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The oddness of dices
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Topic: The oddness of dices (Read 2542 times)
microphil
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Posts: 8
The oddness of dices
«
on:
October 19, 2009, 04:31:27 PM »
Hello everyone!
As I'm german, I'd like to forward my apologies for all mistakes I will commit. Sounds more like a alibi, doesn't it? Additionally this is somewhat long of a post, couldn't keep it shorter. Anyway, I'll try to make my point and I like to read your opinions and thoughts to the mine.
This thread is thought to be a discussion on the core of every roleplay system  the ability, difficulty and the especially the dice(s). For the sake of reducing complexity I will consider only uncrooked sixfolded dices, but the same applies in essence to all types of dices.
The chance to realize a certain number is for all 6 possible outcomes 1/6. That is, the distribution of infinite trials is flat, a discrete uniform distribution
http://en.wikipedia.org/wiki/Uniform_distribution_(discrete)
. The data level of a dice has ordinal scale, since it expresses a more or less between two or more realizations, but lacks a absolute zero point. The range of the distribution is 1 to 6, the standard deviation is not applicable for the mentioned data level of a dice. The same is true for the mean. The mean of a D6 is 3.5, but the data level does not allow this computation, strictly speaking. Additionaly, mode and median can be computed, but doesn't provide any useful information. We only know the span of the distribution for sure.
For spite of the fact that means of dices are often computed, what information does the number provide? It only tells you that for infinite trials, 50% of the realizations are below that number and vice versa. It splits the dice range into two halfs. Lets define the lower range as the acceptance space and the upper range as the rejection space.
In roleplaying games the variables 'ability' and 'difficulty' are assumed to have interval, sometimes even metric data level. Between two values hierarchy and distance can be validly infered. If metric data level is assumed the ratio can infered too. So the value of, lets say strength, 3 is higher than the value 2 (hierarchy) and exactly 1 point higher (distance). Metric level allows additionally to validly infer to the ratio of both values 2/3, 66.6% of 3 points. The difficulty increase or decrease the ability considering the situation of the test, resulting in the probability of the test. Now we have a playable scale, over which tests can be made.
Now the problem enters the scene. Most roleplay systems let you roll a dice and check, if the result is inside or outside the acception space. This way, for infinite rolls, the probability that you will succeed equals the probability of your (ability+difficulty)/scale maximum. Fair enough, one is tempted to think!
1) The check is actually a mix between interval (metric respectively) and ordinal data levels, so the check can only be interpreted on the ordinal level.
2) The dice can show up any number in its range with each 1/6 probability. The chance is absolutely unaffected by the ability and difficulty.
This leads to the following restrictions in the interpretation of the result:
1) Only acception or rejection of the test can be infered.
2) Since the result has ordinal scale, it cannot be interpreted as distance from the cutoff value. No goodness of the test can be validly infered, but this is common practice in virtually all roleplay systems.
3) The random element governs the check completely, each trial. Govern means here that the ability and difficulty does not constrain the random element. The latter two are only defining the cutoff value of acception.
This leads to a certain feeling in roleplay games.
1) Roleplaying means gambling, 100% each trial. Only in the long run one will close up to ones probability of success  this is known, but not directly experienced by the participants. Still, each trial is 100% random.
2) Odd things happen relatively frequently: Easy tasks are missed, undoable tasks are passed.
3) Some type of player underestimate their luck, some type of players overestimate their luck.
4) Gamemasters and/or Players now tend to use rules excessively others forget about rules at all.
5) Because each situation has a different importance for the story and/or for the character(s) (not in terms of difficulty) the problem can get very chaotic.
6) Gamemasters and Players need odd explanations for these random events all the way down their story. A common, implicit social contract for these purposes in groups are: "Don't mention the oddness" or "That's the way it works." or "Bad luck, dude!"
"So you want to play RPG without dices?"
No! My whole argument is about constraining the random element appropriately.
