There’s been some past discussion here of various common game mechanisms that are actually mathematically broken in subtle ways. Attribue + Skill systems, for example.

In the same spirit, I wish to regreftully announce that summed modifiers on linear die rolls are broken.

What do I mean by that? I mean that the probabilities behave badly when cumulative modifiers apply. Summing up cumulative modifiers to a linear die roll is equivalent to combining probabilities by adding them. This is a math error, and I believe it has detrimental effects on systems.

Let's look at an example. Suppose we have a system in which success requires rolling a target number or higher on a d10. Let's say my current TN is 6. My chance to succeed is therefore 0.5 (50%).

Now a modifier in my favor is added in, say a bonus for taking extra time. This is given a +1 modifier, which is added to my die roll (or equivalently it could be subtracted from the TN). What does this modifier represent? It represents a probability of 0.1 (10%) that taking the extra time will turn what would have been a failure into a success.

Now suppose a second +1 modifier also applies -- say, a bonus for being under the influence of favorable magic. This modifier represents a probability of 0.1 (10%) that the magic will turn what would have been a failure into a success.

What's the probability that either the extra time or the magic will make the difference between failure and success? Probability theory gives a formula for determining the combined chance that either or both of two separate possibilities will occur. It's 1 - ((1 - p1) * (1- p2)), where p1 and p2 are the probabilities of the two individual events. Since p1 and p2 in this case are both 0.1, the combined probability is 1 - (0.9)(0.9), or 0.19 (19%). This is really the correct answer. For example, if you roll two d10's, the correct probability that at least one of them will roll a 7 (individually, a 0.1 or 10% chance per die) is 0.19.

But in the normal handling of modifiers in a typical game system, I'd add both these modifiers to my die roll. The modifiers will make the difference between failure and success if I roll a 4 or a 5; these rolls would be failures without the modifiers, and successes when the modifiers add +2. The probability of this happening is 0.2 (20%).

So, there's the problem. The system takes a probability that should be 0.19, and represents it as 0.20.

Okay, now you're thinking, "hey Walt, you had me going there for a while, but now you say it all amounts to a lousy one percent difference? Who the hell cares?" Unfortunately, small math errors have a way of turning into much bigger math errors in a hurry. Accumulate more and/or larger modifiers, and the error becomes much more significant, always in the direction of giving the modifiers a larger combined effect than they should have. Combine two +4 modifiers in this example system and they'll have an 80% chance of that changing the outcome, when it should be a 64% chance. Or a 57% chance, if you consider each +4 modifier as a combination of four +1 modifiers. Not to mention that each +4 modifier is much closer to being the result of five +1 modifiers combined than four of them. To have close to a 40% chance of rolling at least one one when rolling d10s, you’d have to roll five of them, not four.

But it gets worse. The modifiers not only combine improperly with each other, they also combine improperly with the original "base chance" itself. Let's look again at that first example with the two +1 modifiers:

- There's a 50% chance of success initially.
- There's a 10% chance that taking extra time will turn failure into success.
- There's a 10% chance that the magic will turn failure into success.

We could resolve this using the following common sense procedure:

1. Roll a 50% chance. If you make the roll, you succeed.
2. Roll a 10% chance for the first modifier. If you make this roll, you succeed. (Of course, you don't have to bother rolling this if the first roll already succeeded.)
3. Roll a 10% chance for the second modifier. If you make this roll, you succeed. (Of course, you don't have to bother rolling this if either of the first two rolls already succeeded.)

If we follow this procedure, what are the overall odds of success? The answer is 0.595. And this is actually the correct success probability given the situation described. Yet the system will succeed with a probability of 0.7. The modifiers are having more than double the influence they should, increasing the chance of success by 0.2 instead of by 0.095. Why? Because a +1 modifier can only have a chance of turning a failure into a success if the initial roll is in the failure range (1-5, in this case). Since that only happens half the time, when it does happen the modifier has to have twice the chance (0.2, or 20%) of swinging the outcome, in order to swing the outcome 10% of the time overall. That’s what happens when the modifiers are simply added in the system. In order to turn a failure into a success 10% of the time, a +1 modifier added to a 50% chance roll turns 20% of the failures into successes.

By contrast, in the "common sense" procedure above, each of the modifier rolls succeeds 10% of the time, but that success only makes a difference half the time (when the base roll fails), so it actually swings the outcome only 5% of the time (a little less for the second +1 modifier).

