Ygg Action Resolution again (Concessions and Stuff?)

[Christoffer Lernö]

I don't understand.  I gave an example of using 'degrees of successes' as the way of interpreting the dice.  It may have been heavily experimental, but I think it could be turned into a "randomizer" all by itself.

What I mean is. Pick up two d12's and we have what? 78 different outcomes, right? (Distributed unevenly though). Add the dies together and we only have 23. Set a target number and count successes and we are down to 3.

(let's ignore the complication of the d12 for now)

Basically what we have is a distribution with 78 different elements to start with. We can manipulate them in a lot of different ways, but we can't add any information to the whole thing. We *can* add external parameters but if they are predetermined by the situation, they only form a function though which we put grind the numbers the dice has given us.

Now, enter the degrees of success. The number depends on the target number, but this is a way of culling the 78 elements we start with. Do we want to have a wide distribution of numbers or not? At target number 6 we should be having the widest distribution and most balanced distribution.

What is "deciding on a degree of success necessary"? It's yet another way to select the numbers. It's just another function. The underlying randomness do not change.

Let me take an example. Let's say you cheat and put all the dice to read 5.

Does moving the number of dice, degrees of success or the target number introduce randomness into this system?

Not if those numbers are non-randomly determined. Of course if you determine degree of success needed by a another (different) die roll, then of course you are introducing randomness, but that comes from the die roll and not from anything else.

For another example, let's say you have to jump a chasm. If we don't look at how wide the cliff is, we'll get from the rolls a distribution of results which could be interpreted as how far the jump is... maybe 1 degree of success increases the range jumped by half a meter.

If I vary the size of the chasm, then the chance of me succeeding to cross safely varies. What doesn't vary is the distribution of my jump though. That is only dependent on the target number, the number of dice and what I roll.

That's three different 'dials' to affect the chances someone will have at success.  Each has a different character, some change variability, some don't.  The point is, when you make all three a part of your game, your asking the players (including gamemasters) to consider three different variables: How many dice do I use?  What is the target number this time?  And how many successes do I need?  Now multiply that by a factor of how many times a round of combat the participants will need to 'roll for success.'  (Double it if these rolls are opposed.)

The number of dice is never in question, you always use the same as your stat. What is the target number (this is the most unsatisfactory part)? Well that is determined of how favourable the conditions are. (I'd incidentally prefer to simply have 3 levels or so of increasingly high randomness. Having 11 levels of randomness is insanely detailed and not at all what I like). How many successes do I need? For the chasm example, quite easy: just answer how wide the chasm is. Or how good should a character be to be able to jump it under perfect conditions.

For opposed rolls it's even simpler. Here you put in the stats as number of dice. Choose a level of randomness and let them roll. Highest number of successes wins.

Static test:
* Determine relevant stat
* Determine circumstances (probably something like perfect=1, average=5, bad=9)
* Determine necessary degree of success

Opposed test:
* Determine relevant stat
* Determine circumstances

Personally, I'm not fond of a game that requires the gamemaster to intervene in every resolution with target numbers

Something I agree with, but I think a neat "roll up a target number" method in the GM section will do wonders for that.

Now let's say you lock in the target number (say at 7 or higher on 12) and the number of successes needed (1 is enough); every time a roll is needed, the player grabs his skill number of dice plus bonus dice, minus penalties. One quick roll and the resolution sequence is complete. The same scheme works with whatever is chosen as the singular dial to affect the probabilities.

Of course, this is completely ignoring the reason why I choose the resolution to work as it did in the first place.

If you roll x dice with target number 7. That's basically flipping a coin. What's the distribution of that?
1 coin: 50/50
2 coins: 0: 25% 1: 50% 2: 25%
3 coint: 0: 12.5% 1: 37.5% 2: 37.5% 3: 12.5%

and so on.

Basically the more dice the more spread out.

I've already written:

Why is this important? Because this system is an adaption of the karma mechanics of higher than stat wins, lower than stat loses equal is 50-50. Turn the dial to 1 and you essentially have this system.

