d10-d10 thing (many games like FUDGE do just this). Or some other balanced method. Then ratings work just fine as target numbers. If, on the other hand, we're looking at going to the all-opposed method, they'll point out that a stone has no resist lifting skill rating. To which I'll reply that it should. Or rather, you'd have to set a difficulty in a target number system; the same methodology is no more difficult to apply to creating "skills" or ratings to oppose any roll.

The point is that any well-designed resolution system can be used to adjudicate any situation. One does not need to have separate systems for opposed vs. unopposed situations as long as the method is designed properly. Which takes no more effort than creating a system that is not designed to handle such.

As usual in my rants, this is not a revolutionary idea, or something that I came up with by myself. Certainly many systems exist in which there is a single resolution system for everything. It's just one of those problems that I see crop up again and again and the assumption of the necessity of such dual systems irks me. As always I'll caveat this and say that such dual systems are not broken or unplayable, just that they could have been put together in a more coherent fashion with just a bit more thought.

Or at least that's how I see it.

Mike

Mike,

I like your rant - it makes sense, and it's definitely something to think about when designing games.

I'd like to throw an example system at you and see if it works for you. I have to admit self-interest - it's the system for Paladin.

Players roll a number of dice equal to an attribute (1-5) and attempt to roll 5 or 6. Each 5 or 6 is a success. You need a certain number of successes to perform a task (1 for most things, 2 for hard things, and 3+ for superhuman tasks.)

However, when competing against an opponent, you both roll. You still need the minimum number of successes to perform the task. However, the person with the most successes "wins." The nature of this, of course, is determined by the task, but is usually measured in speed.

Example: To run a mile, one would need only 1 success - it's an average task. If running against an opponent, if you got 1 success and the opponent got 2 successes, both of you ran a mile. The opponent ran it faster, however.

Does this system have the same problems? (I have to admit I'm not mathematically inclined enough to know.)

Awesome Mike, you never fail to impress.

Quote from: Mike HolmesWhen RPGs started resolution rolls were all of the "Roll vs. Target" type. Soon thereafter, however, somebody invented the idea of the "Opposed Roll." Where does this come from?

...Let’s look at an example. In a particular system you roll d10 + Skill to get over a target number to succeed, the level of success being the number by which you succeeded. The corresponding opposed mechanic is to have both sides roll d10 + Skill and subtract the lower from the higher, leaving the higher roller with the difference in levels of success. What's the difference between the two methods? At first glance there might seem to be a difference but consider this. What if the "opposed" system were to have one person roll Own Skill + d10 - d10 target is the Opponents Skill. This is the exact same system as the regular opposed system, statistically.

...What is different in the opposed system is the number of dice being rolled. What effect does this have? Well, the opposed roll, consisting of two dice gets you the pyramid curve (flat bell). As opposed to the unopposed roll which gets you the flat curve. Which means that the opposed roll is much more likely to come out with an "average" result than an unopposed roll. Yep, that's right, actively opposed conflicts are more predictable, than working against a stationary object. Counterintuitive, no?

...This seems at first glance to cause all sorts of problems. When I say this people inevitably point out certain things. Let's say we're talking specifically about going to an all-target-number system. The objection is usually, "What do I use for a character's target number?" Usually, in the example above, they'll point out that if I roll Own Skill +d10 to exceed Opposing skill, this gives the advantage to the roller. And they're right. What they should do is use that +d10-d10 thing (many games like FUDGE do just this). Or some other balanced method. Then ratings work just fine as target numbers. If, on the other hand, we're looking at going to the all-opposed method, they'll point out that a stone has no resist lifting skill rating. To which I'll reply that it should. Or rather, you'd have to set a difficulty in a target number system; the same methodology is no more difficult to apply to creating "skills" or ratings to oppose any roll.

Okay, I'm gonna go out on a limb here, but I think there's at least one other way to solve the 'not two systems' problem.  For this example, we'll take the 'always opposed' system but make part of it 'covert.'

