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I like mechanics that allow for very remote possibilities but exploding dice don't do it for me. I want to do one toss and be done.

This system uses a fixed 3d20 dice pool.

The variable is the target number to meet or beat.

Number of successes determines degree of success: 1(marginal) to 3(complete).

Abilities are rated from -3 to +3. This is to be analogous to deviation points from a mean. The relevant ability score is applied to each die in the pool.

This is the core. I like the way it rolls so far but probability math hurts my brain :(

Simple multiplication says rolling 3 20s is 1/8000. That I like. Any analysis or criticism beyond that would be much appreciated.

Also, the system is called "Triquetra" because, damnit every system needs a name.

Hi Chris,

Here are the probabilities (as percentages) for all the possible outcomes.

Probability of no successes is 100% minus the percentage in the "1 or more successes" column.

The effect of an ability is identical to shifting the target number by the opposite amount. So, for example, for target number of 10 with an ability of +3, use the target number 7 row.

Target    exactly 1  exactly 2  exactly 3  1 or more  2 or more
Number    success    successes  successes  successes  successes

21+         0.00%      0.00%      0.00%      0.00%      0.00%
20         13.54%      0.71%      0.01%     14.26%      0.73%
19         24.30%      2.70%      0.10%     27.10%      2.80%
18         32.51%      5.74%      0.34%     38.59%      6.08%
17         38.40%      9.60%      0.80%     48.80%     10.40%
16         42.19%     14.06%      1.56%     57.81%     15.62%
15         44.10%     18.90%      2.70%     65.70%     21.60%
14         44.36%     23.89%      4.29%     72.54%     28.17%
13         43.20%     28.80%      6.40%     78.40%     35.20%
12         40.84%     33.41%      9.11%     83.36%     42.53%
11         37.50%     37.50%     12.50%     87.50%     50.00%
10         33.41%     40.84%     16.64%     90.89%     57.48%
9          28.80%     43.20%     21.60%     93.60%     64.80%
8          23.89%     44.36%     27.46%     95.71%     71.83%
7          18.90%     44.10%     34.30%     97.30%     78.40%
6          14.06%     42.19%     42.19%     98.44%     84.38%
5           9.60%     38.40%     51.20%     99.20%     89.60%
4           5.74%     32.51%     61.41%     99.66%     93.92%
3           2.70%     24.30%     72.90%     99.90%     97.20%
2           0.71%     13.54%     85.74%     99.99%     99.27%
1-          0.00%      0.00%    100.00%    100.00%    100.00%

Getting at least one success is pretty likely through most of the target number range, and stays above 50% until the target number goes over 16. And getting three successes stays pretty difficult through most of the range, and is below 50% until the target number goes below 6. The odds of getting three or more successes varies pretty smoothly and steadily through the range. This all looks pretty well-behaved and workable to me. However, in most situations the odds of success will be relatively insensitive to the ability. Also, at higher TNs, an increasingly large majority of all successes will be marginal ones. I would consider calling two successes (rather than three) a complete success and three an extraordinary success or something like that.

- Walt

Wow. Thanks Walt. You're the man.

You're right on the complete-extraordinary distinction. It's an easy choice, seeing it on paper.

You're also correct in that -3 to +3 is not a huge impact on outcomes. I'm toying with a skill system that grades skills from 1-3. Maybe by adding the skill grade plus the ability for a total swing of -3 to +6 it will still work.

BTW, what style of game would you guess this mechanic would fit?

Quote from: Chris BarrettBTW, what style of game would you guess this mechanic would fit?

One where PC ability doesn't matter much? Perhaps illusionary games; where player choice doesn't really matter, and one gets in the roller-coaster.

Quote from: Andrew Martin

Quote from: Chris BarrettBTW, what style of game would you guess this mechanic would fit?

One where PC ability doesn't matter much? Perhaps illusionary games; where player choice doesn't really matter, and one gets in the roller-coaster.

Eek. That worries me because it's not what I'm going for. Could you be more specific on why you feel that way?

The scope of a player's abilities gives a 9 point spread. I thought using the curve of a dice pool would make that spread even more significant than on a single die roll.

