A search for an optimal resolution mechanic

Lago PARANOIA · Post by **Lago PARANOIA** » Sat Feb 25, 2012 4:25 pm

Query:

I want to implement bell curve rolling, but, say that I don't think that 3d6 produces a steep enough curve. Is there anything that I could use that would make the curve modestly more steep while still keeping the odds fairly calculable? I know that 2d10 and 3d6 fit the bill, I don't know of any others.

Username17 · Post by **Username17** » Sat Feb 25, 2012 4:39 pm

If you roll more dice, you get a steeper curve. For 2d10, an 11 comes up 10% of the time and a 20 comes up 1% of the time. For 3d6, 11 comes up 12.5% of the time and an 18 comes up about 0.46% of the time.

For 5d4, a 12 comes up 15.14% of the time and a 20 comes up less than one time in a thousand. As you roll more dice, the curve steepens and the amount of time it takes to calculate probabilities or add up dice for your curve increases.

-Username17

Lago PARANOIA · Post by **Lago PARANOIA** » Sat Feb 25, 2012 6:35 pm

Yeah, that's pretty much what I figured.

Concern 1:

I don't have anything against d20s or linear RNGs, it's just that the fact that a +1 -- as long as you're within the RNG -- is worth as much whether you're in the middle or near the ends.

The problem with this is that even if you are still within the RNG, the cruel fact is that people familiar with the game engine and min-maxxers also tend to be the best people at coming up with situational bonuses. A bell curve appealed to me because I wanted a game where Starfire (played by a newbie who can manage about an average of +10 to attack) benefits more from attacking from higher ground (a flat +1 to attack) than Beast Boy (played by a powergamer who manages an average of about +13 to attack).

Which is pretty okay, the problem is that I also want it such that dice rolls are relatively fast to determine and that people still have a general idea of how much a +1 will help them. Flatter bell curves make probability calculation easier but don't do as much for the Starfire problem. For a game with power ranges like D&D, what do you recommend?

Concern 2:

For games that have a fairly modest range of top end and low end power, dicepools are pretty much the bee's knees. It also keeps the math fairly reasonable. Call me crazy, but I'd like to avoid double-digit addition/subtraction if at all possible and if it isn't possible then to have it adjucated ahead of time.

The problem with dicepools is that you need to have automatic successes for them after a certain amount of power shifting otherwise the resolution gets to be too clunky. Except this raises the entirely sensible question of: if you're going to have automatic successes at all, why use dicepools?

Again, the question goes back to me wanting to limit arithmetic as much as possible, but then again I also suspect that picking through 14 dice to count 10 successes is harder/longer than adding 18 + 23. To me it's shorter, but I'm not sure about other people.

Hell, I'm not even sure if double-digit addition or subtraction is all that difficult for people nowadays. Human beings are more math-savvy and literate than they were 30 years ago.

John Magnum · Post by **John Magnum** » Sat Feb 25, 2012 6:43 pm

Speaking personally: Double-digit addition isn't all that hard, but double-digit subtraction is really annoying. I would much rather do 18 + 23 than pick through a dozen dice.

However, I also do a lot of play-by-post, and it's just as easy to tell my RNG of choice to count successes for me as it is to tell my calculator to do double-digit subtraction.

Previn · Post by **Previn** » Sat Feb 25, 2012 8:10 pm

Can we hack it up?

The base check is 2d6, take the highest 2 dice, so you have a result between 2 and 12.

The DM rolls the difficulty on 2d6 as well, taking his highest 2 dice, subtracting it from your roll.

This means that you've got a range between -10 to +10 which can count as your degrees of success. Better skill, or harder checks add dice respectively. So someone with a skill 4 ends up rolling say 6d6 and taking the highest 2.

The DM does the same thing, adding dice for higher DCs. The range never changes from -10 to +10, nor can you ever cap out from dice.

I would think it would be a relatively quick resolution system from a mathematical perspective as well. It produces a nice curve, and high skill decreases variance, but the shifting DCs could be something of a hindrance.

wotmaniac · Post by **wotmaniac** » Sat Feb 25, 2012 8:49 pm

Lago PARANOIA wrote:The problem with dicepools is that you need to have automatic successes for them after a certain amount of power shifting otherwise the resolution gets to be too clunky. Except this raises the entirely sensible question of: if you're going to have automatic successes at all, why use dicepools?