Let me sketch out an example.  Let's start with the suggested system above Your Skill + d10 versus My Skill + d10.  When you do Mike's conversion, you get Your Skill + d10 – d10 with My Skill as your target number.  The only thing (and Mike's right, this is a really small thing) is that I don't get to hold any of the pretty dice.  When you roll against a static something, it's Your Skill + d10 – d10 against a target number.  Now my personal bias is against having to have someone around to 'judge' these target numbers; I mean if you going to have only one hand rolling the dice, why not keep all the work in one brain?

What am I suggesting?  Why, a completely static target number.  Jump a chasm?  Your Skill + d10 – d10 versus 11 (arbitrary choice).  Pick a lock?  Your Skill + d10 – d10 versus 11.  Bake a cake?  Your Skill + d10 – d10 versus 11; you get the picture.  Simple, non?  Okay, I can already hear you saying, "What if it's a tough lock?  Or an Easybake oven?"  Hey, most one-roll systems have you adjusting for preparation, aiming, target choice, and et cetera anyway, why not just make another adjustment for target 'reaction?'

Now, let's take a moment and do a little algebra.  Couldn't we get rid of the target number altogether by just setting the skill number really low?  This is like using a Skill 'Bonus' that equivalent to the above Your Skill – 11.  That turns it into Your Skill 'Bonus' + d10 – d10 (with modifiers like 'skilled opponent' or 'complexity' or 'easiness').  Heck, since we're in a 'simplify everything' kinda mood, let's toss out having to remember which die is which.  First, toss the "+ d10" and just bump up the Your Skill 'Bonus' the median (I know, that's 5.5 and who wants to count half-points, bear with me).  Instead of going to a straight linear probability, a simple way to keep the 'flat bell' or 'pyramid' curve would be to double the dice.  If you do both at the same time, you get (oh, let's call it) Your Skill Rating – 2d10 (where the Rating is basically the 'Bonus' + 11 which was the original Skill - 11, back to where we started).

Now you roll Your Skill Rating – 2d10 for anything.  If you have the roller make allowances for remarkable situations then the outcome is directly the "level of success," no target numbers, no muss, no fuss.

But wait a second I say (cue the silent movie piano music for the villain), "It's not fair, you're fighting against me and I don't get to roll any of those really cool dice?"  After all the whimpering and sniveling, you have to admit the visceral feel is lost from the 'old fashioned' opposed die rolls.  What to do, what to do.

Well, since we're trying to stay simple here, instead of going back on all of the above, how about we just fake it?  How did we come up with the modifier for a 'tough lock?'  I mean what made that lock so tough?  (Or those Easybake cakes so easy?)  Wouldn't that reflect the skill of the maker?  "Yeah," you might say, "How come they don't get a roll?"  Um, I dunno...maybe they did.  Maybe their roll resulted in the modifier you used to make Your Skill Rating roll.  This might take a little jockeying around with granularity and probability bell curves, but I don't think it's outside of reason that you could make their roll, such as a 'set the trap' roll, have a "success level" number that equates perfectly to your modifier for 'apparently unopposed' rolls.  Good lock design = -1 modifier on a Your Skill Rating roll, the same as 1, the number by which the lock designer succeeded His Skill Rating roll.  Just because it happened in the past doesn't make it any less 'opposed.'

But remember, the opposition is already designed into the Your Skill Rating – 2d10 roll, what we're talking about here is illusionary opposition to satisfy those who feel the opposition should be explicit.  Now let's take this one step farther; let's put those dice back into my hands.  (Whee!  I get to roll!  I get to roll!)  Except now it's actually a faux opposition that I present.  I make a My Skill Rating – 2d10 roll and the result is so low that it winds up being nothing more than a modifier reflecting good fortune for me (or nothing at all, if we ignore failed rolls on my part).  (Can't beat me on a good day, ha!)  Better yet, this allows you to not need to know my skill level, because my rolling against it 'hides' its actual level (a bonus when the gamemaster wants actual skill ratings kept secret).

So what does that leave us with?  Every roll is technically an opposed roll rolled by one person.  Faux opposition is levied by what looks like an opposing roll, but the result is little more than what would be a modifier in a single-person roll.  There are no target numbers, simply Your Skill Rating – 2d10 = the "success level."  It looks like an 'opposed roll/unopposed roll' system because occasionally another person will help determine a few of the modifiers (and gets that visceral feel of using dice while doing so).  Has it been done?  Hmm...Rating – 2d10, lessee....