In my opinion, the excessive dominance of the random element in roleplay games accounts very much for the varying preference of gaming, narration and simulation (see: GNSTheory) between the participants in roleplaying groups. Seen from a broader perspective, Roleplaying Game is all about to play a role. In order to play a role with other participants one needs some rules  that is true for each GNSstyles. Rules here include the explicit rules of a system and the implicit rules, the social contracts inside the group. The moderating variable between GNSstyles is therefore the extend and purpose of the rules applied.
So why the Need for less or more rules? Both is a consequence of the dominance of the random element apparent in roleplaying games. It threatens the consistency of the experiences. The resolutions to the problem might be first, to minimize the influence of the rules (& the dominance of the random element) or second, to maximize the influence of the rules (& the random element if the rules incorporate dice throwing).
The first is a rational solution, from this view point, since it really reduce the diceproblem described above. The drawback is arbitrariness of the described actions  and must be coped by a catalouge of implicit rules, which in turn is often overseen by the corresponding advocates. Thus Narrativist choose implicit rules over explicit rules. This easily leads to conventionism or normative arguments  a special LARP problem due to the lack of explicit rules. I call this style 'RoleConvincing Games'. Nevertheless, this style needs to cope less with the oddities springing from the diceproblem.
The second is a irrational solution, from this viewpoint, since it ignores the diceproblem. More rules, mean more dice rolls, thus aggravating the diceproblem. Not mentioning the loopholeradarplayers, these types of games can never solve the problem of exagerated oddness, because they are advocating the enemy (not rules, but dominant dices!). I call this style 'RollDices Games'.
"Okay, but then how to reduce the influence of dices, dude?"
We have to come from the actual uniform distribution (  ) of a test, to a normal distribution ( _/\_ ), called the bell curve. In science the latter is the ideal situation, and a variable, that is distributed in a uniform fashion is normally considered crap, since it expresses nothing more than randomness. Certainly Roleplay Games are less than random. Characters have certain abilities, the story yields different difficulties, and additionaly you need a moment of chance  accident or fortune. The analogy for chance to science is the error of measurement, produced by not controlled variables.
What describes best the normal distribution? The distribution has a mean, that is the highest point in the curve (if mean = mode). On the left and right hand side the distribution has decreasing numbers of realizations. Thus the probability of a realization falls steeply with increasing distance from the mean, until it smoothes out to the edges of the distribution, approximating the probability of zero. Extrem values are very unlikely, so randomness is probabilisticly bound to an intervall. On both sides of the mean we find a exponential function to a certain base.
"I need a computer to calculate this? I mean, give me a break!"
No! This can be easily attained by  a number of D6 and basic arithmetic operations. Remember, the D6 has a probability of 1/6 each possible realization. Asked for the probability that the dice will show at least a certain number 'x' returns this linear function f(x) = 1−(x/6)+(1/6).
Now if we add a rule that all realizations of 6 are rerolled and summed up the function gets exponential to base (1/6): g(x) = (1/6)^((x/6)−(1/6)). The probability to roll at least 6 = 25%, 12 = 4%, 18 = 0.6%, 24 = 0.1% and 50 = 0.00000044%. Now the random element can be scaled by the following function:
h(x,w) = (1/6w)^((x/6)−(w/6)), where w is the number of dices (german =
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HeTeleports
Member
Posts: 66
The name's Youssef.
Re: The oddness of dices
«
Reply #1 on:
October 19, 2009, 09:16:43 PM »
Hey Phil,
Interesting stuff you've laid out. I especially like the mathematic "rebalancing" for the use of the D6.
Out of curiosity, what game have you most recently played?
One list of yours struck me: the list of disappointments in roleplaying you've done.
It's pretty comprehensive. At some point or another, a thread has been written to address each of those. While rebalancing a D6 is a pretty innovative way to combat some of those disappointments, I think you might find more direct approaches.
I'd recommend looking up these terms and reading the oldest threads you can find.
1) FATE + FITM
2) "I will not abandon you"
3) Capes + "Gamism"
Then, read the article (up at the top, click "Articles") "Dice and Diceless."