Now tell me how the coin system is helpful in this context? Why eliminate the dial which is the main feature of the mechanic?

Sorry Fang, I don't understand what you're suggesting.

* First I don't see the randomizing of the degree of success needed (which if I understand correctly is a thought for some other game, it's not a suggestin to me).

* Secondly I still don't see how the simplifications suggested would help achieving the goals for the resolution mechanic (look at earlier comments for a review of it).

[Le Joueur]

I don't understand.  I gave an example of using 'degrees of successes' as the way of interpreting the dice.  It may have been heavily experimental, but I think it could be turned into a "randomizer" all by itself.

What I mean is. Pick up two d12's and we have what? 78 different outcomes, right? (Distributed unevenly though). Add the dice together and we only have 23. Set a target number and count successes and we are down to 3.

Ah, no.  Math is my strong suit; roll 2d12 and there are 144 possibilities, 12 doubles and half of the remaining 132 are simple reverses.  That does come out to 78, but the 78 number isn't all that useful for calculating probabilities.  The 23 is the total number of additive permutations and is actually less useful than the 78.

I don't get where you get the 3.  Are we talking pass-tie-fail?  Besides, I thought you were using a dice pool mechanic; each die succeeds or fails on its own.

Basically what we have is a distribution with 78 different elements to start with. We can manipulate them in a lot of different ways, but we can't add any information to the whole thing. We *can* add external parameters but if they are predetermined by the situation, they only form a function though which we put grind the numbers the dice has given us.

Now, enter the degrees of success. The number depends on the target number, but this is a way of culling the 78 elements we start with. Do we want to have a wide distribution of numbers or not? At target number 6 we should be having the widest distribution and most balanced distribution.

What is "deciding on a degree of success necessary"? It's yet another way to select the numbers. It's just another function. The underlying randomness does not change.

Does moving the number of dice, degrees of success or the target number introduce randomness into this system?

Okay.  I think I understand our contention.  It has to do with your peculiar use of the word "randomness."  In lay terms, you're talking about either the 'spread' of the probability distribution (the 23 permutations results in a straight-sided bell curve where there is only one chance in 144 of receiving either extreme roll).  Or you're talking about how 'flat' the distribution is (roll 1d12 and every number has an equal chance; roll 2d12 summed and 13 comes up 1 in 12 times, but 2 is 1 in 144).

What I was talking about was randomizers; these are systems of introducing a random factor.  A variable dice pool with a static target number needing only one success is one.  A static dice pool with a variable target number needing only one success is another.  A static dice pool with a static target number with a variable threshold of number of successes is a third.  Each has different probability characteristics.

If I vary the size of the chasm, then the chance of me succeeding to cross safely varies. What doesn't vary is the distribution of my jump though. That is only dependent on the target number, the number of dice and what I roll.

I'm not sure why you aren't getting what I am trying to explain.  Any one of the randomizers provides a way to do exactly what you are describing.  The only difference is in interpreting the results.

Since the input of interpretation of any of them is based on the ability to jump for distance, each can be set up by the designer to provide a consistent distribution.  The distribution you're describing in this case would be a 'sweet spot' around which most of the jumpers leaps center.  Vary the width of the chasm and all you are doing it 'chopping off' part (or all) of this 'sweet spot.'  I know this intuitively looks like changing the target number (linear change to target number compares to linear distance change), but trust me, it will work just as well (using different mathematics) with either of the other systems.

Explaining exactly how, isn't probably necessary, but is highly technical.  I'd be happy to do so in Private Message, but I'm not going to belabor the mathematics here.  Suffice to say, this argument suggests that you should use a static number of dice in your pool; skill becomes the core target number and chasm width becomes a penalty.  I just don't see any justifiable mathematical reason to add the complexity of another function.

Let me stop a moment and explain why I have been highlighting the 'function' terminology.  Quite simply, it shows how much work is involved.  The first function you list is 2d12; according to earlier comments this changes whenever different abilities are brought to bear.  That requires working with different functions.