The idea is to shift the baseline of what is considered "trivial". # of successes indicates the degree of success and/or degree of task difficulty -- rolling a given # of successes says how good you did it; whereas requiring a minimum # of "successes" in order to succeed at the task determines just how hard the task is.

For a baseline mortal, making a sandwich or walking across the room is considered "trivial", and therefore "auto-succeeds". However, shooting someone in the face isn't trivial, and therefore must roll.

For a low-level super, using his Dominate power isn't trivial, and therefore must roll for it. However, for a high-level super, using his Dominate power on a baseline mortal is trivial (no different, in effort, than making a sandwich); but using it on another super isn't.

Now, all this may seem rather elementary, but here's the rub -- having "auto-successes" in a die-pool game runs in to the same problem as linear RNGs do with stacking bonuses; and that is that the more you have, the more trivial the actual roll is.
Just look at Scion:
You get auto-success for your Epic Attributes. Which, in and of itself, is fine, because when you're using those abilities/powers against other scions, they have defenses that off-set those auto-successes -- thus reducing resolution down to just the roll. The problem is in the way those auto-successes scale, and the resulting power discrepancy between just 1 marginal rank in an Epic-Attribute.

A bigger problem that exists is having a game that tries to have baseline mortals and high-level supers operate on the same scale within the same game. A single game shouldn't be expected to have to facilitate having both baselines and high-level supers co-exist.
As a RL analog:
(moral quandaries aside) General McStrongforces does not give one single fuck about Joe Dirtfarmer. However, what General McStrongforces does care about (and rightfully so) is how fast the opposing general can mobilize his air support assets.
What Joe is able to do with his pitchfork is completely insignificant when compared to an artillery barrage followed by a full-frontal assault by a tank unit.
Joe and General McStrongforces are not operating on the same scale, and so shouldn't be trying to operate as if they were. Either concern yourself with Joe protecting his fields from bandits, or concern yourself with the General's strategic implementation; but you cannot do both.

Username17 · Post by **Username17** » Sat Feb 25, 2012 8:51 pm

Speed of resolution is mostly a question of how many operations are performed. Some operations are slower (subtraction is slower than addition, division is slower than multiplication, bigger numbers are slower than smaller numbers), but in the absence of crazy stupidity like taking square roots or raising numbers to variable powers it is the total number of operations that are done that determines the length of resolution time.

So if you have to determine how many dice are to be rolled, then find the highest dice, then add those dice, then determine how many dice are to be rolled in a different pile, then find the highest dice in those, then add those dice, then subtract the two results, that is seven operations. None of them are terribly difficult or time consuming individually, but remember that d20 gets by on four.

-Username17

Previn · Post by **Previn** » Sat Feb 25, 2012 9:12 pm

FrankTrollman wrote:Speed of resolution is mostly a question of how many operations are performed. Some operations are slower (subtraction is slower than addition, division is slower than multiplication, bigger numbers are slower than smaller numbers), but in the absence of crazy stupidity like taking square roots or raising numbers to variable powers it is the total number of operations that are done that determines the length of resolution time.

So if you have to determine how many dice are to be rolled, then find the highest dice, then add those dice, then determine how many dice are to be rolled in a different pile, then find the highest dice in those, then add those dice, then subtract the two results, that is seven operations. None of them are terribly difficult or time consuming individually, but remember that d20 gets by on four.

-Username17

Well, it's a lot of operations, but it's split among 2 people who can do their things at the same time, and then do a final very easy subtraction. Each person has 3 steps and the final 4/7ish step can be done by either depending on the group or DM preference.

There are also going to be times where you don't have to check all the dice, since once you have a pair of 6s, it doesn't matter if you have 4 unchecked dice or 400.

I'm not saying it's perfect, and I'm sure there are issues since it's off the top of my head, but I'm not sure resolution time is really an issue for it.

Username17 · Post by **Username17** » Sat Feb 25, 2012 10:07 pm

Well, it's a lot of operations, but it's split among 2 people who can do their things at the same time, and then do a final very easy subtraction. Each person has 3 steps and the final 4/7ish step can be done by either depending on the group or DM preference.

