Using Charts In Task Resolution

[s3kt0r]

In deciding what type of dice mechanics I was looking for in my RPG, I decided the best method would be using different sided dice and progressing the size as a skill increases.  There would me no skill modifiers to TNs (in general) only a better chance at hitting them.  In a perfect world my system would work like this.

    With no skill you roll a d10 with negative modifiers, depending on attribute level. At Skill Level 1 you roll a d11, at SL 2 you roll a d12, SL 3 rolls d13 and on and on until you reach SL 10 (d20).  From there the die sizes jump by 2.  SL 11 (d22), SL 12 (d24) until you get to SL 20 (d40).

     Now, you shrewder ones will pick up on a glaring problem right away.  These die sizes don't exist and I don't think the odd sided dice could exist.  But, call me crazy, I really like the way the probabilities progress.

    The only way I could think to use them would be to place the probability of rolling the numbers (rounded to the nearest whole number)on a chart.  The chart would have Skill Levels running across the top and TNs (1-20) running down the side.  The GM would then figure out the TN like usual and then refer to the chart to find the probability of hitting that number or above on a given skill level.  The player would then roll a d100 to hit that number or below.  

      I understand this would put a little extra work on the GM, but shouldn't burden down the players any.  I'd prefer not to have to refer to a chart, but I don't think it would be a great trial to have a small chart you'd refer to, especially if it was easy to read.  

    One more thing.  Skill levels 1-10 are suppose to represent the normal human range.  Anything above would have to be reached by either racial advantages or some sort of technological improvement.  Reaching the higher skill levels will be very difficult so I don't see players reaching the "end of the charts" very quickly.  In fact, they would have to focus on one skill and one skill alone for a very long time to reach a level 20.

     So, I guess my question is, Do you think that using charts in this manner will detract from the game?  Do you see them as an unnecessary burden?  Or do you see anything else that just doesn't sit well with you?  Personally, if I could get get rid of the charts, I'd be more comfortable with it, but I can't think of another dice mechanic that gives me this kind of progression.  Can anyone think of another alternative?

[Valamir]

I'm hugely against charts, but that may well be an irrational personal bias.

But I do believe that there are odd die sizes available.  They aren't real dice they're those cylinders that you roll like rolling a #2 Pencil and can have any number of faces they want.  May be worth looking into.

[Paul Czege]

Hey,

...I can't think of another dice mechanic that gives me this kind of progression. Can anyone think of another alternative?

Ryan Keane's article, http://www.beatpeopleup.com/bmstrat.html">Dice Math, is probably worth a look. It describes how to use combinations of standard dice and renumbered blank d6's (and sometimes d10's) to create the equivalents of otherwise impossible dice.

Paul

[Mark Johnson]

Exploring Alternatives To Charts

Roll a die, any die.  If it rolls over your SL, reroll until you roll your SL or under.  I figure an SL 0 will simply roll a D10 and SL 1 and 2 will roll a D12.  Unfortunately there is a huge gap between D12 until D20, and it is conceivable that a person could reroll seven or eight times if they are particularly unlucky.  But it does give you a linear curve between 1 and your SL.

This is where the exploration comes in.  Consider ways to turn that problem into a feature.  Maybe create some sort of penalty for rerolls that are present in play (meaning with an SL 16 can play it safe with a D12 or roll a D20 and take a -1 penalty to the end result for each reroll or somesuch).  Or if they roll over the number, make it a failure, but allow some sort of bonus in future play (bonus tokens that add to successes to rolls).  It really depends what kind of play you want to encourage.

Roll Under Systems

You might want to consider looking at a simple roll under system, it may do a lot of what you want anyway.  Also take a look at a system I playing around with, MUGS (name soon to change) which allows for multiple die curves under a set limit.

Also, why start at 10?  Why not at 0 or 1, there are certainly a lot more dice readily available under 10 than over.  Worth playing around with.  

The Problem With Step Die

One last thing you need to know about any single step die system where higher = better is that characters who have higher traits have more inconsistency to their results.  In your system a character with an SL0 (roll D 10) is many  orders more consistent than an SL20 (roll D40).  

This may be something you want.  But one of the most famous step die systems out there, The Window made lower better because their players felt that highly skilled characters should be more consistent at tasks than lowly skilled ones (who might ocassionally get lucky).  