To say it in a different way (this is confusing, so I'm trying to explain from different angles), there are two different meanings of "a ten percent chance of turning failure into success." The meaning assumed in the "common sense" resolution procedure is "for each event in which you would otherwise have failed, the modifier has a ten percent chance of producing success instead." The meaning assumed in a straight additive modifier system is "for every single roll you make, there’s a ten percent chance that the modifier will convert failure into success, regardless of what your chance of failure is in the first place." If your chance of failure was 100%, 10% of those failures turn into successes. If your chance of failure was 10%, all of those failures turn into successes. If your chance of failure was 0%, somehow those nonexistent failures will still be turned into successes 10% of the time, which is impossible. (What actually happens is, this is where you go "off the table" or off the end of the linear range.) The first meaning makes logical sense in representing a modifying factor in a probabilistic outcome; the second does not.

The overall effect of the math error inherent in adding modifiers to a linear die roll is that modifiers have a larger effect than they should and a larger combined effect than they should. The first problem can be partially fixed by re-scaling the modifiers (all functional systems already take this effect into account in the gauging of the singificance of a given modifier), but the second one cannot. Modifiers simply do not add. As we saw above, when summing +1 modifiers on a d10 roll, +1 + +1 + +1 + +1 + +1 should be much closer to +4 than to +5. Twelve +1’s combined should yield a result close to plus seven, not plus twelve. And the base chance contributes to that effect just as a large modifier does. When you’re near the edges of the linear range, the effect gets really noticeable. Has it ever struck you as strange, for example, that when a character faces long odds for a difficult task, a +2 modifier can triple the character’s success rate?

This is why there are so many rules in role playing games designed to limit cumulative modifiers, despite the fact that being accumulated -- that is, determining the chance of success when many different factors are affecting that chance -- is exactly what modifiers are supposed to be for. Now we know the real reason why fighters couldn’t wear armor and use a dexterity bonus at the same time in 1e AD&D. It wasn’t because armor prevents dextrous movement. We all knew it was really for game balance. But did anyone ever ask why it was necessary for game balance? It was necessary in order to compensate for the math error in the system that improperly combines probabilities by adding them, causing cumulative modifiers to grow out of proportion.

The effect on system design is more pervasive than it appears at first glance. The basis of a flexible and balanced system is the idea that if there is an effectiveness tradeoff that’s reasonable (say, spending char gen currency for greater strength), and there is another effectiveness tradeoff that’s reasonable (say, spending char gen currency for magic ability that can be used to augment strength), then the combination of the two should also be reasonable. This is what gives a system the combinatorial freedom to yield a wide variety of possiilities. When the modifier math literally doesn’t add up, the ability to rely on that assumption is destroyed. The cumulative effect of similar advantages is exaggerated, so complex curbs must be placed to prevent such cumulative effects. Everything’s affected, even so simple an issue as spending char gen currency to augment a single ability. In the ideal case if spending X points for a +1 to a certain ability is reasonable, then repeating that transaction as many times as desired should also be reasonable. But with malfunctioning modifiers, it’s not. Each successive +1 is actually worth more than the previous one, so there’s a point at which the transaction is no longer reasonable. More rules are therefore needed. But in the end, I don’t believe it’s possible to have a truly balanced system with broken underlying mathematics, any more than it’s possible to reliably navigate with a broken compass.

What can you do about this problem?

One, you can ignore it. It’s gone pretty much unnoticed (or at least, the cause has gone unrecognized) for 20+ years in hundreds of different RPG systems, so it’s not likely anyone will complain about it in yours. However, this means you’re missing an opportunity to have your system not be affected by the constant subtle pressure to keep characters’ ability rolls near the center of the linear range, where the system just seems to work better, that is common in these systems.

Two, you can use dice pool rolls instead. Dice pool rolls are naturally better behaved mathematically. By representing each modifying factor as a separate die or dice all rolled independently, dice pool systems can automatically combine many individual chances into one overall outcome distribution that correctly reflects the laws of probability. The drawback is that most dice pool systems are too high a granularity for many tastes, especially when considering small modifiers at low success chances. Also, the probabilities involved can be rather opaque, and the effects of some modifiers (in the form of dice added to or removed from the pool) can still be inconsistent depending on the state of the die pool before the modifier.

Generally, rolling multiple dice and adding (such as in 3d6 or 2d10 systems) do not help the problem with cumulative modifiers. It seems like it should, because it yields differently shaped outcome curves, but it actually doesn’t. Even taking the higher granularity into account, cumulative modifiers on a summed 3d6 roll against a target number actually explode worse than in a linear system.

Another option (call it choice two and a half) is to consider my Symmetry mechanism, which I’m close to posting a description of in a separate thread. Symmetry is a sort of missing link between linear rolls and dice pool rolls. It has some of the advantages (and, I believe, relatively few of the disadvantages) of both, and it’s the best behaved succeed-or-fail resolution roll, mathematically speaking, that I’m aware of.