Oh wait, that's Scattershot.



Fang Langford

p. s. Sorry Mike, I couldn't resist.  It's so hard to describe the algebra that goes into a die mechanic; you gave me the perfect stage.

I think this common problem jumps up from two beliefs:

• Critical Success/Fumble Rules
  "Both people need to roll, because there is a chance either one could critically succeed/fail"  In most cases, I think this is a weak argument, but there are many systems that incorporate sliding odds of doing exceptionally well, or bad, based on skill, special abilities, etc.  On the other hand, no one wants to start giving rocks weight skills, hardness skills, etc. to make opposing rolls.

• "But I want to roll dice!"
 Which is really,"I feel disempowered".   I can certainly attest to this feeling with D&D's AC system("I run up the wall, kick off, throwing my cloak into my enemy's face as I somersault over, and land behind him!", "Ok, your AC is still 12..." "What !?!").   While this makes a lot of sense for players, not a lot of GM's really want to roll for stones' resisting actions.

Neither of these reasons are that great, but usually are the line of logic behind the TN/Opposed roll decision.

Chris

PS-Love the rants Mike, keep up the good work :)

But first, Gordon's Impromptu Rant #1 - Mike, a standard numbering system begins at one (or zero, if you want to go THAT route) and ascends from there.  Considering these are largely mathematical issues, I'm wondering what demon of perversity possesses you when you number your Rants :-)

OK, that's out of the way.  How I see it (probably just a rephrased version of Mike's thoughts) - opposed vs. unopposed (target number) is a myth.  The opposed roll situation simply uses a randomizer (die roll) as part of establishing the Target Number.  Consider what happens if we don't roll "at the same time", but rather have one side (say, the GM) roll first.  He's set a target number, and now the player can roll against that number.

Thinking this way, the issue becomes one of timing (IIEE, perhaps? Or just details of timing with EE?), and establishing the granularity of what is resolved/established by a "roll."  I think it likely most opposed vs. unopposed, target number vs. die roll issues are really about these broader subjects.

Gordon

One aspect of game design is involved with keeping people interested. This takes many forms: Ron's five elements of role-playing, snacks and drinks (or their lack), player skill, and many other things. One factor is the interest provided by the mechanics of the game. The board game Trouble, for example, is a bad simplification of Parcheesi except for the plastic dome that you pound to make the dice bounce. In the same way, one thrill of some games – admittedly a cheep thrill – is playing with all the platonic solids. As a personal confession, that cheep thrill is what initially interested me in role-playing games at a tender age past.

 Beyond novelty, though, there is a serious role to be filled by mechanics. I will illustrate this with a worst-case example, a kind of reductio ad absurdum. Imagine a system so constructed as to call for opposed rolls in all cases of character conflict. To pick a hypothetical system, let's make the roll '1d10+skill vs. 1d10+skill'.

 Suddenly, in a flash of dust and a burst of light, the world is turned on its ear and all those rolls are shifted into half as many 'skill+1d10-1d10 vs. skill' checks. This is statistically equivalent. But lo! This is a game played with a Game Master (as is often the custom), and only the characters run by the Game Master receive rolls. "What's this?" you ask. Yes, the character's sheets all contain numbers, but the players never roll. Whenever a player-controlled character takes a swing at a foe, the GM rolls two dice (adding one and subtracting the other) and explains the results.

 Already some of you may be grumbling about this, but consider this in light of player interest and the rest of you may rapidly see my point. A player could say, "My character, Foo, attempts to lodge his saber deep within the infidel's vitals." The GM would roll, and announce, "You fail, but your opponent does manage to hack off your arm in a clean stroke." Remember, the GM rolls all the dice; he rolls for all the players as well as his own characters.

 Player interest could rapidly wane in such a situation. Players, no longer drawn into the physical act of playing the game with their dice, could drift off and act only when their character did something, and then only by speaking. Their characters could even engage in combat by proxy; the players would all give auto pilot orders, go out for pizza, and come back to find that the GM had made all the rolls required by the system and determined the outcome of combat for them!