Not really, no. When the player is determining how many dice they roll, this is a form of bargaining with the MC. The player will want to roll move dice, and the MC will either grant or not grant their request.

While technically the actual rolling and counting could be done simultaneously, this is generally distracting and not done. Perhaps more importantly, a player rolling dice is the center of attention, and the MC ignoring them to roll dice behind the screen is incredibly rude.

Seven steps is seven steps. It's not insurmountable, but it's not fast. And it will never be fast and no matter how much lipstick you put on that pig it's still a pig. If you have 7 operations during your resolution, you'd better get something out of it. I am at a total loss as to what you're attempting to achieve with this frankly baroque setup.

-Username17

Lago PARANOIA · Post by **Lago PARANOIA** » Sat Feb 25, 2012 10:49 pm

So here comes some more questions!

Concern 3
Assume that you had the typical 3d6 + whatever die rolling mechanic. Now assume that you did Dragon Age: TTRPG's setup where one of the d6s was a 'Dragon Die' that occasionally did something special.

Could the generic increase in resolution time be traded for something that'd be worth it, gameplay-wise? What appeals to me about this setup is that even though it'd increase resolution time, it's already folded up into something you'd want to do anyway. So it seems that in the long run you'd actually be cutting down on time spent resolving actions if you did something with that Dragon Die.

Anything come to mind?

Concern 4
So. Damage rolls.

I have no idea how to make damage rolls satisfying. The closest thing I've ever seen to a system that actually makes you care about a damage roll in a way that the attack roll does not is 4E D&D. And that's some sad, sad shit right there.

The basic problem with damage rolls in my opinion is that people want them to be a lot less deterministic and swinging than attack rolls. And frankly I think that very few okay are okay with the idea of a greataxe and a dagger both doing 1d8 base damage.

But on the other hand, scaling damage rolls becomes almost impossible as things go on if you don't want to go 1d8 + 25; which pretty much no one wants to do anyway. The [W] idea was actually the best idea they ever had but it still doesn't work, because people accrue damage bonuses in an extremely asymmetrical way.

What to do?

Previn · Post by **Previn** » Sat Feb 25, 2012 11:04 pm

FrankTrollman wrote: I am at a total loss as to what you're attempting to achieve with this frankly baroque setup.

-Username17

Just trying to toss out ideas to try and keep the thread moving. In this case I was trying to get something of a cross between a dice pool and FATE dice. If they're not good I expect you guys to let me know.

tussock · Post by **tussock** » Sun Feb 26, 2012 2:30 am

@Concern 1: Careful, if you're worried about critical failure (falling off a cliff), +1 is awesome for people with high skill, but if you're worried about critical success (killing the goblin), +1 is best if you have low skill.

If all you want is DOT, you still get proportionately more out of it for low skill. Chump goes from 6 to 7 (+16% damage), while champ goes from 12 to 13 (+8% damage).

@Concern 2: If you don't want arithmetic, use roll under. Skill 13, challenge 4, so you roll over 4 and not over 13.

@Concern 3: you can't do much with a result that comes up 1/3 or 1/6 of the time. Better to do something with triples on 3d6, 1 in 36 can be crits or whatever.

@Concern 4: Scale your monsters to something in range. So if you like a top end hit to be 3d6+6, and top Fighters to have 3 attacks, the Tarrasque and other gods have about 150 hp, and Epic fighters about 70 or 80. Spells max out around area 10d6 with a save for half, or 15d6 on one target with save for 1/3.

tenuki · Post by **tenuki** » Mon Feb 27, 2012 12:08 pm

tussock wrote: @Concern 2: If you don't want arithmetic, use roll under. Skill 13, challenge 4, so you roll over 4 and not over 13.

Humm. I don't share the knee-jerk aversion towards roll-under some others have displayed in this thread, but a roll-between mechanic looks problematic to me for a TTRPG:

Challenges below 3 are meaningless on 3d6 for obvious reasons. Challenge 8 means that ANYBODY has at least a 26% chance of failure, even if their skill is 25. That does not leave you much room to play with. I could totally see your suggestion as a mechanic for a tactical boardgame where individual units don't matter that much, but in a TTRPG... dunno.

