I'm cutting and pasting from my Ygg document here. I kind of came up with an idea that seems to work. Advantages and Concessions seem to be a little more natural as well. But I only just worked it out. If you would have a look, then that would be nice.

Basic Resolution System
This is how it is done: pick as many D12 as you have for the relevant statistic. You want to jump? Well that's Movement. Armwrestle? That's Power, and so on.

Roll these dice and for every D12 which is equal to the Difficulty (more about that later) you score one degree of success. If you roll a 12 on a die you not only get a success but also an extra die to roll.

Now round up the successes and compare them with what you need. So what do you need? Well that depends on the test. There are two types of tests: Opposed and Static.

Opposed Tests
This is when someone or something else is also trying to win. Armwrestling is a good example. To find the winner, simply compare who has the highest degree of success. The one with the highest wins. In the case of a tie, there is a second test and so on until a winner has been found.

Static Tests
If you want to jump a chasm or just see if you can make out Mount Doom in the distance, you do a static test. The GM gives the required degree of success required to make it.
A vague rule of thumb might be:

1 Trivial
2 Anyone can do it
3 You can do it
4 Not everyone can do this
5 Pretty advanced
6 Most can't do this
7 Almost noone can to this
8 Only the extremely skilled could ever do something like this

Difficulty
The difficulty describes how easy it is to do a task and how big the chances are that an action is performed at it's optimal efficiency.

1 Perfect conditions
6 Sucky conditions
11 The most random conditions

Concessions and Free Advantages
If you have a higher degree of success than you need to complete a task, then you can trade those in for other benefits. Benefits include improving the time to complete an action or the quality of it. These benefits are called Free Avantages.

The opposite of Free Advantages are Concessions. You can do concessions before or after you rolled. By making a concession (which is basically making the quality of your action worse in some respect) you get another die to roll and add to your degree of success. Note that you can mix both conessions and advantages, for example taking longer time to complete a plainting in order to get a higher degree of success to put into improving the quality of the painting.

When & What About Concessions
Concessions can be made before or after the normal dice are rolled. There is no penalty to doing it before or to do it afterwards except for the fact that you can't make concessions change things that took place before the action was performed. Say that you're jumping a chasm. You roll and you fail. Now at this point you can't take a concession saying you took off your backpack and jumped without it nor that you did it with a running start. On the other hand you might be able to get away with jumping over but losing the backpack in mid jump (for another die).

When & What About Free Advantages
Just like concessions, there are limits to what can be taken as advantages after the action is rolled for. For example, you can't make the jump then declare that you were wearing the backpack, if you weren't supposed to be wearing it in the first place. However, if it's before the jump you can say you're jumping with the backpack, but that will increase the necessary degree of success. So if you fail, you have to take concesssions to get over, and these concessions can't be that you forgot to put on the backpack.

I would simplify this by dropping "static tests". See this Rant. I apollogise in advance if you've already read and disgreed with this.

Simply replace "degree of success" with opposing difficulty dice rolled by the GM. Makes any test possible for anyone theoretically, and gives you the same scale of success for both "types" of rolls. As such, then, one net success means that you barely made it. One net success for the chasm means that you barely failed. Then Advantages are just spent successes, and Concessions are just purchased successes.

Straightforward.

Mike

Mike Holmes wrote: I would simplify this by dropping "static tests". See this Rant. I apollogise in advance if you've already read and disgreed with this.

Simply replace "degree of success" with opposing difficulty dice rolled by the GM.

You might want consider the changes made in the recent versions of the WW storyteller system. Use a fixed target number, say 7, as it makes scanning the dice for successes easier.

Andrew Martin wrote: You might want consider the changes made in the recent versions of the WW storyteller system. Use a fixed target number, say 7, as it makes scanning the dice for successes easier.

Pale Fire wrote: And except for scanning the dice, why give up movable target numbers when I actually use the target number as a way to turn the randomness dial.

Pale Fire wrote: And I don't have the possibility to browse through any material here in Taiwan (all my stuff is back in Sweden).

Le Joueur wrote:

Pale Fire wrote: And except for scanning the dice, why give up movable target numbers when I actually use the target number as a way to turn the randomness dial.

Why? Because you already have one? That'd be the number of dice rolled. Harder task? Take away a few. Easier? Add a couple. No 'target number dial' needed. It's redundant anyway.