Next you include a "degree of success necessary" function.  I'll have to assume this is the target number.  Adding this function means taking the first function and then applying a second.  That's two functions and more work than one.

Elsewhere, you discussed something that sounded like requiring a certain

number of successes in order to complete a task.  Determining what this threshold is, is yet another function.  That's three functions that must be employed on every roll.  I think that's a lot, especially when both the 'spread,' 'flatness,' and 'cut off' can be done with any single one of these functions mathematically.[/list:u]

The number of dice is never in question, you always use the same as your stat. What is the target number (this is the most unsatisfactory part)? Well that is determined of how favorable the conditions are.

It is in question; the question is, "what's my skill for this action."  It may not come up with your group's social convention, but with playtesters and customers it will.

There is no single "unsatisfactory part."  The question (not a matter of satisfaction at all) is whether you understand the complexity you are introducing using three different functions on every roll.  I believe you have commented in the past that simplicity and speed are a plus; this three-part resolution scheme denies that implicitly.  But that's not my question.

It is what you want (knowing about this complexity)?

(I'd incidentally prefer to simply have 3 levels or so of increasingly high randomness. Having 11 levels of randomness is insanely detailed and not at all what I like). How many successes do I need? For the chasm example, quite easy: just answer how wide the chasm is. Or how good should a character be to be able to jump it under perfect conditions.

For opposed rolls it's even simpler. Here you put in the stats as number of dice. Choose a level of randomness and let them roll. Highest number of successes wins.

Static test:
* Determine relevant stat
* Determine circumstances (probably something like perfect=1, average=5, bad=9)
* Determine necessary degree of success

Opposed test:
* Determine relevant stat
* Determine circumstances

My question is, why can't you do all this with one function?  The probability mathematics can certainly be tailored to have exactly the same conditions; is it necessary to do each of these things in a totally different fashion?

Why is this important? Because this system is an adaptation of the karma mechanics of higher than stat wins, lower than stat loses equal is 50-50. Turn the dial to 1 and you essentially have this system.

Now tell me how the coin system is helpful in this context? Why eliminate the dial which is the main feature of the mechanic?

Sorry Fang, I don't understand what you're suggesting.

I'm suggesting sticking only with the "main feature" dial and skipping the other two 'dials.'  Believe me, I am halfway through a minor in math, we can tailor your "main feature" to do all you have required of the probabilities without using three separate functions.

* First I don't see the randomizing of the degree of success needed (which if I understand correctly is a thought for some other game, it's not a suggesting to me).

We aren't "randomizing" the degree of success.  I'm suggesting that its an 'extra dial' you don't need to have the same mathematical distribution.  Making the "degree of success" requirement variable on top of the other functions is wasted complexity.  Pick one method, it can easily (and simply) be made to do what you want.  Which is the main feature?  Use that one.

* Secondly I still don't see how the simplifications suggested would help achieving the goals for the resolution mechanic (look at earlier comments for a review of it).

Is complexity a goal for you?  Do you believe requiring three different mechanics for each test is necessary when it can easily be done with one?

Take this example: Static test:
* Determine relevant stat What's my stat for this test?  This equals the number of dice.
* Determine circumstances What's the difficulty for this test?  This equals the target number on the dice.
* Determine necessary degree of success How many successes do I need to succeed?  (If that doesn't sound redundant, I don't know what does.)  This determines the threshold of successes.

Static test, Scattershot style:
* Determine relevant stat What's my stat for this test?  This equals the target number.
* Determine circumstances What's the difficulty for this test?  This equals the modifier on the success rolled.
* Determine necessary degree of success The 'necessary amount' is pre-calculated as a modifier on the success rolled.

The dice pool is static 2d10, everything else are 'plusses and minuses' on the outcome.  Because it is summed, the sigmoid graph gives a 'non-flat' distribution.