BTW MUGS is also a step die system but allows characters to roll multiple dice so that more talented characters tend to have sharper higher probablity curves toward the top of their skill spectrum.

Good Luck,
Mark

[M. J. Young]

Of course, you could use chits or cards, or include a spinner with the game that was divided for each of the dice you would have included.

A lot of the dice you want can be generated fairly closely with existing dice. Here are a few tricks you'd find in Multiverser's appendix on dice curves.

For a d16, roll a d8 and any other die; the other die is just odd/even where even means 8 plus the die roll (or 9-16) and odd means just the d8 roll (1-8).

You can use the same trick in more complicated ways to produce other dice. A d18 can be produced by using two distinct d6's, where one determines whether it's 1-6, 7-12, or 13-18. A bit more complex, you can use a d10 and a d6 to generate a d15, by using the d10 in halves. Thus a roll of 6 on the d6 would mean 10+, and then a roll of 7 on the d10 would mean (7/2 rounded up) +4, so you'd have 14.

If precision is not as important as speed, one trick I've used for rolling d13 is to roll 2 d12's that don't match. If the two dice match (one chance in 12) you treat it as 13; the extra number comes by reducing the probability of rolling any other number by one twelfth its original probability. Thus the probability of rolling 13 is 8.33%, and the probability of rolling any other number is 7.64%, which is usually close enough.

14 is tough; the quickest is probably to roll a d8 with an even numbered die, and reroll all 8's.

If you don't need linear results, there are a lot of ways to get what you want by rolling two dice and subtracting one. Thus d6+d8-1 will give you a balanced curve 1-13, but the probability is strongly toward 6-7-8 (it's a flat topped curve, explained in the aforementioned appendix). 2d8-1 will give you 1-15 with a push toward 9. d10+d8-1 gets 1-17 and 2d10-1 gets 1-19.

That may give you viable options for all possibilities, but you might find chits, cards, or spinners best.

--M. J. Young

[Jack Aidley]

I agree with the above posters regarding the mechanic.

However if you wish to press ahead, I would strongly suggest that using a electronic randomiser (i.e. a computer) is preferable to using a chart. Make sure you use a really good random number generator though (for example: a Mersenne Twister) - the default random number generators in almost all programming languages are truly awful.

[Walt Freitag]

Just to provide a dissenting point of view, I have nothing against charts myself. I used them for many many years. I've even added charts to chart-free systems when doing so would streamline otherwise awkward dice rolling mechanics.

Would I design a chart-based system today? Perhaps not. But I'd prefer a chart to either using an electronic randomizing device at the table, or having to memorize and use a whole slew of alternative dicing rules (e.g. skill of 3 means rolling "d13" which means either rolling d20 and rerolling the 35% of rolls that go over 13, or rolling a d8 with a 50-50 +8 and still rerolling 3 times out of 16).

Whether you end up using it or not, I strongly recommend creating the chart for your mechanism, just so you can examine the numbers and see whether they behave in the way you intend, relative to the variables. (For instance, does a one skill level increment make as much difference in the chance of success as you wish it to, throughout the relevant range of difficulty factors?) One nice thing about a chart is that you don't have to stay with your original generating rule. You can change the numbers in the chart however you want to get the behavior you want. If you find yourself making extensive changes, you might be able to find a different (and more practical) dicing mechanism that approximates the behavior of the modified chart, which would give you the option of getting rid of the chart in the final version.

- Walt

[Lxndr]

As a fan (still!) of Rolemaster and other games, I've definitely got nothing against charts, per se.  But it sounds as though your particular implementation would have higher handling time, as the GM has to decide something, look at a chart, etc. etc.  My experience with Rolemaster has shown that the handling time is a lot quicker if everyone has their own chart, and can look at it.

On the other hand, you've only got one chart, not the multitudes that rolemaster has.  I have to wonder if it's possible to minimize said chart and actually put it on the character sheet, thus solving my worries.

And just to make this abundantly clear, 'cause if you're using TNs in some other way this could cause issues:  the higher the TN, the harder something is, and dice have to roll TN-or-HIGHER, right?

[s3kt0r]

the higher the TN, the harder something is, and dice have to roll TN-or-HIGHER, right?

Yes, that's how it works.  Higher TNs means its more difficult and you'd have to roll that or higher if it wasn't for the intermediary step of converting it into probability, first.