- Walt

Don't really have anything constructive to add (of course, since I use probabilities regularly in my job I knew of this problem long ago). Just wanted to give props to your well articulated treatise.

wfreitag wrote: The overall effect of the math error inherent in adding modifiers to a linear die roll is that modifiers have a larger effect than they should and a larger combined effect than they should. The first problem can be partially fixed by re-scaling the modifiers (all functional systems already take this effect into account in the gauging of the singificance of a given modifier), but the second one cannot. Modifiers simply do not add. As we saw above, when summing +1 modifiers on a d10 roll, +1 + +1 + +1 + +1 + +1 should be much closer to +4 than to +5. Twelve +1’s combined should yield a result close to plus seven, not plus twelve. And the base chance contributes to that effect just as a large modifier does. When you’re near the edges of the linear range, the effect gets really noticeable. Has it ever struck you as strange, for example, that when a character faces long odds for a difficult task, a +2 modifier can triple the character’s success rate?

Another option (call it choice two and a half) is to consider my Symmetry mechanism, which I’m close to posting a description of in a separate thread. Symmetry is a sort of missing link between linear rolls and dice pool rolls. It has some of the advantages (and, I believe, relatively few of the disadvantages) of both, and it’s the best behaved succeed-or-fail resolution roll, mathematically speaking, that I’m aware of.

Hey Walt,

Great post, lots of good information. I found it really thought provoking. However, you collected a lot of functional and dysfunctional games with one simple unwritten assumption.

The problem is IF you are assuming that all systems are meant to model probability (or I think more accurately probability distribution) accurate to reality. (I will accept that your thread title is true when the design goal is model accuracy.) However, as your first edition Advanced Dungeons & Dragons example points out, "It wasn’t because armor prevents dextrous movement. We all knew it was really for game balance." (Or, more accurately, 'for that application of game theory.') That's why it's neither broken nor a problem.

Now, I'm the first to admit that many of the game designers who add further mechanics to 'repair' the flaw you indicate, are falling for the same misconception you seem to. No matter what kind of mechanics are put into a role-playing game, it isn't real. Having reality for a goal is misleading and potentially distructive.

When you begin designing rules for a role-playing game you immediately leave the realm of 'realism' and enter the arena of game theory. Game theory is not really a matter of 'balance' but having the result desired at the frequency you are interested in. While I grant that much of this has been an 'unconscious art' for nearly as long as role-playing games have been made and sold, it doesn't need to be.

I make no excuses for perceiving the potential of collectible card games as a product and deciding to make Scattershot's combat¹ compatible with the like in a 'modular swapout' fashion. It really let me look at the combat engine in a new light and directed my thoughts about game theory and role-playing game mechanics. One of the first 'flaws' experienced gamers usually bring to my attention in Scattershot is that, even without linear-addition modifiers, the system allows you to have target numbers well outside the range that can be rolled. (Can you roll under a 25 with two ten-sided dice?)

What I primarily had to do was 'let go' of the 'reality model of probability.' Once I embraced the game theory aspects I began more clearly questioning what the function of the Mechanix in Scattershot was. It certainly wasn't to accurately account for the accumulation of increased chances in a realistic fashion. It took a while, but after I realized that there were a number of different choices available, I decided that my priority was to use it 1) as a manner of articulating non-realistic events (show me the language of 'real magic') and 2) to stimulate narratives along the lines I desired (hence all the Genre Expectation stuff). The reason I created the Critical Juncture cut-off (and Epic Index) system was not to retard the effect you eloquently describe above; far from it, it was to stimulate the types of narratives in accordance to the game's 'main thrust.'

For this reason, Scattershot also has some 'dinosaurs of role-playing game design' like point-based character generation; and yet with twists that seem to confound readers. (Why have point-based character generation if don't use character point cut-offs to stimulate game theory optimization?) These are all in service of the two goals above (as well as the unspoken goal of seeming very 'old school' in design).

That's why your primary assertion only counts so far as modelling reality in game theory elements, and I'm not too sure of the value in that in the first place. (I'm sure my opinion differs from many on the 'realism' issue.) Ultimately, a game can work just fine 'broken' (as you put it) if the goal is not 'realism,' in fact some work even better for it. (The classic example would be the 'rolled too high' rules in first edition Teenagers from Outer Space. It has an attribute plus roll mechanic, but if you succeed 'too well' cartoon mayhem ensues. That suits the game's design perfectly; taking advantage of the 'flaw.')

Still, I really like what you have to say and I think it will be highly useful for people who have 'realism' as a goal (especially unconsciously). Good work!