 Now, I must concede that there is more to combat that rolling dice. There is drama and adventure and dilemma. But, there is something visceral about rolling a couple of dice that connects you to your character's fate. If nothing else, asking a player to roll - when his character is in peril of a blow to the head, for example - makes the player sit up and take notice; something is about to happen! The player is engaged not just in talking about the game, but also in the game's actual resolution.

 I must compare this to a game of chess. One could very well play chess against a computer with only a mouse, in fact many do. But it is not the same thing as sitting down across a coffee table and moving well weighted hunks of ivory and teak across a smoothed and checkered board. Think how much more removed chess would be if you only played by speech, instead of moving a mouse in your hand. This is what is denied to opposing combatants striped if their chance to roll.

 As was pointed out earlier, this is a matter of empowerment. Not some mere empowerment, mind you, but Empowerment with a capitol schwa. It is the function of the design to buffer the player's experience from the mathematics of the system. We could all play on computers with random number generators weighted to reflect whatever probability system we enjoyed - a perfect bell curve, perhaps - but we chose not to. The games we delight in, Sorcerer, The Pool, even my poor introduction to role-playing, D&D, all use dice. At some level they all make a concession to the people playing at the expense of the mathematics. It gives us a feeling of power to hold the winds of fate and the tides of entropy in our hands, drop them, and forge our characters' destinies.

 To conclude, I submit that while it is rigidly proper to condense mechanics in the way discussed above, it is not an imperative of design, and not necessarily even good design, to do so. All of the above admitted, however, I must note that I am no zealot. Any system is a sum of all of its parts and what is lost in one area may be gained in another. I in no way wish to disparage any design with my general discussion of methods. If I wish to comment on any game specifically, I will do so separately.

Quote from: Mike HolmesTo which I'll reply that it should. Or rather, you'd have to set a difficulty in a target number system; the same methodology is no more difficult to apply to creating "skills" or ratings to oppose any roll.

Actually Mike, I'd say it's *less* difficult than assigning standard difficulty ratings. Which makes more sense, saying that it's a difficulty of 6 to lift a rock, or that the rock is Heavy (6)? If you have a scale for assigning such things, giving objects "skills" is much more intuitive than not. It's not really a new idea, as you say, but it is one of those ideas that seems to be perennially "new." Systems that use it are "oh wow, that's innovative" systems. Dunno why... I think all systems should work that way. :)

Fang:

I follow your reasoning, but I wonder if some of the conventions of the mechanic aren't leftover from the starting point (d10 + skill vs. d10 + skill).

In the first place, why the big subtraction? Subtraction is evil in mechanics! (You may not agree, but IME it's generally a concensus.) So, while some type of subtraction might be neccessary in a mechanic without opposed rolls, it should be minimized and isolated as much as possible.

You ended up with Skill - 2d10 to get the result. Why not make that Skill + 2d10. All it does is move the center of the 2 - 20 result range up to Your Skill + 11. The numbers here don't impress me much, but the method does. More below:

In the second place, if you want a system where the roll translates directly to the degree of success using modifiers to represent situational considerations, why do you want a bell curve at all? Bell curves do bad things to modifiers. Seems like it'd make more sense to roll a d20 or a d10.

Let's do something easy like this. Everyone's used to rating thigns on a scale of 1 to 10, right? Why not say that your result is also rated on a scale of 1 to 10, indicated by a d10 roll, adjusted your skill. Let's say skills range from 1 to 5, average being 3. So your roll will be in the 4 - 13 range if you have a skill rating of 3.

Basically it boils down like this: the d10 roll gives you the result quality on a scale of 1 - 10, when compared to your other attempts. Your skill rating puts that result in context with respect to others in the game.

So, if you roll a 3, your attempt was a 3 on a scale of 1 to 10 when compared to your other efforts. But when you compare it objectively, it's a 6.

No need for opposed rolls here. Simply subtract your opponet's skill from your result - "Opponent's skill" meaning anything that hinders you (A chasm being Very Wide [5] for example.)