I'm not attacking your system or your work.  Technically, I'm not attacking anything.  My style of discussion leans heavily on Aristotelian dialogue (the same thing that forms the basis of the American legal system).  You provide points, I provide counter-points, we let the jury (it's your system, you be the judge and jury) decide.  You're starting to respond a little defensively to what boils down to one question.

Do you realize how complicated this is?

If you do, I'm pleased.  If you understand and accept the workload you're putting on your gamemasters and players, I'm glad you got it right.  If you comprehend that all the same probabilities can be achieved with a simpler system mathematically and still have this preference, then I'll defend your system to anyone who argues with it.

However, if you think using three 'functions' where only one is necessary is easier, faster, or 'makes more sense' for everyone, then I just wanted to give you another perspective.

Fang Langford

[Christoffer Lernö]

Sorry for not quoting, but that thing you wrote just now was insanely cluttered. Maybe we're reaching a point where we should take this to pm. I'm not sure.

Dice:

2d12 and 144 outcomes: Any nitwit can calculate that. What's interesting is the amount of information we have available in the system. Since we're not ordering the dice we have 78 DIFFERENT configurations. 12 doubles and 132 which are reverses, so we cut away the reduntant configurations and come to 78 different possible configurations. That means that no matter what function (well actually that is not quite true, but for practical purposes) you use to map these results to R you are not gonna have more than 78 blips on the friggin radar. :)

Now if we crank 2D12 through the fuction of
(Die>=target value is 1, otherwise value is 0), we will have 3 outcomes or values. 0, 1 or 2.

That's the 3 values I talk about. The chances of 0, 1 and 2 respectively might be unevenly distributed. The exact form of this distribution depends on the target number (for example with a 1 it would spike at 2).

What I am talking about is that no matter how you flip the "degree of success switch" back and forth you still won't get any more than 78 possible outcomes from the thing.

In fact, if you make a cut-off "This degree of success or more is success, the rest is failure", you reduce the possible value to 2: "Success" or "Failure"

I am not talking about the spread of the distribution nor the flatness of the distribution. Since the dice creates a discrete probability function there are a limited number of outcomes. The more possible outcomes, the less defined the results. The randomness I'm talking about is the entropy of the underlying system.

We can define the entropy of a finite state system pretty easily.

Now what happens when we box up states and make them identical is that we reduce the entropy of the system. My point is that we can't create new entropy by moving say the degree of successes needed.

The amount of entropy is dependent on the # of dice. How much entropy that is cut away is later determined by the target #. After that we can reduce entropy once more by declaring the result as being either a win or a loss. From a system with many states we reduce it to a simple two-state one. Each of these states will have a percetile die associated with it. That's all the info that is left.

Anyway, my point is that unless you can't introduce more entropy by running it through a function like the degrees of success.

Then it's the whole thing about introducing complexity. While it is not perfect, where is the harm in this:

GM: The chasm is right in front of you.

Player: Hey a chasm, I want to jump it.

GM: Ok, roll movement with unsure footing. Uhm it's 5 meter across so you need (look up distance) 4 successes.

Player: ok I roll my 4 dice with target for unsure footing (5, it says so on the character sheet or something)

Player: 8, 5, 7, 11. Oh, all 4 successful.

GM: Ok, you sail over, barely making it to the other side.


Which is not very different from the rolling damage dice:

GM: Ok roll for damage, his Toughness is 7

Player: Ok, my damage rating is 5. Cool. 11, 2, 5, 7. Two successes for two wound points.

GM: He whipers and falls to the floor as his blood starts looking for a new place to hang out.

Now give me an explanation what's so horrendously complicated with this again.

Oh, I'm quoting something here:

I'm suggesting sticking only with the "main feature" dial and skipping the other two 'dials.'  Believe me, I am halfway through a minor in math, we can tailor your "main feature" to do all you have required of the probabilities without using three separate functions.

WHAT THE HECK would the "main feature" be? Something which already incorporated all conditions?

The "jump over 5 meter chasms with unsure footing conditions" skill?