Pale Fire wrote:
> Aaaa Andrew you evil thing you!

:)

> First I don't know what a "recent" version of WW's system would be.

Trinity and Exalted have the latest versions. You've all ready got the reroll on max die value, and you've dropped the botch on "1". So just stick with the fixed target number (and measure everything in dots) and you'll have Storyteller 2 for D12 real soon! :)

> And except for scanning the dice, why give up movable target numbers when I actually use the target number as a way to turn the randomness dial.

It's quicker. And quicker play is more fun, because it's less time spent on mechanics and more time roleplaying (assuming all else is equal).

Trinity and Exalted have the latest versions. You've all ready got the reroll on max die value, and you've dropped the botch on "1". So just stick with the fixed target number (and measure everything in dots) and you'll have Storyteller 2 for D12 real soon! :)

Pale Fire wrote: ...I actually use the target number as a way to turn the randomness dial.

Hey Christoffer,

So good so far...

Pale Fire wrote:

Le Joueur wrote:

Pale Fire wrote: And except for scanning the dice, why give up movable target numbers when I actually use the target number as a way to turn the randomness dial.

Why? Because you already have one? That'd be the number of dice rolled. Harder task? Take away a few. Easier? Add a couple. No 'target number dial' needed. It's redundant anyway.

Parameters: Randomness, Character "skill" rating, degree of success needed.

The player rolls as many dice as the skill rating gets an extra die on each 12 against the randomness number and counts total number of successes.

Working the skill rating up and down will alter the number of successes as well as the chance of boosting a skill beyond its original level. Randomness number makes success increasingly less certain, but most of all it mixes up the levels.

Pale Fire wrote: For opposed rolls,

Le Joueur wrote: There are traditions that result in 'broken systems,' however.

I don't see any problem here that's that fundamental. I see some practical problems with the system as described, but I don't have a problem with the general idea of a system that has three basic variables:

1. The skill of the person.

2. The difficulty of the task, e.g. the skill of the opponent.

3. The performance variance which depends on the nature of the task.

For example, if I'm trying to outscore an opponent in a single game of pinball, and that opponent's mean score is 50% higher than mine, my chances of winning the game are still reasonable (I'd estimate, based on the variance of my own pinball scores, that they would be in the 10 to 25 percent range). But if I'm trying to arm wrestle someone whose mean arm strength is 50% higher than mine, my chances of winning are extremely poor. That's what Christoffer means by varying the "degree of randomness." It's a variation in how much a given difference in mean performance (skill level) is likely to swing the outcome in a given single instance of resolution.

In any single instance of resolution, it's possible to collapse #2 and #3 together by taking the randomness into account in the scale of the skill scores. Just say that the skill deficit I have in pinball representing a 50% lower mean score is a -3, while the skill deficit I have in arm wrestling representing a 50% lower mean score is a -9, and then resolve them both in the same way. But that doesn't work on a systemwide basis unless every skill has it's own separate score. If I'm basing skills on requisites, then both arm wrestling and cow tipping are strength-based scores. If I think my changes of beating an opponent whose strength is 2 points higher than mine at cow tipping should be much higher than my chance of beating him at arm wrestling, because of the greater influence of random factors involved in the former (e.g. the behavior of the cow), then I need that third variance factor as an independent variable in the system.

I also like the idea of using the variance factor in strategy and tactics. It can be shown mathematically that if one side in a contest has the power to manipulate the level of randomness from one round of action to the next, then that side can sometimes achieve a greater than 50% chance of winning the contest even if its expected outcome in each round is always negative, by adopting the strategy of increasing the randomness when it's behind and decreasing it when it's ahead. There are thirty-two head coaches in the NFL who make their living by grasping this principle. A team that has a perceived talent disadvantage will try to force both sides to play riskier strategies, try to run down the clock if it's not already behind (a "shorter" game increases the variance, though not enough to make it worth running down the clock if you're already behind, usually), and hope for bad weather. If I'm duelling a swordsman with superior skills, I'd prefer to have the fight on a frozen lake, or in a courtyard full of hanging laundry, or in a chicken coop filled with flying feathers... anything to increase the performance variance.