To address the subject of how engaging these sorts of mechanics might be, I'd say that it will all depend on the what single system you choose at the end. I'm not suggeting one sort or the other, just that you have but one. I certainly never suggested that rolls be taken away from the players. I agree with KR that a system where only the GM rolled would probably give players a sense of disempowerment (despite the fact that rolling does not actually empower the player in any way). So, um, don't do that. Use one of the zillion other methods that can be employed.

A good example of a system that uses this principle is InSpectres. In that game, all rolls are made by the players, and the GM never has to roll ever. Herr Sorensen has made it clear that he sees this as a feature. And I agree, it seems very freeing. In any case, that was his choice, and it works well.

Again, I'm not saying what sort of system I like, specifically, we can get to that in another debate (I do have a preference, and it should be obvious from my designs).

One argument I might accept is the esthetic one. That a player might be more engaged by the mechanics because they seem to make more sense intuitively if you were to have two types of resolution. The only question is does the added complexity and other potential problems cost more than the esthetic enhancement. I suppose there is probably some design that can be achieved that could give you that feel, and yet avoid just about all the downsides. But I think that the esthetic isn't worth even a little damage, personally. But, as with all things esthetic, YMMV.

Gordon, to address your point on my numbering, what would make you think that I am not perverse? ;-) Being a programmer, I probably would start with zero. Starting with three however was just a way of saying on my part that I understand that I talk too much, and that you all can probably ascribe a couple of standard rants to me to fill in the first couple yourselves. Or maybe I'm just saving them for something really important that I have to say. Who knows?

As to your reprasing, Gordon, yes, that's a good way to look at it. Statistically all that usually changes is the randomizers, essesntially. Which seems odd when you think about it. Especially in the case of the common split method that I cited.

Which brings us to Clinton and Paladin. Yes, Mr. Nixon, you have fallen right into the opposed roll trap. And in the classic manner. Your characters will have more predictability against living, breathing opponents than they will against pasive tasks. I would avoid this, personally.

In the case of your game, however, it's eminently simple to fix. Just rate an opposing force as though they were active. Thus a jump across a particular chasm could be a roll against 2 dice while a wider one would be 4. In essence, what you have right now is "Most Things" = 0 dice (expected value 0 successes), "Hard Things" = 3 dice (expected value 1 success), and Superhuman Tasks = 6 dice (expected value 2 successes). And then you have to exceed that number to win, of course. An advantage of going all opposed is that you can assign all the difficulties in between as well.

The single roll method for Paladin would be to do something like the following. Each die rolled is worth: 1-2 = 0, 3-4 = 1, 5-6 = 2. This averages one per die. Then the idea is to simply roll over the target's stat. Such a system could be used in an "only the players roll" system, FWIW. This particular method might not work with your other mechanics (I'm trying to remember the Animus rules), and there are certainly many other ways to do it (Hero System Body comes to mind), but you see my point. You can do all these rolls one way or the other rather simply, and thus only have one system.

OTOH, Clinton, the Paladin system is so simple that the "damage" done is pretty minor. You could probably ignore it and the system would suffer only minimally. Again, dual systems never break a game, they are merely unneccessary. The question is do you have a reason to keep it?

Chris is right on it when he says that there is the worry about the critical success/failure thing. As he points out the reply to such objections is to simple. Either go with "all opposed" so that you can get in your crit/fumbles on both sides of each and every conflict, or to go to the more modern system of success granularity that many systems have nowadays. Like in my example, where success is determined by the margin. In that case you have a much finer granularity of results as opposed to the success/crit-success, failure/crit-failure dynamic. But again, that's my personal bias. You can do it any way you want. But a single system can handle these results either way.

And thanks, Fang for pointing out another good example of one of the many systems that have already figured this out. ;-)

Mike

Quote from: PaganiniI follow your reasoning, but I wonder if some of the conventions of the mechanic aren't leftover from the starting point (d10 + skill vs. d10 + skill).

If you read the Scattershot system you''ll see why Fang chose the ranges and other particular mechanics he did. They all make sense in the context of the entire system. The fact that I used a d10 system with two dice as an example was merely coincidental.