Fang Langford

¹ I am only using Scattershot here as an example I am intimately familiar with in terms of design goals. Since I cannot say how much thought any other designer has with these issues, I felt I could not speak specifically on their behalf. This is, in no way, meant to seem like Scattershot is either exemplary or to be highly regarded in this fashion, it is just one counter example.

I don't think "balanced" is the word you're looking for. Any mechanic that has the same effect on all characters is ipso facto balanced.

This is, I think, primarily a problem in S-mode, because it is a departure from "realism." Note that you must make an assumption about the meaning of the +1 modifier ("the magic turns 10% of your failures into successes") in order to arrive at a contradiction. If the modifier is just a modifier with no assumed physical meaning--a perfectly reasonable stance to take in G- or N-mode--then there's no real problem.

I'd like to discourage folks from falling into the easy assumption that this is a Simulationist, number-crunchers-only concern.

I show a strong preference for Narrativist play, but I think one important feature in (at least some) Narrativist designs is that the player "know the stakes." That is, my idea of the risk I'm taking with my PC should be accurate. If I can see through the dice to a reasonable approximation of my chances at getting the story outcome I'm shooting for, I can make intelligent choices in a Fortune-based resolution system. (This is one of the major reasons FUDGE was such a painful disappointment for me--the less-educated gamer I had been assumed it would allow for much more "story-driven" play, but the great chunkiness of its Fortune system combined with using a powerfully bell-curved set of dice made for a truly disastrous whiff-factor.)

Of course, if a Narrativist-leaning player is trying to get his jollies in a more or less Simulationist system, this concern is even more critical.

--JB

Hey,

JB's totally correct, I think. His point is also related to the ongoing tendency for people to forget that all role-playing relies on a core plausibility of in-game causal events, relative to the Setting in particular - that concern is not isolated to Simulationist play.

Best,
Ron

The ability to "know the stakes" is probably higher in a linear-die-roll-with-modifiers system than in any other Fortune system, due to the ease of calculating the odds of success (especially if the roll is d10, d20 or d%, since we are accustomed to thinking in terms of percentages). "Knowing the stakes" and mathematical accuracy have little or nothing to do with each other.

Seth is right. I identified this "problem" long ago and discussed it on GO, IIRC. Walt's point is well taken, that two ten percent bonuses should not equal 20% but 19%. But that's actually much more difficult to calculate on the fly. So if the goal is understanding the odds, then simple addition is best. This also goes to Fang's point that it may not be really necessary to simulate reality so closely in these things. In fact given that most of the modifiers are made up sorta arbitrarily (RM gives a +40 for attacks on prone individuals; OK, sounds good to me, I have no real data to refute it), results of a more mathematically correct system are not neccessarily actually more accurate. In this case, the "ignore it" option starts to sound good. Especially because the other option is likely to have a higher handling time.

OTOH, one of the big problems of additive systems is that they often have probelms with the bounds of their curves. What happens when I am rolling a d6 and have a +5? Do I automatically succeed? Or is there some exploding mechanic that allows for any option? The latter are often clunky and ill designed (though it can be done fairly well). An advantage of a system that does probabilities like Walt suggests (multiplicative) is that you can rig it so that you never have more than a 100% chance of success, or less than 0% chance, either. Not to say that the methods known to get there are elegant, but they exist. Die pools for example often have this ability. The problem with these is, however, that calculating odds becomes less intuitive again.

So what you have is trade-off with these methods. The question is will Walt's new method be both fairly intuitive, and take advantage of the benefits of a multiplicative (as opposed to additive) system, all while haveing a reasonable handling time? Tune in next time to find out.

Mike

hmm . . . I agree that it's a mistake to label this a Sim issue. However, there is an assumption about what the die rolls 'n modifiers are modeling in Walt's excellent analysis. Let me quote here: "Now a modifier in my favor is added in, say a bonus for taking extra time. This is given a +1 modifier, which is added to my die roll (or equivalently it could be subtracted from the TN). What does this modifier represent? It represents a probability of 0.1 (10%) that taking the extra time will turn what would have been a failure into a success. "

It is not of neccesity a "realism"/Sim thing to say the modifier represents a 10% probability that the extra time turns a failure into a success - but it is an assumption. I could just as easily assume (as, I'd assert, most games/players do) that the extra time provides an increase of 10% to your base chance of success - end of story. Another +1 modifier for favorable magic? Another increase to my base chance.

The consequences of that assumption . . . Walt does an excellent job of pointing 'em out. Which assumption is better? More accurate? More likely to be instictively assumed? Very good questions, and I think Walt makes a decent case that in many situations, the more matematically rigorous assumption is what folks instinctively *think* they're doing, when in fact they are instead operating in the "increase base chance of success" mode.