Sure. But doesn't it seem easier to simply have a dial so you can use the same skill for all conditions simply by inputing a value? Or make it useful for other things than jumping also by turning a dial. Or make it possible to use the same rating to calculate chances of jumping 6 meter and 4 meter as well?

I don't quite see the simplicity in making all possible permutations in the skill list just to have a single knob.

Take this example: Static test:
* Determine relevant stat What's my stat for this test?  This equals the number of dice.
* Determine circumstances What's the difficulty for this test?  This equals the target number on the dice.
* Determine necessary degree of success How many successes do I need to succeed?  (If that doesn't sound redundant, I don't know what does.)  This determines the threshold of successes.

You're assuming it works like Shadowrun. The target number is not and has never been the difficulty for the test. From the beginning I have stated that this is the dial to see how random the situation is.

Dials: Player Skill, Randomness, Difficulty

Are are really two of these redundant Fang?

And what workload am I putting on the GM Fang? I just don't see it. You want to set a task that a person with stat value x can succeed with most of the time? Set the required degree of success to that level.

Can an average person do it almost all of the time? If yes, set it (degree of success required) to 3, and so on and so on.

[Le Joueur]

Sorry for not quoting, but that thing you wrote just now was insanely cluttered. Maybe we're reaching a point where we should take this to pm.

As this is turning harshly defensive, I'm taking it to PM.  If anyone else wants an explanation of the complexity Pale Fire is missing, request it there.

Happy to be of service.

Fang Langford

[Walt Freitag]

Hi Christoffer,

The target number is not and has never been the difficulty for the test. From the beginning I have stated that this is the dial to see how random the situation is.

This, though, is the problem. For unopposed rolls, for any given setting of all the other dials, a higher target number always decreases the probability of success. Always. In some cases, quite dramatically.

Increasing randomness (spreading out the outcome distribution) should always mean that the probability of success moves closer to 50%. If it starts out below 50%, it should increase. If it starts out above 50%, it should decrease. If it starts out at 50%, it should stay the same. Your randomness dial doesn't do that. For unopposed rolls, your randomness knob always decreases the probability of success when increased and increases the probability of success when decreased.

Regardless of whether you agree or disagree with Fang's objections in principle to including a separate knob for variance (I don't agree with it, though I do agree with many of his individual points), your randomness dial is broken. It doesn't do what it should do.

Can we put aside the talk of entropy and functions and focus on that point for a while?

The fact that what it does do (in unopposed rolls) is always make success less likely when increased is why Fang and I feel justified in calling it a difficulty setting, even if that's not what you intend it to be. And that's also why it appears to be redundant with the other (number of successes required) difficulty dial in the system.

- Walt

[Christoffer Lernö]

Ok Walt, fair enough.

Well, I envision it as "hidden unfavourable conditions dial" for static tests. One might think it would move up as well as down (acually that is possible if the crit value follows the target number in reverse. For example, the crit is usually at 12 and target at 1, then if I increase my target to 3, maybe crit is on 10+), but I see this as unwanted design.

I assume the randomness only include hidden disadvantages, but I think this is actually a fair assumption.

For those situations where external condiditions can only improve the situations I already have the crit at 12.

To make this more clear, let's look at two examples:

I slip because it's muddy
If the target number is higher than 1 then that is a valid explanation for the reduction in success.

I jump further because of having the wind at my back
This situation can occur if you roll a lot of 12's

I find that in most situations, our performance is not randomly distributed. In fact there is a "standard level" which we usually perform at. If we try really hard we can push this forward. The distribution of an olympic long jump for example would only come from the 12's. I'd assume the conditions were good enough for target #1

So actually, in most cases you'd be using target number 1.

There are only a few cases when the randomizer would be kicking in. The characteristic situation is when we have unknown, random disadvantages.

Let's say A and B are both rolling to discover an ambush. Now in a perfect experiment A is better than B. Let them sit down in a cube and perform some psychological experiment and A is constantly gonna beat B.

