A new resoultion system

[codeman123]

I came up with this idea last night when tinkering around for my new campaign. This idea was based on the all d6 method and thought that i might be cool for ability tests based off the charcters attribute they have the following chances on a d6 of being successful in a task.

3-9 1/6
10-12 2/6
13-14 3/6
15-16 4/6
17-18 5/6

what do you think?

[coffee]

That could work. But the first thing I think of is modifiers.

How about this:

3-8 ...... 1/6
9-12 .... 2/6
13-17 ... 3/6
18 ........ 4/6

That way, you can reward a good plan (or good implementation of a plan) with a +1 and still not go over 5/6. And it still rewards the 18.

[thegreyelf]

Or go with 2d6, which gives you a larger distribution of results AND an average of 7. Use target numbers instead of probability.

So:
3-8 - 9
9-12 - 7
13-17 - 5
18 - 3

[Arminath]

Why not use d12 instead of 2d6? With an average of 6.5 per roll, it maps out nicely with the 1-2 on d6 chance most games I've played in use.

3-4 - 1/12
5-8 - 2/12
9-12 - 4/12
13-16 - 6/12
17-18 - 8/12

[Deleted]

Not the OP but ...

Using two (or more) dice summed gives you the ability to weight results as you desire, whereas as a single die gives a linear probability. HTH.

[thegreyelf]

What dubeers said

[aldarron]

To answer, I like the idea okay. I like the consistency you are trying to get with the find secret doors, etc. old school use of 1d6, but any of these methods that use the ability scores to generate some table that then is diced against is adding a second and unnecessary step - one more thing to remember and or look up. I find it easier, more direct, and just plain simpler to roll against the scores themselves instead of trying to use them to generate some secondary table. Each to his own though, of course.

[Arminath]

Usually I just us the 1-4 on a d12 indicating chance of success, instead of 1-2 on d6. Same percentage chance of success, only 1 dice roll, but allows more modifiers.

I'm no math nut, so weighing probabilities and manipulating the chances by using more dice of smaller amounts doesn't appeal to me. I just use modifiers.

[Deleted]

Oct 20, 2009 15:06:09 GMT -6 Arminath said:

I'm no math nut, so weighing probabilities and manipulating the chances by using more dice of smaller amounts doesn't appeal to me. I just use modifiers.

You don't have to be. Summing two or more dice weights probabilities toward the middle of the range. To take a well known example, rolling and summing 3d6 gives a higher probability of generating an average result of 10 or 11 as opposed to an extreme result of 3 or 18.

Linear probability gives you an equal chance of any result. Roll a 1d6 and you have an equal probability of any result of 1-6.

Bell curves, to slightly simplify the math, weight results toward the middle of your desired range.

[thegreyelf]

Or to put it more simply, there is no true average score on 1d12. Any average number you draw from that is false, because every time you roll a d12, you have exactly a 1 in 12 chance of getting any given result. Your chances of getting 1, 7, or 12 are all identical.

On 2d6, however, you have a FAR greater chance of gaining 7 than you do of 2 or 12.

[isomage]

Oct 20, 2009 20:28:05 GMT -6 thegreyelf said:

Or to put it more simply, there is no true average score on 1d12.

The average is 6.5. If you mean that you can't ever roll equal to the average, then that's true for an even-sided die, but there definitely is an average (more precisely, the "expected value", or mean, which is basically a long-run average and is equal to the average of all the values on the die, so is commonly just called the average).

[thegreyelf]

No, I mean there's no average. If you roll a d12 twelve times, you will not come up with 6.5 as an average. You will not roll each number once. Every time you roll a d12 you have exactly a 1-in-12 chance of getting any given result. You will not roll 6 or 7 more often than you roll 1 or 12.

The probability changes significantly when you roll 2d6 and you have a much greater chance of rolling 6-7 on that method--it's a true average.

[isomage]

"Average" doesn't mean "most likely to occur" or "most frequently occurring".

If you roll a d12 twelve times, you will not come up with 6.5 as an average. You will not roll each number once.