No, I don't have a hidden counterstance to what you've proposed. The reason I recommend the reading is that I would like to see how those ideas (which seem to cover similar ground as what you have) affect your post. We all design with the tools we know of. We can increase our awareness by experience (playing the games, which takes players and lots of time) and by reading (which takes a little bit less time).
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"Oh... be careful. He teleports."
microphil
Member
Posts: 8
Re: The oddness of dices
«
Reply #2 on:
October 20, 2009, 01:29:30 AM »
Thanks for your feedback!
I played mostly The Dark Eye, D&D, Shadowrun, White Wolf, StarWars, InNomine. Guess these are the most common, and I play / gm all of these still with fun.
Dissapointments:
Rather a bias in dices, that produce these feelings in virtually all RPG systems. One can combat these problems or dissapointments very direct, but I argue that these are some of the results you get, simply by rolling dices. Consequently, if you can reduce the bias you reduce these problems.
From my experience, to combat directly these problems is uneffective (please prove me wrong). Aggravating the thing is, that most RPG folk got settled with this (odd) type of dice mechanics.(Discrete uniform distribution)
The baseline of my idea is: the test distribution of your dicemechanic must become a normal distribution. How you accomplish that is up to you.
Diceless:
If a group can handle a situation without a dice  perfect  as long as all agree. They just created instances of an implicit rule. In the example the rule was that the gm allows charactercanwhatplayercandescribe.
Couldn't find your post regarding 1),2)&3) but I'll match up!
Best
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microphil
Member
Posts: 8
Re: The oddness of dices
«
Reply #3 on:
October 20, 2009, 03:13:45 AM »
Read this thread:
http://www.indierpgs.com/forum/index.php?topic=4830.0
Both techniques of conflict resolution are good to go with, imho. Sometimes it even appears to be important to switch these modes, because of a mindset of players or characteristics of the situation or system as Ron pointed out.
Concerning my thoughts it does not matter if you describe retrospectively from fortune or you describing the fortune. In the end your fortune is a normal dice, a random number generator that is in no way restricted in its span of randomness. Lets say you got a score of 15 in gambling. You need to throw a D20 equal or below your threshold. The span of randomness is 1 to 20. This results in a discrete uniform distri (  ), not in a normal distri with the threshold as its mean (_/\_).
Now you hit 13 and infer, "Good 2 points left, gimme the cash!"  Now the good action may be described and fleshed out retrospectively (FITM), but the inference to the goodness of test is not valid. The odds that I have 2 points left is the same as if I have 10 points left and of course is the same as if I missed the test by 1.
Now the simulationist (as Ron pointed out, but not limited to) come on the scene and say: Lets describe your action in greatest detail and let the dice decide (binary). 1 hour description and table looking and discussion on the reasonability of the modified threshold (now it is 13, by the way) you are diceing a 1. "Damn, I should have described my action more riskier, anyway gimme the cash!", the player might think and say. Now the FITE process is also prone to the diceproblem, that is the uniform distribution. It should be getting exponentially improbable to roll extrem values on the scale. This way you can upheld interval data level and treat the scale as you want to.
Okay that's at least what springs to my mind for these processes, right now.
By the way I conventionally use FITM. But I have situations where I like using FITE.
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HeTeleports
Member
Posts: 66
The name's Youssef.
Re: The oddness of dices
«
Reply #4 on:
October 21, 2009, 09:45:22 AM »
Hey Phil,
I'm just posting to let you know I'm still reading to figure out your meaning (not in the "translatingtoEnglish" sense; in the "talking about difficult concepts" sense.)
This thread is largely talking about the role of competition
in a game based on storytelling.
(Capes fans, I'm aware I'm overgeneralizing.) Between the lines, you'll see a game design addressing the disappointing effects in your list, "This leads to a certain feeling in roleplay games."
At first blush,
this post by Meguey Baker
seems to be in the middle of a discussion. Actually, she's defining two design styles that actually impact No. 5 on that list more directly than most believe.