On the other hand, what if they are riding down a path, together with others?

A might be engaged in a conversation. B might be distracted by the beautiful princess riding next to him.

To the GM, the exact circumstances are unknown but they MIGHT be negative.

However, if the GM already knows the circumstances, then he/she simply adjusts the degree of success needed and turn the knob to 1.

So we have scenarios:

Many possible negative modifiers, GM does not want to choose: Fixed degree of success needed, turn the randomness knob.

Negative modifiers but known by the GM. Adjusted degree of success, turn off the randomness.

Perfect conditions. Fixed degree of success needed, turn off te randomness.

Advantageous position. Adjusted degree of success, turn off the randomness.


What's "missing" is: "Many possible unknown positive modifiers" which is what I think is the core at your opposition to it Walt? (And the combined condition "Many possible unknown positiveand negative modifiers)

Well, I think that this situation simply does not occur very often. Except in role playing games as a result of the flawed randomness model.

I guess my assumptions can be summed up by

* You usually perform at your peak level or less than your peak level
* Major random situational modifiers are always negative

The exception of "beyond the usual" performance is covered by the crit on 12. Does that make it any clearer?

[Walt Freitag]

Thanks, that really clarifies your intent. "Hidden unfavorable conditions" is an unusual meaning for "randomness" which is why I was misinterpreting the intended effect of that dial.

The "missing" condition "Many possible unknown positive and negative modifiers" is exactly what the variance inherent in most systems (and in human performance bell curves) is supposed to represent.

Your model of performance:

* You usually perform at your peak level or less than your peak level
* Major random situational modifiers are always negative

is therefore very different from most, in which the primary statistic represents the mean rather than the peak. Knowing what this model actually is, I can at least try to work those dials correctly.

What remains is the actual mathematical behavior. Let's say I have a skill of 7. This should be pretty good, considering that it allows me, under ideal conditions, to succeed in things that "almost no one can do" more than half the time. (Presumably, almost no one can do them even when their conditions are ideal.)

Turn that randomness knob to 11, and now I have only a one in three chance to do something that "anyone can do." (The chance of getting zero successes or one success in the roll is about 66.6%, and that's taking into account the exploding twelves.) I would have a less than 2% chance of reaching a degree of success 4 (I'd have to take three or four concessions most of the time). I can certainly imagine conditions under which this severe a shifting of the odds might take place, but I can't imagine them happening very often, and even more important, I can't imagine them happening without the GM "choosing" by providing some in-world explanation. "Okay, the odds are against my veteran archer hitting a target at twenty paces that even an untrained person with a bow could normally hit... and why is that? Oh, there's a hurricane-force crosswind blowing. I see." But isn't that now a known factor, best implemented by raising the straight difficulty (successes required)?

The remaining issue here is not (now that the math matches the model as described) one of mathematical validity, but of end-user usability. Having two different difficulty dials that interact in mathematically complex ways makes it likely that GMs will make bad rulings.

For example, a superhumanly skilled (skill 9) archer wants to shoot the flying Smaug in the one vulnerable spot on his stomach. Wouldn't most GMs look at the situation and say, "OK, this is a degree of difficulty 8, because only the extremely skilled could do it, and it's randomness 11 because it's a chaotic scene just filled with random factors (wind, fire, wild flight, panic)"? That makes the chance of success, to a very high degree of precision, zero. Unless the player could think up the five or six concessions that would most likely be needed to bring about a success, he's hosed. ("Um, I take extra time to aim, and, um, I fire the Perfect Arrow that I've been saving all these years, and, um, I stand right in the dragon's path to get the best angle, so if I miss he'll flame me for sure... what? Three more?!")

Even a randomness of 6 would make an outright success very unlikely (about a 2% chance).

It would, I fear, require a GM with an unusually analytical mind to evaluate the situation and say:

"This is a shot that almost no one could make, so it's degree-of-success 8, but there's very low randomness here because the archer is concerned only with the target and, despite the motion and the fire and the chaos, it's mostly his pure skill that will decide the issue."

