View Full Version : [3.5] Bell Curve variant rules

My player told me today that he hates rolling d20 for everything, because the result is highly randomised, and at lower levels the result of a d20 roll is often all that really matters, making character skill less noticable.

We talked it over and agreed that we would both like to change to the bell curve variant rules (http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm) in Unearthed Arcana, replacing all d20 rolls with 3d6 to create more realistic results that favour skill over luck (more often).

Before I make it official, are there any known issues I need to account for, or any problems with the system you can think of?

pasko77

2010-03-06, 09:48 AM

My player told me today that he hates rolling d20 for everything, because the result is highly randomised, and at lower levels the result of a d20 roll is often all that really matters, making character skill less noticable.

We talked it over and agreed that we would both like to change to the bell curve variant rules (http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm) in Unearthed Arcana, replacing all d20 rolls with 3d6 to create more realistic results that favour skill over luck (more often).

Before I make it official, are there any known issues I need to account for, or any problems with the system you can think of?

You must be more careful when designing encounters. If you hit, say, on 15+ a monster, it can still be viable with a d20, you will hit 1/4 of the times. With 3d6 you will never hit.

So be careful not to throw too strong opponents.

Also, remenber that magic +1s are much stronger. You should tone down every spell that gives +X to any test (mage armor and shield).

Moreover, with the rules of 3.5 for save or dies, remember that a high difficulty save will never succeed, making even more effective SoD spells from an optimized caster.

ericgrau

2010-03-06, 09:57 AM

It's not really true that low level encounters have any more to do with luck than high level ones. Whether you're adding a d20 to 3 to try to hit 13 or adding a d20 to 13 to try to hit 23 it's all the same. And in either case a +1 means 10% more successes (1 more out of 10).

Since the results are weighted towards the average, I can see this variant making a big difference on opposed rolls. Being just a little better will make you hard to beat at all. Even on regular rolls this will hold true to some extent. So be careful about sending the party against anything whose individual CR is too much higher or lower than the party level. ECL calculations will probably have to change. 4 CR 6 creatures are no longer a standard (easy, but resource consuming) fight for a 10th level party; it's a trivial fight. You might need 4 CR 7 or CR 8 creatures for the same difficulty. Play around to figure it out, or do the statistical math to figure out how bad a -4 is on 3d6 vs. 1d20.

You must be more careful when designing encounters. If you hit, say, on 15+ a monster, it can still be viable with a d20, you will hit 1/4 of the times. With 3d6 you will never hit.

So be careful not to throw too strong opponents.

Also, remenber that magic +1s are much stronger. You should tone down every spell that gives +X to any test (mage armor and shield).

Moreover, with the rules of 3.5 for save or dies, remember that a high difficulty save will never succeed, making even more effective SoD spells from an optimized caster.

Good point you'd only roll a 15 or better on 9% of rolls rather than 25%.

Are magic +1 actually a lot stronger? You're getting results with less variantion, but the mean result is the same. :smallconfused:

Saves that require high rolls did come to mind, yeah, I don't really know the numbers on saves too well, but I would think normally it's enemies that have higher save DCs, so I'd just need to make sure not to overoptimise DCs, and there are a lot of ways to boost saves, so classes with weak saves might not have trouble as long as they actually pay attention to those methods. Or am I deluding myelf there? XD

It's not really true that low level encounters have any more to do with luck than high level ones. Whether you're adding a d20 to 3 to try to hit 13 or adding a d20 to 13 to try to hit 23 it's all the same. And in either case a +1 means 10% more successes (1 more out of 10).

Since the results are weighted towards the average, I can see this variant making a big difference on opposed rolls. Being just a little better will make you hard to beat at all. Even on regular rolls this will hold true to some extent. So be careful about sending the party against anything whose individual CR is too much higher or lower than the party level. ECL calculations will probably have to change. 4 CR 6 creatures are no longer a standard (easy, but resource consuming) fight for a 10th level party; it's a trivial fight. You might need 4 CR 7 or CR 8 creatures for the same difficulty. Play around to figure it out, or do the statistical math to figure out how bad a -4 is on 3d6 vs. 1d20.

I was speaking proportionally though, 1d20 is a far bigger proportion of your ability when you only have a +4 than when you have a +24. But at all levels really, the d20 is too random for us. It just feels more pronuonced early on.

Normally the PCs are the one a little better, but in a hard battle I suppose it could be the opposite. I'll need to be careful not to create foes too much stroger, as you say.