As to the other comments, I'd have to agree with Walt.  I'm not really keen on using electronic randomizers or using a different dice rolling method for each skill level. Also, I've thought of cards or chits, but you would require a different bag or different deck for each skill level, meaning about 21 decks of cards.  And I'm not sure I'd want to make special cards.  

you might be able to find a different (and more practical) dicing mechanism that approximates the behavior of the modified chart, which would give you the option of getting rid of the chart in the final version.

This was my original intention and my problem.  I can't find a dicing mechanism that approximates the behavior of my chart.  These are my requirments.  Maybe someone else can find something.

1)At the lowest level, very difficult tasks will be around a 5% or lower probability.  By the time you reach an unmodified world-class level, that same task has a 50% chance of success.  At the highest, "I'm modified up to the ying yang, including my racial advantages, best in the universe" class that same task would be about 75%.

2)No diminishing returns as you progress as in dice pool systems.

3)At no point, will something that was an average task become "always possible" at higher skill levels.  There should always be a slight chance of failure, no matter the skill level, at things you one time struggled with.  And this can't be taken care of with a static critical failure, such as I always fail on a roll of 1, etc.

4)Above all, it should be a simple, near transparent mechanic, at least for the players.

I haven't been able to find a system that meets these requirements, but there's probably other dice mechanics I'm not aware of.  Am I asking for too much?

[Mike Holmes]

Just a clarification on electronic random number generation. Most times these days, rand functions are hooked up to the clock on the computer. Since these rolls are made at random intervals, any randomizer like this is just fine for anyone's purposes in play. Rand like this only really becomes problematic when doing programmed applicaitons that occur in a very regimented fashion.

Distribution is another potential problem, but few generators today are any less balanced than the dice people may use. If you can't discern the difference, then it's probably not an issue. Basically this is a technophobia issue, IMO.

Further, if that's not enough for ya, here's a tip to make it seem more like you're rolling. Have a button that you can hold down while numbers are generated. Then when the player lets go, the number that's up is their number. I use Excel for this, and just hold down the F9 (recalculate) button. Seems just like rolling.

Yeah, I wouldn't base my Mars program on it, but it's good enough for gaming.


I'm surprised that Walt didn't mention Symmetry. Would probably be perfect for this situation.

Mike

[Walt Freitag]

Am I asking for too much?

You might be. It depends on what you mean by your requirement #2, "No diminishing returns..."

The problem is, a probability of success can't go over 1.0 (100%). To progress means to get closer to that 1.0 chance of success, but to get closer and closer to a fixed number without ever reaching it (as per your requirement #3), one of two things has to be true: either you must approach the limit in small increments (and limit the number of increments that can occur), or there must be some kind of "diminishing returns" in effect.

For instance, let's look at a condensed version of the probability-of-success table for the system you've described.

Code Select Expand

Diffi-      Skill Level
culty       0     1     5     10    15    20
(TN)       d10   d11   d15   d20   d30   d40

2          .9    .909  .933  .95   .967  .975
6          .5    ,545  .667  .75   .833  .875
10         .1    .182  .4    .55   .7    .775
15          0     0    .067  .3    .533  .65
20          0     0     0    .05   .367  .525

(Note that since you said "roll [the TN] or higher" I left off the row for TN=1 which would always succeed with any size die; the minimum meaningful TN is 2.)

Consider a TN 6 task. With no skill you have a 0.5 (50%) chance of success. Add ten skill levels, and your chance goes up to .75 (75%). Ten more skill levels bring your chance to .875. Isn't this diminishing returns? The first ten skill levels increase your chance of success by a factor of 1.5, and by an absolute difference of 0.25. The next ten skill levels, despite the doubling of the die-size increment above skill level 10, increase your chance of success by only a factor of 1.17 and by an absolute difference of 0.125. Similarly, at TN=10, the biggest jump in your chance of success with increasing skill comes with the increase from no skill (skill level 0) to skill level 1. Every subsequent skill level increment increases your chance of success by a smaller factor and by a smaller absolute amount. In fact, this is true for every TN under 10 as well. And for TNs over 10, the biggest increment comes with the first skill level that brings a greater than zero chance of success, which happens when skill level reaches the TN minus 10. So diminishing returns are the rule here.