Or perhaps say:

"There are all kinds of wildly random factors going on here, so the randomness is 11. But, if it weren't for those random factors -- if the dragon were a stationary target at the distance where the archer intends to loose the arrow, and there wasn't all that fire and smoke and wind and panic, then it would actually be a relatively easy shot, so the degree-of-success needed is 3."

Yet, that (one or the other, or some even more counterintuitive middle ground between the two, such as "sucky conditions + degree of difficulty not everyone can do it" -- randomness 6, degree of success 4 -- which badly de-dramatizes the situation) is exactly what the GM must do here to make the system work.

- Walt

[edited to fix a typo "on" instead of "one" which made a sentence difficult to parse]

[Walt Freitag]

Sorry, erroneous post deleted.

- Walt

[Christoffer Lernö]

Walt, can I sum up your comment as: "Hmm... you should look into the behaviour of the varying conditions before you commit to it"

It's a valid complaint. The definition of "sucky" conditions was fairly liberal.

If we look at a "good" stat of 6. A useful sub-division of that would be:

"On average 6"
"On average 4"
"On average 2"

These would correspond to 1, 5 and 9 for target numbers. Alternatively one level each of 1, 3, 5, 7, 9 putting the average on 6, 5, 4, 3 and 2 respectively (ignoring the exploding 12)

Let's look at that and see if the behaviour is better:

Code Select Expand

    1    3    5    7    9   11
0   0%  <1%  <1%   2%   9%  33%
1   0%  <1%   2%   9%  24%  37%
2   0%  <1%   7%  20%  30%  20%
3   0%   4%  18%  27%  22%   7%
4   0%  15%  28%  23%  11%   2%
5   0%  31%  26%  13%   4%  <1%
6  59%  31%  14%   5%  <1%  <1%
7  30%   3%   5%   1%  <1%  <1%
8   9%  <1%   1%  <1%  <1%  <1%
9   2%  <1%  <1%  <1%  <1%  <1%

The randomness is useful about up to 5 or maybe 7, then quality fairly quickly goes gravitates towards zero and as you point out Walt, this makes decisions pretty hard for the GM.

At the first two levels, say 1, 3 and 5 however it seems to be useful. However, it looks a little broken none the less. The question is: Is it acceptable even if the randomness used only involve these first three target numbers (1, 3 and 5)?

[Christoffer Lernö]

Following a discussion with Fang by PM, we kinda figured out I left a little too much out of that the posting to be clear with that it was for.
Although Walt seem to have gotten what I mean, I apologize for the unnecessary confusion.

[Walt Freitag]

I think you could make a pretty good case for randomness up to 7. If you look at the distributions in your chart, you can see that raising the randomness at first widens the distribution of outcomes (as the likely number of failures increases), then it narrows it again (as failures come to predominate and the whole distribution is driven toward zero). It's at 7 where each die has a 50-50 roll, so it makes sense that that's where the widest distribution (the most actual randomness) occurs, though I haven't proven this analytically. Beyond that, the variation in the outcomes is decreasing, so it's no longer in any sense an increasing randomness dial, just an increasing difficulty dial.

It's also relatively easy for GMs and players to undestand that a maximum randomness of 7 means half the expected degree of success on average.

There's an interesting effect with regard to the skill level. The higher the skill, the more dice are being rolled, so the more consistently center-weighted the outcome becomes. At randomness 7, a character with skill 3 still has (disregarding the exploding twelves for the time being) a 12.5% chance of performing at his maximum. A character with skill 6 has only a 1.6% chance of performing at his maximum. However, the higher skill will still outperform the lower, so maybe this isn't much of a problem.

There's another way you could do the randomness that appears to give more precise control and gives more benefits for higher skill.

Set a randomness, from zero (lowest) to (some max to be decided later).

If skill <= randomness, roll d12s equal to your skill, each 7+ is a success.