That's a problem, for the reasons JB and Ron outline. Is the solution to change the linear system, or to find a way to get our mindset in synch with the realities of modifiers in such systems? I'm not sure, but it does seem to me that either is a valid approach.

In other words . . . everyone should *understand* Walt's issue, but not everyone has to solve it. If you understand how modifiers work in linear systems, such a system might well continue to work for you.

Gordon

Walt's point is well taken, that two ten percent bonuses should not equal 20% but 19%. But that's actually much more difficult to calculate on the fly. So if the goal is understanding the odds, then simple addition is best.

Jaif wrote:

Walt's point is well taken, that two ten percent bonuses should not equal 20% but 19%. But that's actually much more difficult to calculate on the fly. So if the goal is understanding the odds, then simple addition is best.

The difficulty is dependant on the system in use. If you roll 2d10 looking for a 1 on either die, you correctly model that probability with no mental analysis needed.

I guess I'm gonna chime in with the rest here.

Yes, linear systems do have some problems, especially the cut-off at high bonuses is a glaring problem which you have to solve one way or the other.

One way of solving the bonus problem of course is removing modifiers altogether. Another is keeping the modifiers low compared to the roll. A third is providing a table on how to combine modifiers.

There are many ways out. I too find that "knowing the stakes" is very important for me personally as a player. A good example of a bad system here is Earthdawn (to take a fantasy RPG). Earthdawn uses dx+dy+dz+... if you're bad enough you only get one die, which is upgraded, something like this: D4, D6, D8, D10, D12, D6+D6, D6+D8, D6+D10 and so on.

Unfortunately you still got a pretty good chance of rolling low (if you maxed the result on a die you got a bonus roll incidentally). No matter what, you could never rely on your skill because you could just as easily kick ass and take names as stumble over that stone and impale yourself on your sword. Or that was the feeling anyway.

So yeah, I'm all for the linear approach despite it's problems because the odds are very clear. And besides, do we always need a chance to fail (I'm talking about the +5 modifier here). Isn't this just something we got used to? I mean if I'm good enough to have a +5 modifier to a D6 roll, am I not world class? And if it is, isn't it deprotagonizing to have me fail just because I had really shitty luck with the dice? Does this really ADD anything to the game play?

It's like the talk about having skills deteriorating with time. I've played games which took that into account. Did it make it the game more fun? No. Did it make it feel more realistic? No. Did it take more time? Yes. Was it needed? No.
Just say no to too much "realism" which isn't real anyway.

Another solution would be to have a computer based system.

For example, EarthDawn attempted to have a straight linear system. I.e. at each level (step) your expected value would go up by one. (Dice exploded also)
The main problem with this idea was you were limited to existing polyhedral dice and it required a level of indirection. it also gave a rather large range of results.

With a computer based system you could basicly have any distribution you wanted and modify it in fairly complex ways to account for modifiers. (For instance, say you normal roll a D6. If you had a +5 modifier you could roll a D11. )

Most systems seem to assume that having the posibility of failure is ever present, same with success. Thus critical failure/success mechanics. OTOH, few systems make you roll for everything, even if this is realistic. (I've failed my 'Open Door' roll a few times on unlocked doors, maybe 10 times in my life).
What I'm say is that some point you just go over to Drama mechanics. (Ok, +5 it just works)
I feel an occasional specatular failure can add something to play. I like it when there is some limits here. In DnD the probablity of critical failure is fixed(1/20), while in Shadowrun, the probability goes down with skill.

For people who should have succeded I tend to describe the failure as bad luck, rather than a botch on their part. Say the best swordsman in the world drops his sword. It's because a tapestry fell and ripped it out of his hand, that sort of thing. That's my take on this.

I really agree with most of what’s been pointed out here so far. (Sorry for the slow response, I got called away yesterday just after starting this thread.)

Xiombarg's point (also reiterated by Seth) is very important: if the behavior that a system actually generates is the behavior you want, then there's no problem. In particular, if you want the system to drive toward guaranteed success and guaranteed failure, then additive modifiers are better than probabilistic modifiers added "correctly," (e.g. a dice pool roll) because the latter will not generally yield a 0% or 100% probability. I like the way X put this, that it represents the multiple factors having a "greater than the sum of the parts" synergistic effect. The other side of that coin is that I see many players and game designers using systems that drive toward guaranteed success or failure doing a lot of work to counteract that drive, to keep the resolution rolls within a moderate range.

And the answer to all this is Gordon's point, which is that the most important thing is understanding the behavior to make good design decisions, whether you end up wanting to "fix" anything or not.