Of course, probability of success isn't the only measure of effectiveness. Suppose, for instance, that each time I drive a round trip in my car, my chance of arriving safely without an accident was .99. Would I care about the difference if the chance were increased to .9999? I might reason that it makes little difference because my chance of success would have increased by only a factor of 1.01, and by an absolute difference of less than .01. But actually, I wouldn't be looking at my chance of success incresing slightly, I'd be looking at my chance of failure decreasing by a hundredfold! At .99, driving one trip per day, I'd be almost certain (97.45% likely) to have an accident within a year. At .9999 it would take almost 20 years of daily driving to have a 50% chance of having an accident. I'd care about that difference quite a lot. The point is that relative chance of failure is just as meaningful and important a measure of effectiveness as relative chance of success.

In your system, the chance of failure at a TN=6 task at skill level 0 is .5. At skill level 10 it's .25, a decrease of a factor of .5. At skill level 20 it's .125, a decrease (relative to skill level 10) of a factor of... .5 again. Voila! No diminishing returns.

And that's how the "diminishing returns" in dice pool systems work too. Suppose you have a system of rolling a pool of d6s, and any roll of 6 indicates a success. A four-die pool gives you about a 52% chance of success. Add one die, and your chance increases to about 60%. Another die (6 total) gives you about a 66.5% chance. The twelpth die added to the pool increases your chance from about 86.5% to about 89%. It looks like diminishing returns. But actually each added die, whether the fifth, the twelfth, or the hundredth, is decreasing your chance of failure by exactly the same factor.

Your mechanics generate a reciprocal decay in the chance of failure with increasing skill (increasing die size). Dice pools usually generate an exponential decay in the chance of failure with increasing skill (increasing number of dice in the pool). The behavior is actually pretty similar.

Let's try the following mechanism, using your skill and difficulty (TN) scales. If your skill + 6 is greater than or equal to the difficulty, then roll 1d6 for every point by which your skill + 6 exceeds the difficulty. Also roll 1d10. So, if your skill is 0 and the difficulty is 8, roll 2d6 and 1d10. Any die rolling 6 or higher (that is, a 6 on any of the d6s or a 6-10 on the d10) is a success.

The probability table (probability of success) looks like this:

Code Select Expand

Diffi-      Skill Level
culty       0     1     5     10    15    20

2          .759  .799  .860  .961  .984  .994
6          .5    .583  .799  .919  .968  .987
10         .?     ?    .583  .833  .933  .973
15          ?     ?     ?    .583  .833  .933
20          ?     ?     ?     ?    .583  .833

The question marks indicate that we don't yet have a rule for what to do if skill + 6 is less than the difficulty. (A common problem with dice pools is that they clearly resolve different gradations of easy tasks but cannot do so for difficult tasks.) Here's the rule: if the skill level + 6 is less than the difficulty, roll a d6 for every point by which the difficulty exceeds the skill level + 6, along with a d10. But in this case, any roll of 6 or more now indicates failure.

Let's also get rid of the need to constantly add six to the skill level, by shifting the difficulty scale so that a difficulty of zero is defined as the difficulty at which a skill level of 0 has a .5 chance of success. Difficulties can be negative to indicate an easier than average task (and skill levels can be negative to indicate a disability, if you wish). Now the number of d6s in the pool is always the absolute value difference between the skill and the difficulty. All situational modifiers add or subtract from the difficulty (or act oppositely on the skill, it doesn't matter). If the skill and the difficulty are the same, just roll the d10 alone (and a high roll of 6-10 succeeds).

Here's the resulting probability-of-success table. You'll notice that just as the chance of success never reaches certainty no matter how much the skill exceeds the difficulty, it also never reaches zero when the difficulty exceeds the skill.

Code Select Expand

Diffi-      Skill Level
culty       0     1     5     10    15    20

-4         .759  .799  .860  .961  .984  .994
0          .5    .583  .799  .919  .968  .987
4          .241  .289  .583  .833  .933  .973
9          .097  .116  .241  .583  .833  .933
14         .039  .047  .097  .241  .583  .833

As Mike mentioned, I call this dicing mechanism (along with its many variations) Symmetry. All Symmetry variations are based on exponentially decaying chance of success on one side of a (usually 50%) dividing line and an exponentially decaying chance of failure on the other. One key variable is the decay rate, which depends on the dice used. For instance, to make each point of skill or difficulty just about twice as significant as in the above mechanism, roll a a d10 for each point of difference between skill and difficulty, along with one d6, and a roll of 1, 2, or 3 on any die represents success (if skill equals or exceeds difficulty) or failure (if skill is less than difficulty). For more variations and discussion about the rationale, see this thread. (Ironically, for most of my role playing gaming history I used the Symmetry probability curves as charts.) Along similar lines, there are systems where a larger advantage or disadvantage means more dice are rolled, and if it's a disadvantage the lowest number rolled is used, while if it's an advantage the highest number rolled is used.