Luckily I only use CR as a very rough guide anyway, and mostly just 'eyeball' things, so I'll just need to slightly reassess my balls. :smallbiggrin:

Good thing I'm doing statistics in school. Just yesterday I was working out the variance of 2d6. xD

Thanks to you both for taking the time to help! :smallsmile:

magic9mushroom

2010-03-06, 10:23 AM

Are magic +1 actually a lot stronger? You're getting results with less variantion, but the mean result is the same. :smallconfused:

+1 is a lot stronger. +1 normally is +5%. +1 in Bell Curve is more complicated, but is a lot bigger than +5% when near the average.

+1 is a lot stronger. +1 normally is +5%. +1 in Bell Curve is more complicated, but is a lot bigger than +5% when near the average.

Yeah, but the overall result is the same on average.

magic9mushroom

2010-03-06, 10:39 AM

Yeah, but the overall result is the same on average.

No, it's not. Instead of being 20 possible rolls, there are 16. The "overall result" is +6.25% instead of +5%.

theMycon

2010-03-06, 10:45 AM

It's not really true that low level encounters have any more to do with luck than high level ones. Whether you're adding a d20 to 3 to try to hit 13 or adding a d20 to 13 to try to hit 23 it's all the same.

These numbers are correct, but... At level 1, a character could reasonably have a skill mod from -1 to 8 - Anything any on character could make on a decent roll, everyone could make on a good roll.

At level 10, without any particular focus, a character could have a skill mod from -1 to 20-something, dependant on skill ranks & stat focus. Some characters can now auto-make rolls which other characters cannot make at all.

I think this is the point the OP was trying to make.

(Also, +1 is +5%, for an extra 1 in 20.)

No, it's not. Instead of being 20 possible rolls, there are 16. The "overall result" is +6.25% instead of +5%.

Ah, yes, I see now what you guys are talking about. Sorry, I was thinking about total results rather than percentages.

But is a 1.25% increase on the effective bonus worth making large-scale changes for? It doesn't bother me too much, unless there's some resulting effect I've failed to realise.

DragoonWraith

2010-03-06, 11:03 AM

Ah, yes, I see now what you guys are talking about. Sorry, I was thinking about total results rather than percentages.

But is a 1.25% increase on the effective bonus worth making large-scale changes for? It doesn't bother me too much, unless there's some resulting effect I've failed to realise.

I feel like that is the point of doing it this way, to reward people with ranks in something with actually being better at it.

I definitely agree with his players' complaints. "My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. :smallannoyed:"

Greenish

2010-03-06, 11:10 AM

I definitely agree with his players' complaints. "My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. :smallannoyed:":smallconfused:

You aren't supposed to be a renowned anything at level 1.

I feel like that is the point of doing it this way, to reward people with ranks in something with actually being better at it.

I definitely agree with his players' complaints. "My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. :smallannoyed:"

Yes, this, a thousand time this! :smallsigh:

As long as we're not going to break the game, we really want to dump that silly randomness.

His backstory is that he's a martial arts prodigy, and yet on a bad roll he can't hit a stationary object.

I can see how static bonuses will be better, but we want them to play a more central role - your actual ability shouldn't be eclipsed by random chance on about a third of attempts.

I would also suggest, that a roll of 18 is automatically a critical hit, without making a secondary roll to confirm. The chance to roll an 18 on 3d6 (0,5%) is much lower than rolling a 20 on 1d20 (5%).

Bell curve rolling also makes weapons with larger crit ranges better in comparison to other weapons. The chance for a critical hit is 4 times as big with a crit range of 17-18 and 9 times as big with a crit range of 16-18. (As opposed to 2 times for 18-20 and 3 times for 18-20).

I found this table (http://www.darkshire.net/jhkim/rpg/systemdesign/dice-methods.html) that compared %-chances for 1d20 and 3d6 rolls, which seems quite useful to set DCs.

Let's assume an average human who gets a +0 bonus to every roll.

A DC of 10 has a chance of success that is 50% for both 1d20 and 3d6.

To get a chance of success of 25% however, the 1d20 DC is 15 and the 3d6 DC is 12.

DC 15 on a 3d6 roll has a chance of 5%, which would be a DC 20 on an 1d20 roll.

I don't know how to best translate this in difficulty rating for DCs, but it's something to keep in mind.

I would also suggest, that a roll of 18 is automatically a critical hit, without making a secondary roll to confirm. The chance to roll an 18 on 3d6 (0,5%) is much lower than rolling a 20 on 1d20 (5%).

Bell curve rolling also makes weapons with larger crit ranges better in comparison to other weapons. The chance for a critical hit is 4 times as big with a crit range of 17-18 and 9 times as big with a crit range of 16-18. (As opposed to 2 times for 18-20 and 3 times for 18-20).

I found this table (http://www.darkshire.net/jhkim/rpg/systemdesign/dice-methods.html) that compared %-chances for 1d20 and 3d6 rolls, which seems quite useful to set DCs.

Let's assume an average human who gets a +0 bonus to every roll.