Using a roll difficulty of 11, where normal chances for a complete success would be even, player ability could make that as easy as 89.6% or as difficult as 28.2%. The swing is also much greater for an extraordinary success: 12.5%, 51.2% and 4.3% respectively.

What I liked best about the model is that player ability matters most when attempting the most difficult actions.

It may also help to know that actions requiring more specialized skills, say writing a program in C++, cannot even be attempted without a 1 in the appropriate skill. The swing in this case is +6 to -2 but there is also an ability divide there for the characters.

The feel I'm going for is S>G>N or maybe S=G>N. Do you think this mechanic is innappropriate for such a game?

I'll be outlining the skill system in a different thread, maybe it will be easier to judge with more context.

Thanks for your input.

Quote from: In my previous post IThe odds of getting three or more successes varies pretty smoothly and steadily through the range.

Sorry, that was a typo, I meant the odds of getting two or more successes vary pretty smoothly. It looks like people understood what I meant, but I wanted to clarify anyway just in case.

QuoteBTW, what style of game would you guess this mechanic would fit?

You know, the odds distribution in the "two or more successes" column looks a lot like an ordinary roll of 1d20 against a target number, but curved a little to make the behavior more reasonable at the edges and to make modifiers more significant near the center (that is, a small edge has its largest effect when the odds are closest to even, which I think makes sense). This suggests that it would work well in a system emphasizing character advancement and/or a setting where ability levels in all sorts of abilities and the relative difficulties of all sorts of challenges range between wide extremes (e.g. there are both super-salesmen who can sell almost anything to almost anyone, and super-customers who can resist almost any salesman's persuasion). The setting of the target number based on the GM's assessment of the difficulty of the challenge, and/or some kind of overall character effectiveness scores (read: experience level or hit dice) that modify the target number, would be generally more significant than the skill score. The skill score would distinguish differences between individual characters' areas of effectiveness the way certain feats and requisite bonuses do in d20. So, overall this could be d20 with a slightly altered curve and an additional degree-of-success element in the outcome, that is, the chance of getting one (marginal) or three (extraordinary) successes.

Alternatively, if GMs keep target numbers close to 11 for most situations, you have a system with a high emphasis on fortune (luck), where most rolls could go either way. Or, GMs could keep target numbers close to 11 but call for rolls only when the odds are close, otherwise declaring longshots automatic failures and near-sure-thing situations automatic successes. That would be a crunchier version of a Karma-Fortune mix sometimes seen in freeform play: "if one side has a clear advantage, that side wins, otherwise flip a coin." However, this is almost the opposite of what you started out saying you wanted, "mechanics that allow for very remote possibilities."

For a well-behaved roll with long "tails" of remote chances for success and failure at the extremes, consider using a variable sized dice pool where lots of dice mean either a very long longshot or a very close-to-sure sure thing. Most dice pool mechanisms give you one or the other extreme but not both, but there are various ways to make them symmetrical by reading the dice differently if the net situational advantage score is negative. For instance, you can roll a number of dice equal to the absolute value of the advantage/disadvantage score, but take the highest die (or dice) if it's an advantage and the lowest if it's a disadvantage.

Or, you can try this Symmetry variant: roll one d12, and an additional d10 for each point of net situational advantage or disadvantage. Any roll of 7 or higher means success if there's a net advantage, but means failure if there's a net disadvantage. (If no net advantage or disadvantage, roll just the d12 and 7 or higher succeeds.) Each two points of net advantage or disadvantage makes the challenge about twice as easy or difficult. Rolling at -10, for example, gives a 2.8% chance of success; at -20 it's a 0.08% chance, or about 1 in 1200. (There are no edges, so you can roll at -100 if you want, for a 1 in 3 quadrillion chance, but you'd need a lot of d10s!)

- Walt

Thanks Walt. I really appreciate your insight here. You're like Neo seeing the matrix :)

The thing about varying numbers of dice though, is that it adds another layer of complexity. There's something to be said, I think, for the simplicity of using a single 3 dice toss for everything. Maybe I'm just trying to have it both ways.

Still, you've definitely illuminated some problems.

What about this: instead of partial successes and adding the skill level to the rolls, what if skill level determined the number of successes you needed.