Well, you might, but there's no guarantee -- the guarantee is that in the limit as the number of rolls goes to infinity, the frequency of each outcome goes to 1/12. The mean is a long-run average.

The probability changes significantly when you roll 2d6 and you have a much greater chance of rolling 6-7 on that method--it's a true average.

The average for 2d6 is 7. If you roll 2d6 eleven (or thirty-six, or whatever) times, you will not necessarily come up with 7 as an average -- again, it's only a long-run average that will be obtained as the number of rolls goes to infinity.

[isomage]

You may be thinking of the mode, not the mean. For a given set of rolls, the mode is the value that was obtained the most often. For a distribution, it is the value which is most likely to occur.

The mean of a particular set of rolls is just the arithmetic average -- the sum of all the values obtained divided by the number of rolls. For any finite set of rolls, this value will not necessarily equal the mean of the distribution, which is the "expected value" referred to above, the long-run average.

So if you roll 2d6 three times and get 6, 5, 6, the mode is 6 and the mean is (6 + 5 + 6) / 3 = 5.666... The mode and mean of 2d6 in general, however, are both 7. The mean is what people usually refer to when they speak of the "average" of something like Nd6 (although the mode and mean, along with a number of other quantities, are all informally referred to as "averages").

[thegreyelf]

There is no "expected value" on a single die, as there can be no weighting of probability given that every single time you roll that die, the probability resets to its base: each result has a 1:x chance of showing, where x is the number of sides on the die. Therefore, you cannot reliably expect to roll any number more often than any other.

On 2 dice, however, there is indeed an "expected value," given that the probability weights heavily towards the middle range since there are more number combinations that, when added, give that middle range than any other result.

I have someone with a doctorate in statistics coming to explain this shortly...he's lurked here for awhile but rarely (if ever?) posts.

[isomage]

Nov 4, 2009 13:34:02 GMT -6 thegreyelf said:

There is no "expected value" on a single die ... you cannot reliably expect to roll any number more often than any other.

"Expected value" doesn't mean what you're interpreting it to mean. From the link I gave earlier:

'The term "expected value" can be misleading. It must not be confused with the "most probable value." The expected value is in general not a typical value that the random variable can take on. It is often helpful to interpret the expected value of a random variable as the long-run average value of the variable over many independent repetitions of an experiment.'

I have someone with a doctorate in statistics coming to explain this shortly...he's lurked here for awhile but rarely (if ever?) posts.

He should confirm what I'm saying

[thegreyelf]

So you are arguing for the sake of arguing, then? The question is why people would use 2d6 instead of 1d12. I answered that, and you're making an argument out of a nitpick.

[isomage]

I only posted to correct some misinformation; the argument was entirely unexpected. Has your statistician friend explained everything to your satisfaction?

[Deleted]

Ok,

I read this all and hopefully I can provide a solution.

I am Tim, Jason's friend. When not playing games I write and teach stats.

In a sense you are both correct, you are just not talking about the same things.

On a 1d12 there is an "average". That is to say there is a mean and that mean is 6.5.
On a 1d12 every number has the same chance of being rolled (1 in 12), but the one number you can never roll is 6.5.

On a d26 we have a similar range (2 - 12) of outcomes. We have an "Average" of 7. That is the mean, median and mode. In this case 7 is the most likely outcome.

Personally, I'd never use the tem "expected value" in this context. It is too ripe for misunderstanding and expected values work best with large ranges. Best just to stick to means and probable outcomes here.
The expected value of a 1d6 is 3.5, but it is not a probable outcome. It also doesn't have anything to do with "3" or "4" as outcomes either.

Hope that helps.

Tim

[isomage]

Yep, that's exactly what I was saying.

Personally, I'd never use the tem "expected value" in this context. It is too ripe for misunderstanding

Yeah, it was a tradeoff between that and being precise -- I was careful to explain several times that it was a long-run average and not a most probable value, but it was the very idea of an average in that situation which was being denied. I suspect the source of thegreyelf's confusion may have been a misapprehension that an average value must be more likely to be rolled than other values (his reasoning for there being no average was that all outcomes were equally likely).