A DC of 10 has a chance of success that is 50% for both 1d20 and 3d6.

To get a chance of success of 25% however, the 1d20 DC is 15 and the 3d6 DC is 12.

DC 15 on a 3d6 roll has a chance of 5%, which would be a DC 20 on an 1d20 roll.

I don't know how to best translate this in difficulty rating for DCs, but it's something to keep in mind.

Well, for premade DCs like the difficulty of identify an animal, etc, it should be fine, but for setting things like AC it's something I'll need to be mindful of.

The boost in power for high crit range weapons is something I'm not entirely happy about, but I'm not sure how to change it. I can live with it.

DragoonWraith

2010-03-06, 11:49 AM

Also, some discussion (http://www.giantitp.com/forums/showthread.php?t=144325) that might be enlightening.

BenTheJester

2010-03-06, 12:07 PM

Why not just roll 2d20 and divide the result by 2?

This also creates a bell curve effect

Why not just roll 2d20 and divide the result by 2?

This also creates a bell curve effect

Because this is a nicer bell curve and doesn't require you to divide and round every roll.

ericgrau

2010-03-06, 12:19 PM

...

(Also, +1 is +5%, for an extra 1 in 20.)

A common misconception. 5% more attacks hit, but the actual increase in hits is always more than 5%. 10 out of 20 to 11 out of 20 is both 10% more hits and 10% more damage per round than before. 15 out of 20 to 16 out of 20 is 7.5% more hits & damage per round. And when you have 5 different sources of +1's, they add up fast and that d20 doesn't seem so big anymore.

I can see how at low levels 0 BAB and 1 BAB may not be all that much different for hitting. But people rarely make level 1 focused builds and thus the fighter with a high strength will still be ahead of the rogue who can't get weapon finesse yet and the cleric who is MAD. Or even on a level 1 focused build their other attributes are still valuable; a high strength rogue still suffers greatly from lower AC and HP. He must sacrifice a great deal of defense merely to be almost par on offense.

While theoretically you can have a wider variation at higher levels, practically this is not so except with poor players. When everyone is optimizing the classes that are worse at something tend to be only a few points behind on anything worth attempting (wizards will not wield a greatsword, for example, so their poor BAB is a moot point). Mid BAB is at most 5 points behind full BAB, and poor saves are at most 6 points behind good ones. Even then the mid BAB classes that still fight tend to have buffs to close the gap. Those with poor saves actually only gain a -3 compared to good saves over the span of 18 levels, since 2 points of the difference happens at level 1 and the last point doesn't happen until level 20.

sofawall

2010-03-06, 12:34 PM

"My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. :smallannoyed:"

Hey, at least you have a chance to tell them apart. Most people won't know at all.

2xMachina

2010-03-06, 12:42 PM

If you port the system to the real world, everyone is dead, cause they're all idiots, even at 120IQ.

pasko77

2010-03-06, 12:50 PM

Good point you'd only roll a 15 or better on 9% of rolls rather than 25%.

Are magic +1 actually a lot stronger? You're getting results with less variantion, but the mean result is the same. :smallconfused:

I meant if I have a +1 item and you don't, with d20, whatever, with 3d6 i'm seriously gonna kick your ass. :)

So beware of classes that can stock modifiers.

Pechvarry

2010-03-06, 12:52 PM

:smallconfused:

You aren't supposed to be a renowned anything at level 1.

A common farmer in the American Frontier in the days of the Oregon Trail could probably:

-Reasonably forecast today's weather

-Thatch his leaking roof

-Plane some rough beams and use them to fashion a shed

-Go hunting for dinner

This is all in addition to his true, farmerly tasks such as tending animals, keeping them from getting anxious, birthing their young, and all that "growing and harvesting" plants bit.

ALL of that is a level 1 commoner. I'd like to see even a 1st level Ranger accomplishing all of that reliably. Could he waste some skills on craft and profession and then still have some for survival? yes. But he's probably a good 50% likely to fail at any attempt to do the above.

-----

@ericgrau: I think it's kind of misleading to say "a common misconception". It's more accurate to say a miscommunication.

An increase from +10 to +11 is 5% more success rate. Against DC 21, you go from 50% success rate to 55% success rate.

However, it's a 10% increase from your previous standing. This is because 55% is 10% more than 50%.

---

Why not roll 2d10? This seems like it'd hit the same range as 1d20, have half the bell curve of 3d6 but twice that of 1d20. Natural 20 becomes Natural... 2x10. Which happens like 1% of the time. I must be screwing up my math because an 18 should only turn up on 3d6 once every 216 rolls.

pasko77

2010-03-06, 01:02 PM

Why not roll 2d10? This seems like it'd hit the same range as 1d20, have half the bell curve of 3d6 but twice that of 1d20. Natural 20 becomes Natural... 2x10. Which happens like 1% of the time. I must be screwing up my math because an 18 should only turn up on 3d6 once every 216 rolls.