Mike

Quote from: Mike HolmesThis all seems well and good until you consider that you've just created two entirely different resolutions systems for a single game. Now I can go on and on about the benefits of only having single systems for resolutions, but the advantages should be pretty obvious.

Actually, I'd argue that point. It is being considered more or less a truism these days that to have but a single die mechanic is better and easier (this can become quite ridiculous when D&D 3E is said to be simple because of a unified mechanic, despite tons of rules and variations). More importantly, sometimes having only a single mechanic is not a good idea. Many tables in GURPS would be easier if they hadn't to be forced into an xd6 format, but used percentile dice or something along the sort. Attribute checks in D&D 3E have a d20 with its huge variance added to a tiny modifier, making it more a crapshoot than test of ability. In both cases, the games would have benefited from having different mechanics for fundamentally different things.

In fact, there are games that do this. Ars Magica has various types of rolls, depending on the situation. D&D 3E still has percentile rolls instead of d20 rolls for certain situations. Castle Falkenstein has different mechanics for sorcery than for skill checks.

Quote from: Mike HolmesThis is the exact same system as the regular opposed system, statistically. What this points out is that it does not matter who rolls the die or dice, effectively the systems are the same. In the end there are randomizers, and you get an output number. All rolls in all systems are opposed by their difficulty. There are no "unopposed" rolls. The dichotomy is a myth.

Consider this and this article. The point being, while the methods are statistically equivalent, they are not semiotically equivalent. This is a point often overlooked: a common example is people saying that word-based systems such as Fudge could just as well replace words with numbers. Mathematically, this is right. Semiotically, it is nonsense. Words have totally different connotations and significance than numbers.

A similar example occurs when you compare the basic mechanics in GURPS and Fudge. You can roughly map one to the other, since both rely on bell curves. Yet people have a hard time understanding why a modifier in GURPS has different effects at different levels, while the Fudge way -- a bell curve centered around zero, where you perform at your skill level most of the time -- seems to be much easier to grasp.

Opposed rolls vs. unopposed rolls have similar advantages: if you roll skill + 1d10 vs. skill2 + 1d10, then each die roll represents an action. You can read the result and translate it into a description. A good attack vs. a good defense has a different description than a poor attack vs. a poor defense, something that's lost in the skill + 1d10 - 1d10 vs. skill2 approach. Rolling both skills into a single value -- 2d10 < skill2 - skill + 11 discards and hides even more useful information.

-- Reimer Behrends

I was afraid I hadn't made this terribly clear.  I'm sorry if breaking this down to a point by point response bothers anyone; I'd like it to be clear I hear what Paganini's saying, but I need to lead the conversation through his misunderstanding.

Quote from: PaganiniI follow your reasoning, but I wonder if some of the conventions of the mechanic aren't leftover from the starting point (d10 + skill vs. d10 + skill).

Actually, this isn't the starting point, it is exactly, squarely where the mechanic remains.  The "reasoning" is a demonstration of the 'mask' pulled over the mechanics to 'fake' the both opposed/unopposed roll appearance.

No matter what it looks like, mathematically it is identical to (Your Skill + d10) – (My Skill + d10).  That's what makes it so hard to explain how it doesn't suffer from either the problem Mike so tellingly describes and an effect (I think) Ron refers to as needing to either allow 'flexible target numbers' or 'opposed rolls' and not both.

Quote from: PaganiniIn the first place, why the big subtraction? Subtraction is evil in mechanics! (You may not agree, but IME it's generally a consensus.) So, while some type of subtraction might be necessary in a mechanic without opposed rolls, it should be minimized and isolated as much as possible.

I get this comment a lot.  While I agree with the sentiment that "subtraction is evil," I think that 'better ratings are smaller numbers' is so significantly more counter-intuitive, that it outweighs the "evil."

First of all remember, this is an opposed-roll mechanic.  That's why it simplifies to Your Skill + d10 – d10 versus My Skill.  The subtraction is inherent and unavoidable.  Wouldn't you agree that having addition, on top of subtraction, is more "evil"?  That's why I swapped the "+ d10" for twice "- d10 versus (5½ points of My Skill)."  (Thus eliminating My Skill from the calculations.)  The probability permutations are identical but you don't add then subtract.

