Reconsidering Task Resolution

Okay, I don’t think I’ve posted on task resolution here beyond an expectation of being similar to Revised System Reference Document (RSRD) task resolution, but a post today on google+ got me thinking.

That thinking was that I am not happy with how the skill system was working out.  The shape of it is lovely (skill-related talents let you do things unskilled or lesser-skilled characters can’t), but the numbers really weren’t working in my favor because characters several tiers apart really didn’t face check DCs all that far apart because the DCs were based almost entirely on Level Bonus.  A Epic character (level 25..28) has a level bonus of +2..+4.  A Basic character has a Level Bonus of +12..+14.  Even without training the Basic character might actually be capable of succeeding at an Epic-tier task, assuming it doesn’t need specific training.

This doesn’t suit me well.  I am entirely okay with the idea of Falling off the RNG, as long as it is done at different levels.  That is, at any particular level I want everyone to be on the RNG, but between tiers it is quite acceptable to not have even a credible chance of success.

Potential Task Resolution Mechanic

I think rather than doing something d20-based as I had originally expected, I’d like to explore the possibility of using 3d6.  This provides something of a bell curve and magnifies smaller bonuses.  It also allows me to consider something like Dragon Age’s Dragon Die, an off-colored die that can be used for additional effect.

Roll % Chance % At Least
3 0.46 100.00
4 1.39 99.54
5 2.78 98.15
6 4.63 95.37
7 6.94 90.74
8 9.72 83.80
9 11.57 74.07
10 12.50 62.50
11 12.50 50.00
12 11.57 37.50
13 9.72 25.93
14 6.94 16.20
15 4.63 9.26
16 2.78 4.63
17 1.39 1.85
18 0.46 0.46

Rolling 3d6 has a mean value of 10.5.  Rolling 11 or higher happens 50% of the time, and this seems like a pretty decent default behavior.

Since a character has a Level Bonus of Level/2, each tier will see Level Bonuses equal to 2*(tier-1)+1, plus or minus one.  Through the magic of magic and probability this leads to a reasonably-looking check DC of 10+tier*2.

That is, a task with a DC of that value will be successful 50% of the time for a character at tier levels 2 and 3, where he will spend most of his time.  The untrained character can expect to succeed at tasks of this difficulty when he rolls 11+ on 3d6, or half the time.  If he is lower level than that (first level in the tier) he will be at a slight disadvantage (Level Bonus one lower) to this expectation, meaning he will have to roll 12 or better (37.5% chance).  Similarly, a character at the top of the tier will have a Level Bonus one point higher and will succeed on 10+, or 62.5% of the time.

This is a significant difference, and the differences slow as you get to even higher or lower levels.  Four levels difference (one whole tier) is about 24% difference in success rates, Eight levels difference (two whole tiers) is almost 41% difference.

This means that if a challenge is ‘suitable for your tier’ then in the absence of other modifiers you have about a 50% chance of succeeding, varying by 12.5% either way based on your level.

That looks okay so far.

Skills and Trained Abilities

I originally planned to have skill training provide a +4 bonus to checks, and typically better results possible (such as a trained smith being able to craft masterwork items, while an untrained smith simply cannot because he lacks the knowledge required).  This would have been a 20% improvement in success rates.  A +4 bonus on 3d6 is much larger, closer to 40% when success is pegged at 11+ on 3d6 (from 50% to 90.74%).  A +2 bonus is much more in line with the originally-intended effect.

Similarly, I considered giving another +4 at Master tier training, which would be a 40% difference.  When you need 11+ on 3d6, +8 amounts to 50% difference… which is to say, cannot fail.  This might be a little too good (I have considered Master tier granting Skill Mastery, which allows you to always Take 10… which would likely mean always succeeding on same-tier challenges).  Reducing this from +8 to +4 keeps the dice relevant, even for higher-tier tasks.  You would still succeed some 90.74% of the time, but that’s not the same as always.

Rather than the 10% difference made by a two-point difference in Level Bonus in a d20-based model as you move from tier to tier, you can quickly find yourself out of your weight class as you start running up against challenges from higher tiers, without making it absolutely impossible.  Challenges below your tier become similarly easier.