On 3d6, there are different suggested values for critical hits.

For instance, a "nat 20" should be considered a 16+.

A 19+ becomes 15+

etc.

Or you will face a severe decrease in weapon damage (no more critical hits) and of feats that rely on those results.

Bye, Pasko

Sliver

2010-03-06, 01:03 PM

Why not roll 2d10? This seems like it'd hit the same range as 1d20, have half the bell curve of 3d6 but twice that of 1d20. Natural 20 becomes Natural... 2x10. Which happens like 1% of the time. I must be screwing up my math because an 18 should only turn up on 3d6 once every 216 rolls.

Not exactly the same range of a d20.. You don't have a 1 with 2d10, and the 2 becomes a 1 in terms of fumbles I guess..

2xMachina

2010-03-06, 01:58 PM

And it's slightly higher in average. 1d10 averages at 5.5, thus 11 for 2d10s, while 1d20 averages at 10.5

BruteSquad01

2010-03-06, 03:36 PM

Try 1d8 + 1d12 instead. I've never used it, but I knew a DM once who swore by it. This was back in 2ed days.

ericgrau

2010-03-06, 03:43 PM

A common farmer in the American Frontier in the days of the Oregon Trail could probably:

-Reasonably forecast today's weather

-Thatch his leaking roof

-Plane some rough beams and use them to fashion a shed

-Go hunting for dinner

This is all in addition to his true, farmerly tasks such as tending animals, keeping them from getting anxious, birthing their young, and all that "growing and harvesting" plants bit.

ALL of that is a level 1 commoner. I'd like to see even a 1st level Ranger accomplishing all of that reliably. Could he waste some skills on craft and profession and then still have some for survival? yes. But he's probably a good 50% likely to fail at any attempt to do the above.

-----

@ericgrau: I think it's kind of misleading to say "a common misconception". It's more accurate to say a miscommunication.

An increase from +10 to +11 is 5% more success rate. Against DC 21, you go from 50% success rate to 55% success rate.

However, it's a 10% increase from your previous standing. This is because 55% is 10% more than 50%.

Arguably a DC 10 survival check, if you even need a check at all. This could be assumed to be common knowledge. Heck I'll make a decent enough guess as a child. Survival only lists a DC 15 for as far as tomorrow's weather, plus 5 per day. Ditto for the next 2 as common knowledge. Likewise finding food is a DC 10, which you could do untrained by taking a 10. Or even if you don't take a 10 you may have a 45% chance of failure but you also have a decent chance of getting enough food to last you multiple days. This is more of an issue of cruel DMs setting arbitrary DCs when the DC should be low or when you shouldn't even need a check at all. Under a bell curve these arbitrarily high DCs will only be harder to make untrained whenever you can't simply take a 10.

-----

Yet if you look at anything that matters, like your actual damage output or number of successes, then a 7.5%-10% increase per +1 is more accurate. This is a key point when the complaint is that a d20 provides too much randomness for a +1 to matter. Success rates are typically 50% if you're okay at something and 75% if you're good at it. That's only a 5 point margin before random chance is gone entirely. This is why I poked fun at Pathfinder Alpha for throwing out arbitrary +5 and higher bonuses (in addition to the normal bonuses) as you reached higher levels. It's a horribly broken idea that almost lets you come to games without your d20. Fortunately the later versions toned things back quite a bit.

Caphi

2010-03-06, 04:29 PM

You require players to roll knowledge skills for trivial knowledge? Telling a squirrel from a deer should be free with the description of the area, certainly not a skill challenge.

Also, level 1 characters are glorified mooks. He can be "a renowned woodsman" at 4 or 5.

Quellian-dyrae

2010-03-06, 04:47 PM

A house rule I was fiddling with recently, which may be helpful here, was really limiting the bonuses that can apply to attack rolls and AC (it's a high-power game, and I wanted to cut down the possibility of one character having an AC of 30 or so and another 50, or something). Basically, both attack rolls an AC bonuses were equal to BAB + appropriate ability score + an enhancement bonus of up to +5. Haste and size bonuses still applied, and I added armor-boosting feats similar to the weapon-boosting feats, and they applied. All other sources of attack roll bonuses (stacking rules allowing) get doubled and added to damage rolls, and all other sources of AC get added to a stat called Resilience, which was basically like DR.

Anyway, it's part of a large list of house rules, so there's a bit more to it than that, but if you do something like that, you won't have to worry as much about a few extra bonuses completely skewing probability.

randomhero00

2010-03-06, 05:20 PM

I also agree about disliking the randomness of the d20. Not sure if doing 3d6 is a safe way to improve it though.