Fang's point is superficially similar, but actually very different. He points out that concern for realism is often misguided. I agree. But I also think there's a valid concern for consistency that can apply even if reality is not being modeled. The real universe is very consistent, so one often draws on reality as a means of achieving consistency, but consistency can be desired even if reality is not. Consistency is harder to achieve when the system's outcome doesn't behave the way you think it does.

More important, many system designs do appear to aspire to both intra-player-character effectiveness "balance" and combinatorial flexibility. Whether they should or not, and how important balance really is, is an issue on which I believe I agree with Forge consensus. But I also believe that if a system is going to attempt to achieve both, it should find a way to really do it. The biggest problem with additive modifiers, as I said before, is that they rule out the simplest way to combine balance with combinatorial flexibility, which is being able to apply the principle "if a is balanced, and b is balanced, then the combination of a and b is balanced." That doesn't mean if you use a dice pool or Symmetry that principle will suddenly apply everywhere, but it does remove on major source of problems. (Taking the elephant off the roof of the car doesn't guarantee that the car will then win the Indy 500, but it's guaranteed not to win if you don't.)

Pale Fire addresses a slightly different issue, the whiff factor and deprotagonization that all fortune-based systems can suffer from. I don't see a resolution system that frequently goes off the table as a solution to that problem, except in the same rather unsatisfying sense that having your TV break down solves the problem of which program to watch. If you're happiest with a system when the circumstances eliminate fortune, then perhaps a fortune-based system isn't what you want. If you do want fortune, but don't want whiffing, then use a concessions or fortune in the middle mechanism, which takes care of all outcomes including those where a character with world class skill gets unlucky with the dice.

James, the biggest problem with using a computer is having to give the computer the information it needs to make a determination. (Unless all the information is already in a computer, which has other profound implications for how the game is conducted.) Sure, a computer program equipped with tables of modifiers and a few probability calculation algorithm could quickly determine what the exact chances should be, and then do the necessary random "die rolling" to determine success on the basis of that chance. But you’d have to tell the program all the currently applicable situational factors for it to be able to use that information. (Or you could tell the computer all the individual modifiers, but then you’ve already done half the work.) Designing computer tools to augment game play is something I’m very interested in, but it’s also something I approach with great caution.

Anyway, I meant to post Symmetry yesterday an hour or two after starting this thread, but didn't get a chance to. It's posted now, in the Indie Game Desgin forum. It's not the miracle that I seem to have raised hopes of here (for one thing, there is some handling involved), but I think it's pretty darn close.

- Walt

wfreitag wrote: Pale Fire addresses a slightly different issue, the whiff factor and deprotagonization that all fortune-based systems can suffer from.

...

If you do want fortune, but don't want whiffing, then use a concessions or fortune in the middle mechanism, which takes care of all outcomes including those where a character with world class skill gets unlucky with the dice.

James, the biggest problem with using a computer is having to give the computer the information it needs to make a determination. (Unless all the information is already in a computer, which has other profound implications for how the game is conducted.) Sure, a computer program equipped with tables of modifiers and a few probability calculation algorithm could quickly determine what the exact chances should be, and then do the necessary random "die rolling" to determine success on the basis of that chance. But you?d have to tell the program all the currently applicable situational factors for it to be able to use that information. (Or you could tell the computer all the individual modifiers, but then you?ve already done half the work.) Designing computer tools to augment game play is something I?m very interested in, but it?s also something I approach with great caution.

wfreitag wrote: Pale Fire addresses a slightly different issue, the whiff factor and deprotagonization that all fortune-based systems can suffer from. I don't see a resolution system that frequently goes off the table as a solution to that problem, except in the same rather unsatisfying sense that having your TV break down solves the problem of which program to watch.

This can have worse effects than you would normally anticipate. Think about all of the times when the oponets defense is equal to 20 and your attack is 1d20+19. Didn't it frusterate you when you rolled a one? Dicepool systems are an excellent option that allows for a realistic curve and a reasonably versitle chance of failure and success. I have yet to try the symetry system, so I'll post when you do.

Pyron: No, I don't think that's a bad effect. Chances you keep rolling 1's are pretty low. Once is nothing. Twice is a habit.

Let's look at system I thoroughly dislike: Earthdawn. Let's assume the opponent's defense is around 9.

You kick ass so you roll D10+D6. That give's you an average of what? 9? I don't remember if it's beat defense or roll equal or over. Let's pretend it's a 50-50 chance. Now let's say you up that significantly. From 10 to 17. That's a big jump. I think it's like D20+D10. Averaging of course 16. So far so good, but what's the odds of missing? (I'm assuming 9 is a miss here).. I think that's 18% (you can check that). A fairly significant chance although you ought to KICK ASS AND TAKE NAMES at that skill level. Even worse, if you're playing a character with D20+D10 attack roll, you're probably beating on enemies with friggin thick hide, so you pretty much need armour defeating hits, which would mean kicking up that target number to 20 or something.