Combine that with the rule that if you have a related talent at a tier higher than the challenge (such as an Expert smith crafting an RSRD-masterwork sword) you don’t have to roll the check and you can greatly reduce the number of rolls needed.  If you want to craft an Expert-quality sword you must have at least Expert-tier smithing (Basic doesn’t do it) and you need to roll (succeeding about 75% of the time), while a Heroic smith will simply succeed.  In other words, just roll when it might actually be interesting.  Then again, if there is a Dragon Die or other means of critical success you may still want to roll.

Combat

This is where things get a little bigger.  I had originally expected to use two talents in tandem to model D&D 3.x Base Attack Bonus.  Each increases the Martial Training Bonus, which goes into your armor class and attack bonus, up to a total of two points per tier.  That all looked like it was going to work well, and it still will if I stick to a d20-based model for combat resolution.  I may or may not still do that.

If I were go to a 3d6-based model as with skills, it would be necessary to halve the Training Bonus.  At first I didn’t like this because it reduces an important character ability to a single talent.  That could be done, but it’s not right for me.

I think splitting the benefits up will work.  I could have one that is strictly offense (+1 to attack rolls per tier) and one that is defense (+1 to defense rolls per tier), each granting an ability at each tier that is actually interesting, but what if they alternated offense and defense in opposite tiers.  That is, Warrior Born provides a +1 bonus to offense at Basic, +1 to defense at Expert, +2 to offense at Heroic, +2 to defense at Master, +3 to offense at Champion, and +3 to defense at Legendary, while Martial Training does the same but starts with defense rather than offense (defense, offense, defense, offense, defense, offense).

A character who takes both at each tier will have +1 per tier to both, but unlike the model that splits them on offense and defense you can have a slight difference but can’t fully neglect one or the other.

This means also that even without the supplementary abilities there is a mechanical difference between Warrior Born and Martial Training, and that appeals to me.  It only comes up with a character doesn’t keep them at the same tier, but that’s okay.

Shields and Armor

Obviously armor cannot add to the target value needed to hit a character.  Full plate granting +8 makes a character more or less unhittable at the same tier, and I think I don’t want armor to be quite that good.  I think it would be best to make armor damage reduction instead.  I think I might keep shields as ‘active defense’ that makes it less likely that you are hit, since you can deliberately apply them.  This is likely to still be a +1 or +2 bonus depending on the size of the shield.  Natural armor still acts as armor that cannot be removed and does not stack.

Saving Throws

Clearly these would need to change from +2 per tier to +1 per tier.  Otherwise I don’t know that they need to change.

Other Thoughts

A few things to think about relating to this.

Training

Perhaps rather than a flat +2 bonus to Skill checks for Basic training, going up to +4 at Master, a straight +1 per tier would be better.  Expert characters (where PCs start) are at +2 in their tier-equivalent talents, Master are still +4, and the higher the tier the more you get.  When you get to the eighth tier (that is, the one above epic) you cannot fail at tier-appropriate checks and thus don’t need to roll for simple success (but might still want to for special effect).

Eh, BECMI eventually allowed you to hit on rolls less than 1 (less than 0, the amount you could be below zero became a bonus to damage — if you could hit on -4, you got +4 to damage).  If you can do it, sure, why not?

Hit Points

Hit point calculation will likely have to change again, in part because the Martial Training Bonus and base hit point modifier for the Great Fortitude talent will change, but also because of the increased damage reduction for armor.  These might more or less cancel out, though, I’ll have to see.

Spell Casting

I’m not sure what to do about magic.  I may keep the Caster Training Bonus mechanic as I have it, so it controls the maximum castable spell level and the number of magic points.  Or I might do something else, replacing the spells as written with a different range going from 1 (probably cantrips) through six (Legendary spells) that are granted strictly by talents similar to the Eldritch Thread talents.  I don’t actually roll using the Caster Training Bonus right now so it doesn’t harm anything to leave it as it is.

Or maybe change to a different magic system entirely, perhaps something like Green Ronin’s Black Company or Thieves’ World setting, where you can have to roll to cast spells and there can be distinct tiers of casting ability.