In this case skills would be graded from 3 to 1. A skill of 3 meant you needed 3 successes while a skill of 1 meant you needed only 1.

This allows for very remote failures at the low end for the highly skilled and very remote successes at the top end for newbies.

What do you think?

Quote from: ChrisThe thing about varying numbers of dice though, is that it adds another layer of complexity.

Not necessarily, if the number of dice is the only thing that varies -- that is, all factors that might have modified the target number modify the number of dice instead, and the target number is fixed. Fixed number of dice, variable TN is about the same complexity as fixed TN, variable number of dice. (But, of course, variable number of dice might be undesirable for other reasons, such as needing more dice and more room to roll them.) It's when you vary both (like in Storyteller) that situational judgments take a jump in complexity.

QuoteWhat about this: instead of partial successes and adding the skill level to the rolls, what if skill level determined the number of successes you needed.

In this case skills would be graded from 3 to 1. A skill of 3 meant you needed 3 successes while a skill of 1 meant you needed only 1.

This allows for very remote failures at the low end for the highly skilled and very remote successes at the top end for newbies.

This could work for you. You can see in the table how the probabilities go. Each increment in skill level would be enormously important. For a skill of 3 (poor skill), only the lowest target numbers give a likelihood of success -- target numbers that would make it practically a sure thing for another character present with the same skill at 2 or 1. Likewise, a difficulty high enough to challenge a skill 1 (high skill) would be a longshot for another character with the same skill at 2 or 3. So, consider how numerous, varied, and specific skills will be in your system. For instance, if combat resolution is based on a single "combat" skill that everyone has (or equivalently, on a weapon skill for each character's weapon(s) of choice), then combats will tend to be either exactly evenly matched or one-sided. Similarly, a "secondary" weapon skill that's one less than a character's main skill would only be useful when the character was forced to use it. And if two characters in a party both have the same skill at unequal levels, the one with the lesser skill level might as well not bother.

On the other hand, if there are no general combat or weapon skills (replaced, perhaps, with very specific situational skills like "fend off bear attack" where even a small chance of succeeding is better than none) and little use of opposed rolls, the large granularity of the skill levels might not be an issue.

Whether these characteristics of the mechanism are problems (or, for that matter, benefits) can only be judged in the context of your overall game design and its goals.

- Walt

Someone on another forum pointed out that 1-20 diffuculty range might be hard on the GM and likewise players might prefer more range for their skills. Do you agree?

It sounds reasonable to me. What if it was the skills that went 20-1 and the difficulty was 1-3; is that a better model?

There is also an issue that lower number = better skill is counter-intuitive for some people. I could go the other way and make it roll-under, but for me personally, I like high numbers = success so there's a problem either way I guess.

QuoteSomeone on another forum pointed out that 1-20 diffuculty range might be hard on the GM and likewise players might prefer more range for their skills. Do you agree?

It sounds reasonable to me. What if it was the skills that went 20-1 and the difficulty was 1-3; is that a better model?

I agree that some players and GMs will have such preferences. My own preferences aren't really useful data here, but if you want to know, as a GM I'd probably wish for more control over difficulty levels, so I'd end up using modifiers to players' effective skills to adjust the difficulty. Which would work but lose the simplicity.

QuoteThere is also an issue that lower number = better skill is counter-intuitive for some people. I could go the other way and make it roll-under, but for me personally, I like high numbers = success so there's a problem either way I guess.

Yup. However, you could have higher skill = better = higher target number, and count the rolls over the TN, then you'd be counting setbacks or complications instead of successes. Add that count to the difficulty, and if it equals or exceeds 4, you fail. But that's a lot of inelegance to add just for the privilege of rolling over instead of under.

Chris, as much as I love discussing this kind of nuts and bolts, I have to change tack here. This dialog started out on a reasonable "does this mechanism behave the way I think it behaves?" level. But it's now descended to "how do people on message boards think my system's resolution mechanism ought to behave?" That's not going to get you anywhere. You have to know what you want for this kind of discussion to be productive. Design by Internet consensus doesn't work, not even at the Forge. No offense, I'm not saying that because I don't want to help, but because that's the most helpful advice I can give at this point.

- Walt