Here's several other options:

1. For anything out of combat (if they have high/max ranks), assume they succeed on anything not-that-important. Like knowledge roles, or anything else that makes sense and wouldn't mess up balance too much.

2. When rolling 1d20, have a minimum basically. So if you're out of combat, and you roll a 2, you can take 10 (or 5 or whatever you want) even after the roll was made. If you're in combat, make 5 the minimum (or no minimum for combat.)

Rolling 1s could be the exception though, so if you roll a 1 you auto fail.

This would leave you pretty flexible. You could do that until they hit level 5 or something. /shrug, just some ideas I had.

ericgrau

2010-03-06, 06:32 PM

Hmmm, what about 3d10-6 or something along those lines? The idea is to give a bell curve but still have an ok chance of high and low rolls. Ya, now you can get a little higher or lower than you could on a d20, but the chance of such is super low... or should be. Better apply your statistics and make sure first.

For skill checks, that's what taking 10s are for. If you're out of combat and otherwise not in danger you usually can.

Thanks again to all of you for posting. ^^

Hmmm, what about 3d10-6 or something along those lines? The idea is to give a bell curve but still have an ok chance of high and low rolls. Ya, now you can get a little higher or lower than you could on a d20, but the chance of such is super low... or should be. Better apply your statistics and make sure first.

For skill checks, that's what taking 10s are for. If you're out of combat and otherwise not in danger you usually can.

Well, I think 5d5-5 would be a better option, but really these variations are more complex than they need to be. 3d6 is close enough to a d20, and already written up in Unearthed Arcana. Also it's more fun throwing d6s. :smalltongue:

Tyndmyr

2010-03-07, 07:57 AM

No, it's not. Instead of being 20 possible rolls, there are 16. The "overall result" is +6.25% instead of +5%.

Its even worse than that. The odds of getting. The same result twice in a row on 3d6 will be much higher than on 1d20 due to the decreased variance.

I suggest 2d10 as a halfway point

Its even worse than that. The odds of getting. The same result twice in a row on 3d6 will be much higher than on 1d20 due to the decreased variance.

I suggest 2d10 as a halfway point

How is getting the same result more often a bad thing? :smallconfused:

my group changed from 1d20 to a 3d20 take middle system. works fine so far.

we adjusted the crit ranges, with slightly reduced chances to land a crit. it is a way more predictable system, but still random enough to have those "woohoo! natural 20!" moments.

I did some statistics, it's not exactly a bell curve, the edges are much steeper.

Hmmm, what about 3d10-6 or something along those lines? The idea is to give a bell curve but still have an ok chance of high and low rolls. Ya, now you can get a little higher or lower than you could on a d20, but the chance of such is super low... or should be. Better apply your statistics and make sure first.

That is a lot of extra calculation for every single roll in the game.

ericgrau

2010-03-07, 10:36 AM

Well something like that. I imagine you could also do 3d10 but increase all the DCs and AC by 5 or 6. Hmm... still a lot of work when working with existing material. I know, rewrite the numbers on your dice or buy custom dice already rewritten. 0 is 0 not 10. Maybe change the 9's to -1's too, or into more 0's if that's simpler.

Unwitting Pawn

2010-03-07, 01:55 PM

Crikey! I never thought I'd see a thread like this here. Normally, I see threads on the SJGames forum from new players/GMs wanting the reverse of this, because they're so used to rolling d20 rather than 3d6 :smallwink:

To the OP, here (http://forums.sjgames.com/showthread.php?t=57039) is one such thread which has some discussion of the percentage chances for any particular 3d6 result. That may help. And few posts down that thread someone has included a bunch of further links on the topic of rolling 3d6. :smallsmile:

Eloel

2010-03-07, 03:08 PM

my group changed from 1d20 to a 3d20 take middle system. works fine so far.

That sounds like a strangely good idea.

Another idea I've been playing around with is using d100 instead of d20. Sure, it takes some time to get used to, but it gives any curve you wish.

The following is my replacement:

1 - 1

2 - 2,3

3 - 4,6

4 - 7,10

5 - 11,15

6 - 16,20

7 - 21,26

8 - 27,33

9 - 34,41

10 - 42,50

11 - 51,59

12 - 60,67

13 - 68,74

14 - 75,80

15 - 81,85

16 - 86,90

17 - 91,94

18 - 95,97

19 - 98,99

20 - 100

What do you think?

Malificus

2010-03-07, 03:11 PM

That sounds like a strangely good idea.

Another idea I've been playing around with is using d100 instead of d20. Sure, it takes some time to get used to, but it gives any curve you wish.