No. 5 was "Because each situation has a different importance for the story and/or for the character(s) (not in terms of difficulty) the problem can get very chaotic."
It sounds like you know what I'm referring to with FITM and FITE (or Fortune At The End).
I might have missed the target with my referral to the
Dice and Diceless essay
. In that essay, Eric Wujcik describes how he played diceless to secure more successes in D&D than he would have had rolling dice.
Hmm.
After reading your post a few times while researching the above links (hope I got the tagging right), it occurs to me that you seem to be on a logical road heading toward
Ludic Fallacy
, which means "the misuse of games to model reallife situations."
(Before anyone mentions it, no, that's not an argument against simulationism or even exploration, so don't go down that road.)
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"Oh... be careful. He teleports."
microphil
Member
Posts: 8
Re: The oddness of dices
«
Reply #5 on:
October 21, 2009, 12:28:48 PM »
I want to address one thing offtopic:
I get a
503  Server temporarily not available
, on this forum very often. Please, venerable admin, tell me what I am doing wrong or if you know why I am sitting frustrated behind my screen. The server seems to be difficult to access. Do others experience the same?
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microphil
Member
Posts: 8
Re: The oddness of dices
«
Reply #6 on:
October 21, 2009, 01:34:56 PM »
Hey HeTeleports,
thanks for your reply! I began wondering if I missed the spirit or goal of this community. But I might not, since it is, to me, about 'game design' and improving games, which way ever you define it.
After reading your post I think we both are on the same trial. The Ludic fallacy certainly plays a role, but I think about the implications yet. Ah, please, can you give me a comprehensive explanation what "Capes" actually mean. Could'nt find any, thus cannot include this concept in our line of thinking!
My point is about dicemechanic and the concrete 'diceproblem' that is apparent in all games that include dice throwing. So I'am arguing NOT for or against a certain GNSstyle in the first place.
Second, if one say: "I never had a single problem with rolling dices in RPG!", I think this is more than valid! I do playing these games all along too, having a great deal of fun. If one thinks this, it is perfectly understandable to me to skip this thread.
On the other hand, if one did have a (reasonable) problem with dicing in games, we should join and discuss the fact that we roll dices and consult checks, implies a certain understanding of how the random element should work and how dices actually work.
Diceless:
If I enjoy my wife and she does me, it is a diceless roleplaying!
)) Would be waaaaaay strange if she began asking a dice to see if I could acomplish the role I assume  and I vice versa. But lets imagine this odd behavior for a moment: She has a ability (called 'mojo') of 10 on a 1 to 20 scale (with a lower bound acceptance space). My difficulty to be satisfied is +5, so I'm easy to satisfy! Her actual acceptance space is 115, each night, she rolls her dice. Anyway in 5 nights out of 20 (25%) I will not be satisfied. Is that the way a random element can, for human understanding, work? No, I would say  its very improbable that she will dice results deviate much. < And that is the very problem  "Honey, but the dice say you missed the test!"
So yes, the diceless game mechanics article you posted later on, is a great way to interact, but very uncommon in normal RPG groups, I suppose. Eric achieved more successes than he would have while rolling dices, because he used his ability as a player to apply scrutiny on locks. Very narrative approach, and it worked only because the gm and his fellows didn't object to this proceeding. I mean, pick a lock this way is good for all character, so no one, except possibly the gm, had reasons to object, this is on the other hand a very gamist stance of the player! (Not prefering any GNSstyle)
In my opinion, if you handle a situation without dices, good! Some RPG situations will require a random element anyway.
It is that random element, that I try to address! I has some implication for the gamemechanics and how the game feels (16, especially point 5 in my first post).
Cheers!
PS: This german beer is really good!
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microphil
Member
Posts: 8
Re: The oddness of dices
«
Reply #7 on:
October 22, 2009, 10:26:56 AM »
Hello!
chance.thirteen wrote to me in order to clarify the concept of poling the random element:
"Now give one of these dice(s) a different colour and apply the second rule: this dice poles the direction of the deviation. 13 reducing the difficulty, 46 increasing the difficulty. This way a base difficulty becomes a (personal) actual difficulty while the player applies his random factor."