- Walt

[Jack Aidley]

Distribution is another potential problem, but few generators today are any less balanced than the dice people may use. If you can't discern the difference, then it's probably not an issue. Basically this is a technophobia issue, IMO.

Yeah, you're probably right, standard rands are probably good enough. But I'd argue it's more technophilia than phobia; I developed a deep mistrust of random number generators while developing computer games.

[Mike Holmes]

I say Phobia, you say Philia, its all about how people feel about their computers. For some reason they're good for a lot of things, but for RPG aids somehow many people get turned off.

But, personally, I do so love the idea of using the natural log function for decay. Just seems so "right". :-)

Good explanation once again, Walt.

Mike

[s3kt0r]

Wow.  Thanks alot, Walt.  This is very much along the lines of what I was looking for.  

I guess what I meant by no diminishing returns is that, yes my "probability jumps" decreased over time, but I felt I was making that up by the fact each new die size opened up one or two numbers within my possible range.  But, that's not a big deal.  

My concern was in a game like Shadowrun, which uses pools of d6, I never really felt "world-class" with a skill level of 8 when next to the Mr. Skill Level of 4.  Our odds of hitting a 6 were about the same and I really didn't have a better chance at hitting the higher numbers because the difficulty of higher TNs leveled off so abruptly, epsecially at 6 and 12.  That maybe because it used exploding dice of a small size, though.  I guess I meant that I wanted high level characters to feel powerful, but I just said it in unclearly.  But, I think your system handles this nicely. The curve is alot less drastic for higher numbers.

Anyway, thanks alot.  This will help with my system or at least jog my brain in a new direction.

[Walt Freitag]

You're welcome, Sektor.

Tinkering with probability curves is all about how to allocate the influence of skill levels (or other favorable situational variables) over the finite range of possible success probabilities. This is especially challenging in systems with a lot of advancement.

Typically, if you have two starting characters, and one has a certain skill at 3 and the other at 1, you'd want and expect the skill 3 to be noticeably better than the skill 1 against a challenge appropriate for starting characters. But you also expect a skill 10 to be much better still against the same challenge. The more of an advantage the skill 3 has over the skill 1, the less room there is for the skill 10 to be much better than the skill 3. You can do this:

Skill 1: 50%
Skill 3: 60%
Skill 10: 95%

... but you won't see much difference between Skill 1 and Skill 3 for normal skill checks. (Requiring cumulative successes over multiple skill checks, as in D20 combat for example, amplifies these differences -- which is why D20 does pretty well with its linear 5% increments, at least when things are balanced so that target numbers don't stray outside the 4-17 range.) Or you can do this:

Skill 1: 50%
Skill 3: 80%
Skill 10: 95%

... but the Skill 10 isn't going to feel all that superior to the Skill 3, certainly not seven skill levels better. Or you can do this:

Skill 1: 10%
Skill 3: 20%
Skill 10: 55%

... which differentiates clearly between Skill 1 and Skill 3, and between Skill 3 and Skill 10, but which is going to make your low-level characters feel pretty ineffective.

Ultimately, this balance comes down to a matter of taste. Symmetry with the 5/6 decay rate (using d6s rolling 6 to succeed) gives you, against a difficulty or defense value of 2:

Skill 1: 42%
Skill 3: 58%
Skill 10: 90%

And with the 7/10 decay rate (using d10s rolling 1-3 to succeed) it gives you:

Skill 1: 35%
Skill 3: 65%
Skill 10: 98%

If you're casting about for ideas, I should mention one other generally useful method for mathematically well-behaved (that is, yielding reasonable distributions of outcomes in extreme as well as in routine cases) success rolls. Look into die pool rolls that are opposed by other die pool rolls. Advantageous factors such as skill level increase the size of the pool (that is, the number of dice) the player rolls, and adverse factors such as difficulty level increase the size of the opposing roll. To succeed, instead of rolling above a specific target number or rolling more than a specific number of successes, the player must roll a higher single-die maximum or more successes than the opposing roll.

- Walt