The following is my replacement:

1 - 1

2 - 2,3

3 - 4,6

4 - 7,10

5 - 11,15

6 - 16,20

7 - 21,26

8 - 27,33

9 - 34,41

10 - 42,50

11 - 51,59

12 - 60,67

13 - 68,74

14 - 75,80

15 - 81,85

16 - 86,90

17 - 91,94

18 - 95,97

19 - 98,99

20 - 100

What do you think?

You might as well just use 2d10. Unless you like referencing charts every roll I suppose.

Eloel

2010-03-07, 03:11 PM

You might as well just use 2d10. Unless you like referencing charts every roll I suppose.

2d10 kills the chance of rolling a 1 - this variant keeps all rules intact.

All these alternatives seem less appealing than just using 3d6. xD

Most require extra work, or slow things down.

Unwitting Pawn, nice links. :3

erikun

2010-03-07, 07:26 PM

Watch out for bonuses. Bonuses mean a LOT more in 3d6 than in 1d20. 80% of the rolls on a d20 fall in the 3-18 range, or a range of 16 numbers. 80% of the rolls on a 3d6 fall in the 7-13 range, or a range of 8 numbers.

It is also a lot harder to determine how much a bonus means on a roll. +4 will always mean an addition +20% chance of success on a d20 roll. On a 3d6, that same +4 will be anywhere from +40% to +10%. It also depends on what the target number is, and what other bonuses are involved.

The 3d6 roll shouldn't cause too much trouble at lower levels, although watch out for minmaxing. It is far easier to setup a virtual autowin/autolose situation through stacking bonuses. As I pointed out, having an additional +4 above the "expected" value for an encounter grants you a 90% chance of success. This also applies to higher/lower CR monsters; simply having 4 more points of AC above what they "should" can make them almost unhittable.

My player told me today that he hates rolling d20 for everything...

How about giving players the option to roll either 1d20 or 3d6?

Malificus

2010-03-08, 01:45 AM

How about giving players the option to roll either 1d20 or 3d6?

No, you gotta mix it up. Flip a coin and roll a d10

If the coin goes heads, add 10 to the roll. If the coin comes up tails,don't.

No, you gotta mix it up. Flip a coin and roll a d10

If the coin goes heads, add 10 to the roll. If the coin comes up tails,don't.

Woah woah woah, you can't just flip a coin, much better to roll 4d100/2-1! :smallbiggrin:

Koury

2010-03-08, 02:26 AM

Woah woah woah, you can't just flip a coin, much better to roll 4d100/2-1! :smallbiggrin:

Or you could /2 if its even and x3-1 if its odd!

ShneekeyTheLost

2010-03-08, 03:05 AM

4d6-3 gives 1-21. That's not bad.

Really, though, a bell curve makes bonuses more important, if the DC is anywhere near the median.

However, the die roll is fairly meaningless in higher end games where you have a target number around 40ish, with a decent 100+ to your roll...

Gralamin

2010-03-08, 03:09 AM

my group changed from 1d20 to a 3d20 take middle system. works fine so far.

we adjusted the crit ranges, with slightly reduced chances to land a crit. it is a way more predictable system, but still random enough to have those "woohoo! natural 20!" moments.

I did some statistics, it's not exactly a bell curve, the edges are much steeper.

Hmm, I'm interested in this, so I'll do some math:

We have three dice, Given that we always call the lowest one A, and the Highest one C, then what does the distribution of the middle die B (Such that A <= B <= C) look like?

After crunching some numbers (that I may of screwed up, a bit sleepy), we get a pdf of:

P(B) = (21b-b^2)/1560

This has an expected Value of 10.5, which means the mean is the same, and a variance of 21.85, compared to a d20's variance of 33.85

Math used:

Getting 1s: 20 possible rolls (1,1, X) (X >= 1)

Getting 2s: 19 possible rolls (1,2, X) (X >= 2) + 19 possible rolls (2, 2, X) (X >= 2)

Getting 3s: 18 possible rolls (1, 3, X) (X>=3) + 18 possible Rolls (2, 3, X) (X>=3) + 18 Possible Rolls (3, 3, X) (X>=3)

This is where I found I could generalize:

Getting n: n(20-n+1) = 21n-n^2 (Formula A)

Generate list from 1 to 10, double it: Get 1560 results. Divide Formula A by 1560, final PDF.

EX = Sum from n=1 to 20 of n((21n-n^2)/1560) = 1/1560 * Sum from n=1 to 20 (21n^2-n^3) = 10.5

E(X^2) = Sum from n=1 to 20 of n^2((21n-n^2)/1560) = 1/1560 * Sum from n=1 to 20 (21n^3-n^4) = 132.1

Variance = E(X^2) - E(X)^2 = 21.85

So its not a bell-curve: It is a perfect parabolic arc.