And he pushed the right button, so here again comes a big post, but this time with examples.
In order to give an example how the dice mechanics work I will use from now on the YARS^(d6) mechanics.
YARS tests are described as follows:
Goodness of test = (Ability + karma)  (Difficulty +/ chaos)
1) Scale: The scale range from 1 to endless but lays normally between 1 and 100.
2) Dice: the random element is drawn only by a certain amount of sixsided dices.
3) Dicerules:
a) Each dice that shows a 6 can be thrown again and summed up.
b) Chaos throws have at least one poling dice with a different color: This dice decide whether the sum is subtracted from or added to the difficulty of the test. 13 => Addition; 46 => Subtraction. The poling dice is parenthized in [].
c) Karma throws represent the amount of motivation on is willing to put into the action launched to be tested. The amount of Karmapool Dices one can invest, is restricted by the Attribute that corresponds to the test.
4) Ability: Range from 1 to endless but normally between 1 and 100.
5) Difficulty: Range from 1 to endless but normally between 1 and 100. The difficulty levels are defined as:
10 => ludicrous
20 => very easy
30 => easy
40 => normal
50 => challenging
60 => ambitious
70 => difficult
80 => very difficult
90 => improbably
100 => impossible
Example:
Bill, 6 year old boy, just learned to ride his bycicle without training wheels on a flat street in front of his parents house. Due to practice his ability 'Bicycle' values 28. He can invest max 2 Karmapoints for that specific action. The difficulty of riding your bike on flat ground is 20, so very easy. Since Bill has enough time and the street is traffic free, the chaos level (unknown variables) stays on a normal level: 2D6.
Now Bill decide not to invest any karma, he is quite sure that he will succeed and dices the chaos: [1],62 = 9. The difficulty level reduces by 9 to his actual difficulty of 11. The difficulty is subtracted from his ability: 28  11 = 17 points left. He rides all day on the street, feeling happy.
Theory:
In a deterministic universe Bill would manage the situation all times, because his ability (28) is 8 points higher than the difficulty (20) of the action. Since a deterministic universe does not exist, at least not in the universe Bill is living, there is a chance that Bill fails his action in the same setting. In this setting, what are the odds that Bill will not succeed?
The probability that the chaos increases the difficulty is 50% (46 on the poling dice). The probability that the sum of the chaos throw is _at least_ 9 points (or higher) is according to the function h(x,w) = (1/6w)^((x/6)−(w/6)) = 27.6%. Hence the prob of failure is 27.6% * 50% = 13.8%. So in 1 out of 10 cases Bill will fail. If he invest karma he can improve his chance of success.
Contrast:
Now lets assume we would use a conventional dicemechanic on ability + difficulty with a D100. The acceptance space is on the lower range of the cutoff value. The difficulty of 20 now translates to 20 (20 to the D100 roll). This is so, because a difficulty of 40 is considered as normal (see table above) and no modification +0 is applied. Bills ability remain 28. Now he would have to roll the dice and subtract the difficulty (20). Effectively, if Bill rolls 1 to 48 he succeed. But in 5 out of 10 cases Bill will be not able to steer his bike on flat ground. Additionally we could not infer to the goodness of test, because the odds for each point on the dice scale (1 to 100) is 1%.
This is in my opinion the big bias in conventional dicemechanics. This can, as I showed, be overcome while treating the random element as a _modifier_ to the abilitydifficulty equation  and not as a _decider_ on the cutoff value.
It is arguable that how I translated the difficulty in the Contrast section. I could also have tried to construct a difficult number that would have matched exactly the 13.8% (14%) odd of failure. This difficulty level would have been 58. In this constructed translation the range of acceptance would have been 186.