Anyway, thanks for weighing in -- hopefully that will have cleared everything up

[thegreyelf]

Nov 5, 2009 14:20:51 GMT -6 isomage said:

Yep, that's exactly what I was saying.

No, it's really not...but whatever. It's honestly not worth going on about at this point...all that the discussion has done is further confuse the person who only wanted to know why people would choose 2d6 over 1d12.

[isomage]

Nov 5, 2009 14:35:36 GMT -6 thegreyelf said:

Nov 5, 2009 14:20:51 GMT -6 isomage said:

Yep, that's exactly what I was saying.

No, it's really not...but whatever.

If you believe I said anything which was contradicted by Web Warlock's post, I invite you to quote it and demonstrate.

all that the discussion has done is further confuse the person

I apologize if I'm being overly pedantic here, but I think that correct information is important and less confusing in the long run than incorrect information. The OP (or anyone else) is free to disregard our digression, but at least he also has the option of getting accurate information if he wishes.

[waysoftheearth]

Getting back to the subject of the thread...

Oct 5, 2009 19:57:37 GMT -6 thegreyelf said:

Or go with 2d6, which gives you a larger distribution of results AND an average of 7. Use target numbers instead of probability.

So:
3-8 - 9
9-12 - 7
13-17 - 5
18 - 3

An interesting point which I don't think has been raised yet, is that if you choose to use a 2d6 to resolve stuff and you choose target numbers determined by ability scores (something similar to thegreyelf's suggestion, above) then you are actually combining two weighted distributions for the one result; the first is your ability score roll (3d6), and the second is your resolution roll (2d6).

When considering a system for wide use (across many PCs and scenarios in a campaign), this approach would strongly favour middle of the road results.

[thegreyelf]

Absolutely, which is the entire reason why a lot of designers these days favor multi-dice systems; the curve makes exceptional results...exceptional.

[aldarron]

Nov 6, 2009 6:40:56 GMT -6 thegreyelf said:

Absolutely, which is the entire reason why a lot of designers these days favor multi-dice systems; the curve makes exceptional results...exceptional.

While such systems don't make rolling dice entirely pointless, they can come close. A usual argument against rolling dice to check success or failure of a common or fairly easy task - like say running up a stairway - is that if the results are more or less gauranteed, rolling the dice just slows down the game. But if you are using a highly weighted system, you are doing much the same thing, I think. Whereas using a completely random probability, puts the game back in the hands of fate and makes the dice more meaningful. I'm not saying its wrong to use multiple dice, but I am saying the predictability can make rolling less meaningful in a gaming sense.

[thegreyelf]

Or far more meaningful, when you achieve extraordinary results. It's all a matter of perspective.

[Deleted]

Nov 6, 2009 11:23:24 GMT -6 aldarron said:

I'm not saying its wrong to use multiple dice, but I am saying the predictability can make rolling less meaningful in a gaming sense.

It is best, perhaps, to remember the dice are tools and to "always use the correct tool for the job."

Linear probabilities are great if complete randomization is desired. As has been pointed out, one can make certain outcomes more likely by simply adjusting the range.

1 = north, 2 = south, 3 = west, 4-6 = east, for example.

Simply speaking, bell curve probabilities are just a different way of weighting the results of the die roll. Again, going back to character generation to use as an example. Most humans will be average in their stats, with some variation up or down and even some extreme results. Thus, we roll 3d6 to make average outcomes likely, with some individual variation also quite likely.

If I touched off a storm by my initial post in this thread, I apologize. I was merely offering a way to use the tools of the game in a way that my prove beneficial to the harried referee and the campaign milieu.

As always, one should use whatever method with which one is comfortable. Or, perhaps you could try the suggested alternate and see how you like it. You can always go back to your preferred method!

Run you world your way! ;D

[thegreyelf]

I don't think you touched off a storm, dubeers. It opened the door to an interesting discussion about the merits of bell curve vs. flat probability (albeit with a side track to debate--of all things--the common usage of the word "average"). But it was far from a storm.