Unwitting Pawn

2010-03-08, 03:39 AM

Unwitting Pawn, nice links. :3

No problem! :smallcool:

Being a GURPS convert, I looooove the bell curve :smallwink:

A system that starts with the mechanics that mean a basic ordinary person will be able to complete the normal tasks related to their life skills most of the time without incident - is OK by me :smalltongue:

No problem! :smallcool:

Being a GURPS convert, I looooove the bell curve :smallwink:

A system that starts with the mechanics that mean a basic ordinary person will be able to complete the normal tasks related to their life skills most of the time without incident - is OK by me :smalltongue:

Yes indeed, using the d20 for everything was never a good idea. :smalltongue:

Sophismata

2010-03-08, 09:39 AM

I really enjoy the bell curve, but I think 3d6 is actually too steep for general D&D play.

You can get a much more acceptable bell curve by rolling a d10 and d8 together. You get a range of 2-18, with the numbers around 10 appearing more frequently, but evenly so. Give it some consideration.

For people suggesting 4dX and 5dX rolls, adding more dice only exacerbates the problem. Just because the final range lies between 1 and 20 doesn't mean that you won't always be rolling the same number.

magic9mushroom

2010-03-08, 09:46 AM

If you don't like 3d6, try 7d2. That's the other combination that gives the same mean.

Or you could /2 if its even and x3-1 if its odd!

And 7s are wild! :smallbiggrin:

Except on Tuesdays.

Tyndmyr

2010-03-08, 10:21 AM

How is getting the same result more often a bad thing? :smallconfused:

It makes the value of +x things higher.

Let's say you have a +1 bonus over your opponent on an opposed roll. With D20, this means the odds shifted 5% your way.

In 3d6, it's approximately 12%. This is partially due to less results, and partially due to decreased variance. The odds of rolling the same as your opponent(and thus, the combat being decided by the +1) are much higher.

This makes stacking bonuses ridiculously good, and makes balance exceedingly fragile, with encounters generally being a walkover or an impossible fight. Even for well balanced mobs, it means that things playing to their strengths will essentially never fail, making specialization hyper-important.

It makes a mockery of balance, and basically breaks the game, and should never, ever be used.

Tyndmyr

2010-03-08, 10:23 AM

No, you gotta mix it up. Flip a coin and roll a d10

If the coin goes heads, add 10 to the roll. If the coin comes up tails,don't.

This is statistically identical to just rolling a d20.

It makes the value of +x things higher.

Let's say you have a +1 bonus over your opponent on an opposed roll. With D20, this means the odds shifted 5% your way.

In 3d6, it's approximately 12%. This is partially due to less results, and partially due to decreased variance. The odds of rolling the same as your opponent(and thus, the combat being decided by the +1) are much higher.

This makes stacking bonuses ridiculously good, and makes balance exceedingly fragile, with encounters generally being a walkover or an impossible fight. Even for well balanced mobs, it means that things playing to their strengths will essentially never fail, making specialization hyper-important.

It makes a mockery of balance, and basically breaks the game, and should never, ever be used.

Wow, you're massively over-exaggerating there. :smalleek:

It's even suggested as a variant rule by WoTC. And so far it's been working perfectly well for my group. You seem to think that extreme rolls being rarer makes them virtually non-existant.

Tyndmyr

2010-03-08, 11:11 AM

Wow, you're massively over-exaggerating there. :smalleek:

It's even suggested as a variant rule by WoTC. And so far it's been working perfectly well for my group. You seem to think that extreme rolls being rarer makes them virtually non-existant.

In comparison to a d20, yes it does. For example, a 1 or a 20 both have a 5% chance of occuring on a d20.

A 3 or an 18 have a 1/216 chance of occuring on 3d6.

This is a very significant difference. The loss of range of results is also significant, since you've removed a total of 4 results. This cannot possibly do anything but limit the variance in opponents you can face.

It's even more significant when you consider how many abilities work off multiple rolls. Grapples. Crits. Etc. What are the odds that that level 1 commoner can get a lucky crit on a high level PC with a D20? 1/400. On 3d6? 1/46,656. That is virtually non-existant, in that it's unlikely to ever come up in a players lifetime. Sure, you can fudge crit ranges. It's still a ridiculous gap that means that differences in power level are greatly exaggerated.

In comparison to a d20, yes it does. For example, a 1 or a 20 both have a 5% chance of occuring on a d20.

A 3 or an 18 have a 1/216 chance of occuring on 3d6.

This is a very significant difference. The loss of range of results is also significant, since you've removed a total of 4 results. This cannot possibly do anything but limit the variance in opponents you can face.