If one reflect upon this, it springs to mind that the ability and dificulty scale is not synchron in the contrast case, but very synchron in our example case. The reason why is that in the contrast case difficulty means "to modify the cutoff value", while in the example case difficulty means "to provide a cradle". It seems to be the same, but it is not! In the first case the dice decide, while having the full range of randomness available (1100)! In the second case the ability of the person decide!
Now one more example to clarify the just said:
Bill is riding his bicicle together with Jill, his mother. She has a bicicle ability of 58. Now both are riding through the woods and enjoy their time. Suddenly they come to a declining hill and on their way are stones and soft chuckholes. Both have to make a test in order to get to the bottom of the hill. The difficulty in this setting increases to 40, because its still a normal, doable situation rider. For reasons of clarity of this example both do not invest karma points. The chaos does not increase and stays on 2D6. For Jill the chaos roll shows: [4],2 = +6, resulting in a difficulty of 46. For Bill the roll shows [1],63 = 10, thus his difficulty drops luckily to 30. While Jill manages the situation (12 success points), Bill missed the test (by 2 failure points).
Theory:
The odds to miss the test was for:
Jill (+19 points advantage) : = 4.4% (That is the prob that the difficulty will rise over Jills ability)
Bill (12 points disadvantage): = 13% = 100%13% = 87% (That is the prob that the difficulty will not lower under Bills ability)
The odds missing the test would have changed if the chaos level were set to 3D6 (for which there could be reason, e.g. time pressure):
Jill: 16%
Bill: 32% = 100%32% = 68%
Contrast:
Anyway, applying the before said rules to map this situation onto a conventional dicemechanic. The difficulty is normal thus we don't apply a modificator.
Jill: 58, means in 42% of her trials she would miss the test.
Bill: 28, means in 72% of his trials he would miss the test.
You see, the first dicemechanic restricts the random element to a range, where deviation will probably occur. Additionally providing a tool to scale this deviation range. And difficulty means not the same for Bill and Jill, since they are on different sides of the difficulty level.
The conventional dice mechanic on the other hand maps a big weight to the random element  it is not restricted.
Okay, this is a load of information, and it took me a long way, to fuzzle that out. If one does not understand why I put a 100% into the equation for Bill, but not for Jill: It's the same like the alpha and beta error in statistical testing! Jill's ability was bigger than the difficulty hence she was only affected in 4.4% of the possible deviation. Bill was below the difficulty so the 13% was the prob that the difficulty would drop under his ability. so in all other cases Bill would have missed the test.
If the the ability and difficulty are exact equal the alpha and beta error are both 50%, so it is equal probable that you miss or pass the test.
Once again, this crazy stuff here is to design the dicemechanics only! The presentation for the player have to be straight and easy (keep it simple & stupid).
And it is not
Cheers,
Phil
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microphil
Member
Posts: 8
Re: The oddness of dices
«
Reply #8 on:
October 22, 2009, 10:29:44 AM »
Sorry!
Rule 3)b) should read: 13: Subtract; 46: Add
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JoyWriter
Member
Posts: 469
also known as Josh W
Re: The oddness of dices
«
Reply #9 on:
October 22, 2009, 04:00:21 PM »
Have you ever seen a
fudge dice
? What you've largely referred to here is adjusting the standard deviation of a result:
Skill = 30 +/ random factor
Now if that is what you want to do, then fudge dice provide that bell curve you are looking for via a
random walk
approach, just roll more dice for a better approximation. A game that uses them can be found
here
.
But I warn you, I have used them, and they do not solve all problems!
People have differences in preference that go deeper than their fondness for different dice mechanics.
But leaving that aside, I recommend you do not try to make a game for everyone, but for the people you know; perhaps a system using the dice you have suggested or the fudge dice will suit the people you play with, and if so, brilliant!
I was wondering your reason for rolling for "effort"; seen as you already showed your preference for the normal distribution, why not make effort a flat bonus? Or a flat addition that means you also roll more chaos dice? That way the dice are always rolled for the same purpose; adjusting the standard deviation.
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