Moreover, there's a second reason for doing this mathematical gyration.  The way the permutations work out, when you do a Your Skill Rating – 2d10, you get a relatively small number.  I use this to allow a 'faux opposition' roll; the My Skill Rating – 2d10 doesn't function mathematically as an opposing roll (largely because it only counts when positive), it counts as a negative modifier on your 'one-handed opposed roll.'  (It's 'one-handed' because you are, though hidden by the mathematics, rolling both of the opposing dice, thus Your Skill + d10 – d10 versus My Skill.)

Quote from: PaganiniYou ended up with Skill - 2d10 to get the result. Why not make that Skill + 2d10. All it does is move the center of the 2 - 20 result range up to Your Skill + 11. The numbers here don't impress me much, but the method does.

Ah, but that would destroy the utility of the 'faux opposition roll.'  The trick with this mechanic is that when you roll without an 'opponent,' you are still making an opposed roll.  (Your Skill + d10 – d10 versus a target number has exactly the same probability permutations as Your Skill Rating – 2d10  because the target number has been factored out as twice the median.)

If we 'flop' the dice over into positives, we have to 'reinstall' the target number and all of them would have to be calculated as Target Number + 11.  (The normative skill rating is 11, added to 2d10 makes the range from 13 to 31!  That would require target numbers centering around 22!  To me that's counter-intuitive, not only adding target numbers to the mix (beyond the Your Skill Rating), but also making them always land between 13 and 31.  Those numbers impressed me!

Quote from: PaganiniIn the second place, if you want a system where the roll translates directly to the degree of success using modifiers to represent situational considerations, why do you want a bell curve at all? Bell curves do bad things to modifiers. Seems like it'd make more sense to roll a d20 or a d10.

How did he put that?  It was something like 'putting a high-power scope on your rifle doesn't make shooting fish in a barrel as much easier as it does in sniping' (or something like that).  The bell curve (even though, with two dice, the 'curve' looks like the silhouette of a pyramid) creates the 'diminishing returns' effect.  When your skill is 11 (in Scattershot, which uses a 'Your Skill Rating – 2d10 = success level' system) then a single +1 is a difference of 9%; when your skill is 14 a single +1 is 6%.  Following the scoped barrel-fishing model, a flat curve 'does bad things to modifiers;' so I guess I disagree with you here.

The fun part is because we're actually using an opposed roll system, the dimishing returns effect is just gravy.

Quote from: PaganiniLet's do something easy like this. Everyone's used to rating things on a scale of 1 to 10, right? Why not say that your result is also rated on a scale of 1 to 10, indicated by a d10 roll, adjusted your skill. Let's say skills range from 1 to 5, average being 3. So your roll will be in the 4 - 13 range if you have a skill rating of 3.

That doesn't make any sense.  This says that you can roll well enough to beat difficulties that don't exist.  Skills are 1 to 5?  Problems are difficult from 1 to 10?  If you roll over 6 with a skill of 4 it beats non-existent difficulty levels.

Quote from: PaganiniBasically it boils down like this: the d10 roll gives you the result quality on a scale of 1 - 10, when compared to your other attempts. Your skill rating puts that result in context with respect to others in the game.

So, if you roll a 3, your attempt was a 3 on a scale of 1 to 10 when compared to your other efforts. But when you compare it objectively, it's a 6.

No need for opposed rolls here. Simply subtract your opponent's skill from your result - "Opponent's skill" meaning anything that hinders you (A chasm being Very Wide [5] for example.)

Let's see how "easy" that is:[list=1][*]You take your skill [4],

Simple enough (although if

everything is rated from 1 to 10, it doesn't follow that Skills are limited arbitrarily to 5).[/list:u][*]You roll a d10 and add them together (Your Skill + d10),

That's

one mathematical operation (4 + 3 = 7).[/list:u][*]Your target number is a chasm, Very Wide [5],

Where does this number come from?  The gamemaster?  'Two heads are better than one,' eh?[/list:u]

[*]Now you subtract this target number from your total (Your Skill + d10 – Target Number),

That's

two mathematical operations (7 – 5 = 2) and "subtraction is evil."[/list:u][*]This puts your action into objective comparability.