However, ED uses a mechanism where a maximum roll on a die means you get to roll that die again so you can get results that high. Which means it's RM all over again (meaning you usually don't have a chance in hell to succeed in the beginning no matter how high you tried to boost your skills so you pray you roll that 5% to give you a bonus roll D100 roll)

So what I mean. Linear distribution at least is honest with what you get. Now it might suck, like AD&D where chances to hit usually is very small and you end up with long combats of misses. But at least you know what you get.

Now there are more or less opaque systems. ED I think is among the worst ones. I don't particularly like SR, but I think that system is more honest that ED's when it comes to the outcome.

Sorry for that rant.

wfreitag wrote: And the answer to all this is Gordon's point, which is that the most important thing is understanding the behavior to make good design decisions, whether you end up wanting to "fix" anything or not.

Fang's point is superficially similar, but actually very different. He points out that concern for realism is often misguided. I agree. But I also think there's a valid concern for consistency that can apply even if reality is not being modeled. The real universe is very consistent, so one often draws on reality as a means of achieving consistency, but consistency can be desired even if reality is not. Consistency is harder to achieve when the system's outcome doesn't behave the way you think it does.

wfreitag wrote: More important, many system designs do appear to aspire to both intra-player-character effectiveness "balance" and combinatorial flexibility. Whether they should or not, and how important balance really is, is an issue on which I believe I agree with Forge consensus. But I also believe that if a system is going to attempt to achieve both, it should find a way to really do it. The biggest problem with additive modifiers, as I said before, is that they rule out the simplest way to combine balance with combinatorial flexibility, which is being able to apply the principle "if a is balanced, and b is balanced, then the combination of a and b is balanced." That doesn't mean if you use a dice pool or Symmetry that principle will suddenly apply everywhere, but it does remove on major source of problems.

The Computer Stuff:Yeah, I don't think it's practical either. Perhaps in 10 years there will be a fairly common platform that one can count on people having that could be used to povide a mechanic that fit's ones exact needs.

I think it depends on what one wants from a system. Unfortunatly, I think it also depends on the situation.

In some cases, one may like a system where failure is always possible. For example most combat systems features some mechanic so a miss is always possible verses a non-subdued opponent. Conversely a D20 has the coup de grais mechanic. I think the difference is narrative. Missing the sniper shot is dramatic. Missing the the troll body as you hack it up to burn it is silly. Of course on the other side situations can change things. Say if you had one round to kill an enemy before backup arrived and saved them, suddely missing becomes dramatic.

The problem with linear scales + additive modifiers is, in my opinion, not so much the statistical problem adressed by wfreitag, but the 'boundary effects'. Whether it is or is not a problem that +1 and +1 should not be quite as good as +2 is open to discussion... but that it is a problem that a +1 bonus is much better when you have to roll 10 or higher on a d10, then when you have to roll a 4 or higher is only too obvious.

In the first case, the meager +1 modifier effectively doubles your chance of succes, in the second case it gives you only a 17% success-bonus. The effectiveness of a modifier thus depends too much on the situation in which it is used. I think this is a more effective argument against linear-scale + additive modifiers than the one wfreitag has offered us.

Actually, Lord D, what you describe may be a better way of pointing out the problem, but it's the exact same problem. The "statistical effects" I described become more noticeable at the boundaries, creating the effects you describe.

Yet another symptom of the same problem is going off the scale, which really means that the system has yielded a less than 0% or greater than 100% probability of something ocurring.

Fang, I use the adjective "broken" in the same sense that I've seen other mechanics described as "broken" here. One could just as easily argue that calling attribute + skill systems broken is improper, because most designers and players don't mind that such systems create breakpoints and reward minmaxing, and the mechanism remains popular. If there's a consensus against such usage of "broken," then I'll consider another term instead, but so far I think my usage has been comparable to others' examples.

As for my usage of "balance," I explicitly stated the type of balance I was talking about in the text you quoted ("intra-player-character effectiveness balance"). To be more precise, the type of balance I'm talking about is the condition of all options for spending character creation currency being equally attractive from an effectivness standpoint throughout the character creation process. This condition is desirable because it allows players to make char gen decisions based on their character concepts without having to sacrifice effectiveness. A particular option such as, spend one build point for one point of strength, is balanced if the option is worth the cost relative to all other options, being neither a "bargain" nor a "ripoff" from the effectiveness point of view.