Okay, now from principle to practical. The problem with the system presented above is that it doesn't cleary separate out variance as an independent variable. Instead, adjusting variance is accomplished by adjusting the target number, which also has a very strong effect on the mean chance of success in unopposed contests and a strong effect on the mean margin of success (which is important in the system) in opposed contests.

This creates the problem that there are two different difficulty variables (actually three, but only two of them are in effect at a time): the number of dice rolled by the opponent OR the number of successes needed, AND the target number (number to be rolled on a die for it to be counted as a success).

Remember, once we get down to an individual instance of resolution, there's no longer any distinction between the chance of success as influenced by mean difficulty, and the chance of success as influenced by the degree of randomness, at least as far as the success or failure part of the outcome is concerned. There's only just one probability. Higher randomness just means that my chance of success if I have a mean disadvantage, and my chance of failure if I have a mean advantage, are higher than they would be at a lower randomness setting. (While a 50-50 chance, of course, remains a 50-50 chance at any level of randomness.) I could make that adjustment on the fly using just a single combined-chance-of-success knob, such as the number-of-successes-needed. But it's a little tricky.

The problem is, using Christoffer's proposed system, it's still tricky. If I want a difficult unopposed action to have a high degree of randomness, using this system, I have to juggle the two difficulty variables in a complex way. By setting the target number high I supposedly make the randomness higher, but I also have to make the number-of-successes-needed low, or else success just becomes even more unlikely... and making the randomness higher, when I'm at a disadvantage, is supposed to be a way of making success more likely than it otherwise would be. It would be easier to adjust just one measure of the chance of success like in the previous case. It's not quite so bad with opposed rolls -- a higher randomness applies to both sides, so it doesn't skew the mean outcome -- but it makes the mean margin of success lower for a higher-randomness contest, which is exactly the opposite of what you'd expect.

On the other hand, in principle, a truly independent adjustment knob for situational variance/randomness could make it a lot easier to arrive at a die roll whose combined-chance-of-success reflects both the mean advantage/disadvantage and the variance in a sensible way.

I don't see a way this could be fully achieved in the currently proposed system without making major changes. It can be partially achieved by (1) getting rid of the variable target number, make it always 7+ or whatever; (2) add a roll of centered dice (such as Fudge dice) to the number-of-successes-needed in unopposed rolls; the more dice added, the higher the variance; (3) add a roll of centered dice to the opponent's roll to add variance in high-randomness situations. The limitation is that there's no way to turn down the variance in opposed rolls for low-randomness situations.

Another choice would be to keep the variable target number as a randomness knob, but get rid of the unopposed roll that causes the most problems. Instead of setting the difficulty as a number of successes needed, set it as a number of dice rolled, against the same target number as the character (which represents the randomness setting), with the result being the number of successes the character needs. In other words, make all rolls opposed, just as others have suggested... but then you can keep the variable target number as a randomness knob. Just be aware that in that case, the mean margin of success or failure will be maximized when "randomness" is in the middle of its range (7+ on d12s) and then will decrease again as the randomness increases beyond that.

- Walt

Le Joueur wrote: Let me separate the three randomizers, maybe that'll make it more clear:

Pale Fire wrote:

Le Joueur wrote: Let me separate the three randomizers, maybe that'll make it more clear:

Ok. Now you're playing a wholly different game from what I'm talking about Fang.

How you can put the degrees of successes as a "randomizer" is actually beyond me.

Pale Fire wrote: I can't see how you can say that something that does not affect the number of dice rolled (the degree of successes needed) is a randomizer.

How does that change the distribution of the results?

Aren't you mixing up predictability (there are natural boundaries where predictability goes down) and randomness induced by the mechanic? It's only the latter I seek to control.

Le Joueur wrote:
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.

Fang wrote: 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.)

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

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.

Pale Fire wrote: 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.

Pale Fire wrote:

Le Joueur wrote: 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.

Pale Fire wrote: 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?

Pale Fire wrote: 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.

Pale Fire wrote: 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.

Pale Fire wrote: (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

Pale Fire wrote:

Pale Fire wrote: 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.

Pale Fire wrote: * 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).

Pale Fire wrote: * 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).

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.

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.

Pale Fire wrote: 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.

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.

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?

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

Sorry, erroneous post deleted.

- Walt

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] 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%[/code]

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)?

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.

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

wfreitag wrote: 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.

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.

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

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

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?