I wonder if I can find a split in magic, so there are two parts as there are with martial ability, then have two talents interact to calculate up-to-tier-value bonuses.

Lots of possibilities here.

Criticals and Special Results

Dragon Age uses a ‘Dragon Die’, a die of a different color that will be applied when at least one pair of doubles are rolled.

Rolling triples with 3d6 can happen six ways out of the 216 possible rolls – 1/36 chance of triples.

Rolling doubles can happen 90 ways out of the 216 possible rolls – 15/36.

Between them there is a 4/9 chance of a special result, split 15:1 between doubles and triples.  If only successful rolls are considered the overall rate of special results goes down, but the proportion of successes that are special to those that are not special will vary on the chance of success overall.

In any case, around 44% chance of special results seems really high, but if ‘special’ isn’t too big that might be okay.  This can be reduced by almost a third by requiring that the special die be part of the double (still 1/36 for triples, since that requires the special die anyway, but ignoring doubles that don’t include the special die reduces that part to 60/216), from 16/36 to just under a third (11/36).  The ratio on special to extra special will be reduced from 15:1 to 10:1.

I’m not entirely sure what to do with the special results, though.  Perhaps ‘points’ of additional effect (damage on an attack roll, for example) or add to a token pool for the talent being used… I don’t know.

I wonder what could happen if you could replace a standard die with another special die.

Or if you could replace the normal 3d6 with a comparable roll (d4+d6+d8).

Or change the dice altogether, upgrading one or more from d6s to d8s — higher chance of success, lower chance of special result, to start, just going from 3d6 to 3d8 takes you from 15/36 special and 1/36 extra special to 21/64 special and 1/64.  Going to 3d10 takes you to and 27/100 special and 1/100 extra special… but you get +6 to the mean result of the roll, meaning you can expect to succeed at some hard checks.

Modifiers

Perhaps situational modifiers could be represented by additional dice rather than further changess… to values rolled.  Rather than messing with the target numbers or the numeric modifiers to the roll, add dice.  Bad dice are rolled and the highest values removed, good dice are rolled and the lowest dice removed (or perhaps the roller can pick — I can see choosing a lower result if it means getting more doubles or triples).  I’m not sure if the special die (Dragon Die equivalent) can be removed or must remain; if you must keep it it can bring your total down and possibly result in a failure, but if you can remove it you can have a success without chance of special result.  I think I’m okay with either approach.

This might even work for things like ‘ability scores’.  A racial gift for strength might mean an additional die when muscle is involved, such as using heavy weapons or the like.  It gives a better chance of hitting and a better chance of special results (more dice means more doubles or triples likely) that could mean hitting to better effect.

Closing Comments

I think I like this.  I’ll have to give it a try, but so far it looks promising.

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2 Comments to "Reconsidering Task Resolution"

  1. David Lamb's Gravatar David Lamb
    December 1, 2012 - 9:28 am | Permalink

    I like some aspects of this very much. I’ve preferred 3D6 to 1D20 for a long time, but changing the name of your game and site sounds like a big deal! I like the aspect of tier+1 not needing a roll on crafting a tier N.

    I’m reasonably happy with a tier N-1 character having some modest chance of being able to craft a tier N result, but not so much with N+1 or N+2. I don’t have a specific suggestion yet. Maybe failures when trying a higher-tier result are the source of some forms of cursed item, which might discourage people from trying. Perhaps an Appraise check is needed to distinguish ordinary failure (which might be obvious, e.g. a Fine weapon when trying for an Exceptional one) from “cursed failure”.

    You don’t necessarily need to completely divorce armour from AC mods. 3e UA has a suggestion for splitting standard 3e AC plusses for armour into half AC and half DR, roughly, so there’s evidence some people consider it a good idea. Unfortunately it is probably too long before I would have time for an analysis.

    If you go with 3d6 will you retain critical hits (and possibly critical sucess/failure on other sorts of roll)? 16-18 is roughly 1/20. The thing with 3D6 and critical hits is that a wider threat range makes a bigger deal than on 1D20.

    I wish there were a way for me to include hypertext in these replies — I’d have linked to UA at least.

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