If skill > randomness, roll d12s equal to the randomness, add (skill - randomness).

In other words, randomness turns some portion of your skill number from guaranteed successes into 50-50 successes. At zero randomness, your skill translates directly into your success. When the randomness equals your skill or higher, you must roll 50-50 for each success.

At skill 7, randomness 3: I get 4 successes + the roll of 3 dice.

At a given randomness, a character with skill 7 has the same chance of performing at full effectiveness as a character with skill 3. At a randomness of 3, a character with skill 7 will always perform with at least a degree of success of 4.

The randomness number then directly represents the maximum possible decrease in degree of success due to the randomness factors. Half the randomness number is the average expected decrease in degree of success (for characters whose skill is at least equal to the randomness). You can represent unknown positive factors (e.g. a luck spell) by subtracting the randomness from the degree-of-success difficulty, and you can represent an equal mix of unknown positive and negative factors (e.g. for fishing or hunting) by subtracting half the randomness from the degree-of-success difficulty.

- Walt

[Christoffer Lernö]

Beyond that, the variation in the outcomes is decreasing, so it's no longer in any sense an increasing randomness dial, just an increasing difficulty dial.

You're absolutely right. Well that takes care of that. 1, 3, 5, 7 seems like good presets for the target number.

Still not a really slick mechanic but I guess I'll survive. And maybe later I can find something to replace it with.

There's an interesting effect with regard to the skill level. The higher the skill, the more dice are being rolled, so the more consistently center-weighted the outcome becomes.

Well, you can look at it as a percentage thing. For a skill 3 to perform as skill 2... that's a 33% decrease. However, dropping one step from 6 to 5 is only a 17% decrease. (dropping from 6 to 4 however is a 33% decrease. The probability to roll either 6 or 5 is together about 17%)

On the other hand the benefits of exploding 12s is also higher for the level 6 skill. So basically, the mobility of the performance up and down is a percentage of the stat and not an absolute modifier.

If this is a desired thing or not, that's an open question.

There's another way you could do the randomness that appears to give more precise control and gives more benefits for higher skill.

I don't know if this is inherently better or worse. I also had this early idea of adding random version of the stats. So you might have:

Strength 6.

Then you also wrote 4+1D2 and 2+1D4. Looking something like:

Strength 6 (4+1D2/2+1D4)

So for random situations you would use the random stats instead of the fixed ones. Not that the above was a good idea. The distribution sucked. But if you had stats a few magnitudes bigger then one could do something out of it.

Still, the main reason I'm not looking too seriously into alternatives yet is that my biggest motivation to choose this particular method is that it looks like the wound mechanics. It's either that or looking like the fighting mechanics roll (of a single D12) but I'm unsure of how to tweak the latter into giving the same dials. I felt that being able to get all these dials out of the mechanic was little more than a happy concidence.

[Walt Freitag]

What I'm not sure of is whether or not randomness=7 is also the most random (maximum chance of an upset for the character with the lower skill) for opposed rolls, or whether that chance keeps increasing all the way up to randomness=11. That's a bit more complex calculation. (I'll look at it tomorrow, if you haven't already worked it out by then.)

- Walt

[Christoffer Lernö]

Walt, for opposed rolls it keeps going until 11.

Like this (approximate values. I don't feel like calculating stuff so I ran it through a computer program with 10000 rolls, so it might be off with a small percentage):

Target 3
4 vs 3: 83%
5 vs 3: 95%
6 vs 3: 98%
7 vs 3: 99.5%

Target 7
4 vs 3: 67%
5 vs 3: 79%
6 vs 3: 87%
7 vs 3: 92%

Target 11
4 vs 3: 60%
5 vs 3: 67%
6 vs 3: 73%
7 vs 3: 77%

Still, I don't know if this effect (with target 11 even more randomizing) really make things worthwhile (I mean, I don't think I need to include it).
What really are the situations where my mother (Strength 3) would have a 23% chance of beating Arnold Schwartznegger (Strength 7) in a strenght contest?