I don't find your definition of balance (the condition of all characters being subject to all rules and all players knowing their effects going in) at all useful. By that definition, no game could ever be unbalanced unless its rules contain provisions that specifically single out individual players or characters before the game begins. And since the characters don't exist before the char gen portion of the game begins, it would have to come down to singling out players. I've never run across a game with a rule like "Walt Freitag receives three bonus points, all other players receive five," and I doubt this is a very common problem.

Suppose there were a system in which each character had a single effectiveness score that applied to all attempted actions and determined the chance of success as a roll-under target on 1d10. Suppose that score is rolled randomly by each player on 1d10 during char gen. I'd call that pretty thoroughly unbalanced. Would the fact that everybody knew going in that that's how the game would work, and the fact that the rule works the same for every character, prove that it's actually balanced? If so, then you've pretty much defined "unbalanced" out of existence.

- Walt

wfreitag wrote: I use the adjective "broken" in the same sense that I've seen other mechanics described as "broken" here. One could just as easily argue that calling attribute + skill systems broken is improper, because most designers and players don't mind that such systems create breakpoints and reward minmaxing, and the mechanism remains popular. If there's a consensus against such usage of "broken," then I'll consider another term instead, but so far I think my usage has been comparable to others' examples.

wfreitag wrote: As for my usage of "balance," I explicitly stated the type of balance I was talking about in the text you quoted ("intra-player-character effectiveness balance"). To be more precise, the type of balance I'm talking about is the condition of all options for spending character creation currency being equally attractive from an effectivness standpoint throughout the character creation process. This condition is desirable because it allows players to make char gen decisions based on their character concepts without having to sacrifice effectiveness. A particular option such as, spend one build point for one point of strength, is balanced if the option is worth the cost relative to all other options, being neither a "bargain" nor a "ripoff" from the effectiveness point of view.

wfreitag wrote: I don't find your definition of balance (the condition of all characters being subject to all rules and all players knowing their effects going in) at all useful. By that definition, no game could ever be unbalanced unless its rules contain provisions that specifically single out individual players or characters before the game begins. And since the characters don't exist before the char gen portion of the game begins, it would have to come down to singling out players. I've never run across a game with a rule like "Walt Freitag receives three bonus points, all other players receive five," and I doubt this is a very common problem.

wfreitag wrote: Actually, Lord D, what you describe may be a better way of pointing out the problem, but it's the exact same problem. The "statistical effects" I described become more noticeable at the boundaries, creating the effects you describe.

Yet another symptom of the same problem is going off the scale, which really means that the system has yielded a less than 0% or greater than 100% probability of something ocurring.

Suppose there were a system in which each character had a single effectiveness score that applied to all attempted actions and determined the chance of success as a roll-under target on 1d10. Suppose that score is rolled randomly by each player on 1d10 during char gen. I'd call that pretty thoroughly unbalanced. Would the fact that everybody knew going in that that's how the game would work, and the fact that the rule works the same for every character, prove that it's actually balanced? If so, then you've pretty much defined "unbalanced" out of existence.

There's also another point to take into consideration. Now Walt you mention that many linear based systems tries to keep the ranges to the middle, where the system works.

However, I'd like to point out that there's another reason to keep modifiers low in certain cases. If you're using D20 or bigger, additions are gonna be slower the bigger the modifier. 18+15 is not difficult to add maybe, but it's slower than 18+1 or 18+3. So in many linear systems the modifier ought to be small enough that the problem remains insignificant. Now in practice this is not necessarily so, but still.

The argument seems to be something like:

There's a big problem with linear dice rolls. It's broken, and I've got an interresting solution to the problem.

I've known about this for a while. Clarify.

{Clarifies}

The problem isn't that big. Few notice it.

But it has larger reprocussions.

Yeah, but no one care's. Let's argue over semantics of the term broken.


Eh, I like steriotyping problems in semi-humerous ways to simplify the setting. My opinion is that linear dice rolls ARE broken, where the term broken means it's an unusable mechanic for me. It forces them to make even more unusable rules, such as the "coupe de grace" because it doesn't account for range, and other optional rules. This is why I use dice pools.

Pyron,

You can still use straight addition without running into the trap you describe. Consider:

1 - Feeble
2-3 - Poor
4-6 - Typical
7-10 - Good
11-15 - Excellent
16-21 - Remarkable
....so on.

The point being that adding 1 at the bottom of the chart is a lot more important than the top of the chart. It won't be an exact model of adding independant probabilities, but it's easy to do.

-Jeff

P.S. Chart created solely to illustrate a point. I used Marvel's (the good Marvel's) naming scheme because it was cool. 'nuff said.