Compared to what?  The 1 to 10 scale?  Can't be, because you often get results outside of the 1 to 10 range (say the roll above was 9 and the target was 2).[/list:u][/list:o]What does that leave you with?  Five steps, two people engaged in an 'unopposed' chasm jump, not only an "evil" subtraction but a separate addition, and a potentially impossible result; you call that "easy?"

Here's what we have:

[list=1][*]You take your skill rating [13],

Again simple.[/list:u]

[*]You roll 2d10 and subtract them (Your Skill Rating – 2d10),

Admittedly, this could be looked at as addition

and subtraction, but I argue that gamers, used to totaling dice, won't notice the addition.  However, "subtraction is evil."  Also, there is no target number, the player looks at the chart if he's unsure of his jumping ability.[/list:u][*]This is your result.

No more functions; that's it, pretty much an objective comparison.[/list:u][/list:o]Three steps, one person engaged in an 'unopposed' roll (remember,

all of Scattershot's rolls are mathematically 'opposed rolls,' gaining the advantage of Mike's 'normalizing' effect); this definitely wasn't "easy" (to design that is).  Which is better?  That cannot be said; quality is subjective.

It might be argued that in both cases the character may take a run before his leap, instead a straight broad jump.  In Scattershot this creates a bonus on the roll, just as I suppose it does on the other, but it changes 'how far' the character can leap as well; this is not something that can be explained as simply as the suggested system, suffice to say that it still doesn't require a 'second head.'

The difference between these Scattershot and Paganini's system is that, in his, the opponent is disempowered (when played by a player) or the sensation of 'threat' is reduced (there's more suspense waiting for the other die roll) because his is strictly an 'unopposed roll' system.  Scattershot looks like it is a fusion system when actually the 'faux opposition' is only supplying a variable modifier.  This is also the principle reason for the subtraction; it makes the numerical result small enough to be used in place of the modifier it represents that is static in a supposedly 'unopposed' roll.  That's why I call it a 'faux opposition' roll; it doesn't furnish opposition in the 'beat me on a d10' way, it merely masks the actual modifier supplied by active resistance.

I know this is a really tough concept to grasp, I wouldn't have figured it out if I hadn't been working on a math minor in college.  (Well, it could be easy for you, but it wasn't for me.)  If you want, I can explain the mathematics of it in more detail in Private Message, if you're still not 'getting it.'  That goes for anyone who finds these maths, 'over their heads.'

Fang Langford

Fang,

I think that 'better ratings are smaller numbers' is so significantly more counter-intuitive, that it outweighs the "evil."

If not for other reasons you've articulated, you could call the dice output "ranks" and eliminate counter-intuitivity in one fell swoop.

Paul

Hmmm.

Mathematically speaking, Mike's 100% right. However, I personally don't see roleplaying game design as being purely about obtaining an aesthetically pleasing (from a mathematical POV) system - creating a system which is OOC enjoyable to use is also a factor.

Opposed rolls make sense for character-vs-character stuff, since it makes it feel more like a competition. Unopposed rolls make sense for character-vs-passive-thingy stuff, since it makes it feel more like you are trying to overcome an impersonal challenge to yourself.

Sure, Mike's system's more efficient in terms of dice-rolling, but making an opposed roll isn't that much more effort than making an unopposed role, and it feels nicer OOC. I know I'm being all subjective rather than analysing the situation rationally and objectively, but then again fun is a subjective experience. Some folks might get pleasure out of a mathematically efficient system - I prefer a system which enhances the atmosphere, rather than sterilises it. ;)

Darnit Paul,

Quote from: Paul Czege

Quote from: Le JoueurI think that 'better ratings are smaller numbers' is so significantly more counter-intuitive, that it outweighs the "evil" [of subtraction].

If not for the other reasons you've articulated, you could call the dice output "ranks" and eliminate counter-intuitivity in one fell swoop.

I never thought of that.  Oh well, it's too late now; we're very happy with what we've got.  This is no time for a major system overhaul.

Fang Langford