The remedy would be to give experts a way of reducing the challenge level, but that defeats the purpose of avoiding arithmetic in the first place.

shadzar · Post by **shadzar** » Mon Feb 27, 2012 12:25 pm

Lago PARANOIA wrote:Query:

I want to implement bell curve rolling, but, say that I don't think that 3d6 produces a steep enough curve. Is there anything that I could use that would make the curve modestly more steep while still keeping the odds fairly calculable? I know that 2d10 and 3d6 fit the bill, I don't know of any others.

http://www.fnordistan.com/smallroller.html graph the rolling of ANY combination of dice.

tussock · Post by **tussock** » Mon Feb 27, 2012 2:17 pm

@tenuki, yeah, I was thinking d20 (from Concern 1). With a curved probability you have to use pure roll under/over and do math.

But curves are ugly and useless anyway, 3d6 has only half the variation of d20, may as well use a 1d10 system, as it's always less than 5% difference in odds for any number, less than +-1 on d20. That stuff you think you're getting with tiny chances at the tails doesn't matter in play.

OgreBattle · Post by **OgreBattle** » Mon Feb 27, 2012 2:26 pm

what if you did d12+d8

echoVanguard · Post by **echoVanguard** » Mon Feb 27, 2012 5:42 pm

tussock wrote:@Concern 2: If you don't want arithmetic, use roll under. Skill 13, challenge 4, so you roll over 4 and not over 13.

The math on this sort of thing is decidedly non-linear. Asking the GM to compute z-score subtraction on the fly is rather unkind.

That being said, it is an interesting idea - if you were to crunch the numbers on it ahead of time and provide a table of probabilities in your source material, it could be pretty cool.

echo

tenuki · Post by **tenuki** » Tue Feb 28, 2012 12:33 am

OgreBattle wrote:what if you did d12+d8

It gives you a probability distribution that looks like a pyramid with the tip shaved off. Doable, but I don't see significant advantages over 2d10, which is slightly faster to calculate IMO.

Then again, I seriously like 2d10 and have used it for years MCing a Talislanta-based homebrew. Might just be personal preference.

Username17 · Post by **Username17** » Tue Feb 28, 2012 6:29 am

OgreBattle wrote:what if you did d12+d8

That would give you the same range as 2d10, but be much harder to culculate. Specifically, it would give you a bar of identical probabilities between 9 and 13, and then curve off slowly after that.

-Username17

tenuki · Post by **tenuki** » Tue Feb 28, 2012 10:19 am

Lago PARANOIA · Post by **Lago PARANOIA** » Fri Mar 09, 2012 4:44 am

Is there any way to approximately simulate 2d10 or d10 dicepools without actually using d10s? I really don't care for those dice, they feel unnatural and don't roll properly.

erik · Post by **erik** » Fri Mar 09, 2012 4:53 am

Roll d20's and divide by 2 rounding up (even less complicated than it sounds).

Or roll d20s and ignore the first digit.
Or get those old school d20's that had + instead of a second digit.

And... fuck, did I fall for being trolled? I read up the page on this thread and I still feel played.

spaceLem · Post by **spaceLem** » Sat Mar 10, 2012 6:27 pm

Lago PARANOIA wrote:Is there any way to approximately simulate 2d10 or d10 dicepools without actually using d10s? I really don't care for those dice, they feel unnatural and don't roll properly.

I don't know how to simulate 2d10, but you can do dicepools easy enough by having a Unisystem style success table, and roll something like 2d6+X. You can match up the means, but you won't get the increasing variance.

Previn · Post by **Previn** » Mon Mar 19, 2012 3:41 pm

Are there any examples of a dice pool with counted hits that increase the size (number of faces) of some or all of the dice?

Username17 · Post by **Username17** » Mon Mar 19, 2012 4:04 pm

Previn wrote:Are there any examples of a dice pool with counted hits that increase the size (number of faces) of some or all of the dice?

Yes. This is a terrible mechanic because it makes all other modifications to the system (dice number, target number, hit threshold, explosions) incoherent.

-Username17