It's even more significant when you consider how many abilities work off multiple rolls. Grapples. Crits. Etc. What are the odds that that level 1 commoner can get a lucky crit on a high level PC with a D20? 1/400. On 3d6? 1/46,656. That is virtually non-existant, in that it's unlikely to ever come up in a players lifetime. Sure, you can fudge crit ranges. It's still a ridiculous gap that means that differences in power level are greatly exaggerated.

Uh.... We don't want level 1 commoners to get lucky crits on high level PCs 1 in 400 times. :smallconfused:

The differences in power level are greater, although not as much greater as you imply, but that's fine because players fight foes of around equal power. If they instead only fought stronger foes then it would just be a matter of time before their luck ran out and they stopped rolling high numbers.

3d6 condenses the range of challenge you can hope to beat, but it doen't change the average level of challenges you can beat.

Certianly modifiers matter more, but it's not like before you could count on always rolling a 15 when you need it.

Tyndmyr

2010-03-08, 11:27 AM

Uh.... We don't want level 1 commoners to get lucky crits on high level PCs 1 in 400 times. :smallconfused:

The idea is that high level PCs are already pretty powerful against regular guys. Unless you autolevel all the world's characters to match your players, you end up with an MMO feel, where areas that used to be challenging are now utterly trivial. You can casually destroy everything at will.

The differences in power level are greater, although not as much greater as you imply, but that's fine because players fight foes of around equal power. ... 3d6 condenses the range of challenge you can hope to beat, but it doen't change the average level of challenges you can beat.

Certianly modifiers matter more, but it's not like before you could count on always rolling a 15 when you need it.

Condensing the range of challenges available is generally a bad thing, especially considering that CR is hardly accurate.

It's also worth considering that mobs typically have strong and weak areas as well. Thus, you end up with mobs that are only competent at say...grappling. But at that, the players can't hope to match them. It ends up being a very deterministic fight, where you may as well just compare modifiers unless they are quite close.

The idea is that high level PCs are already pretty powerful against regular guys. Unless you autolevel all the world's characters to match your players, you end up with an MMO feel, where areas that used to be challenging are now utterly trivial. You can casually destroy everything at will.

Condensing the range of challenges available is generally a bad thing, especially considering that CR is hardly accurate.

It's also worth considering that mobs typically have strong and weak areas as well. Thus, you end up with mobs that are only competent at say...grappling. But at that, the players can't hope to match them. It ends up being a very deterministic fight, where you may as well just compare modifiers unless they are quite close.

1. I guess so, but that happens anyway, and only in settings where high level characters just sit around in one part of the world only. :smalltongue:

2. Again, I think you're exaggerating quite a bit there, but in any case I largely ignore CR and monsters as written. If is says +4 to grapple but that's not enough, I'll just give it +whatever it needs such that it's a satisfying challenge. :smallsmile:

Unwitting Pawn

2010-03-08, 11:32 AM

The idea is that high level PCs are already pretty powerful against regular guys. Unless you autolevel all the world's characters to match your players, you end up with an MMO feel, where areas that used to be challenging are now utterly trivial. You can casually destroy everything at will.

Aw, shucks! GURPS uses 3d6. I never realised that a game many criticise for trying to be "too realistic" was actually more like an MMO :smallwink:

Sophismata

2010-03-08, 12:03 PM

Aw, shucks! GURPS uses 3d6. I never realised that a game many criticise for trying to be "too realistic" was actually more like an MMO :smallwink:

That's not what he's saying, and you know it.

A 3d6 bell curve makes modifiers and bonuses more important, because they have a more drastic effect in combat.

Thus, appropriate challenges need to be very close to the party's level in order to be interesting. Too high, and the party cannot hit, too low, and the monster cannot hit.

This behaviour is like an MMO, in that encounters are harshly scaled by level. Many MMO's use arbitrary level adjustments for damage scaling, so that you deal more damage to lower level critters and less damage to higher level critters.

For what it's worth, I don't think the 3d6 curve is that bad, but I think the game works better with something flatter - d10 + d8, or d12 + d8.

Unwitting Pawn

2010-03-08, 12:10 PM

That's not what he's saying, and you know it.

Naturally. I wasn't being serious. Hence the wink :smallsmile:

I'm in no position to debate the finer points of the actual D&D mechanics. The last time I played, the company was still called TSR :smalltongue:

What you (and Tyndmyr) say about may well be true, to a certain extent. However, I was merely pointing out that 3d6 does not automatically equals MMO.

Tyndmyr

2010-03-08, 01:12 PM

What you (and Tyndmyr) say about may well be true, to a certain extent. However, I was merely pointing out that 3d6 does not automatically equals MMO.

Never stated that. My comment was definitely in the context of D&D.

The same assumptions regarding level, CR, etc do not hold true across all systems because not all systems have the same variation in CR to begin with. A limit on range of possible encounters is a huge problem when a great many encounters exist within the lost range. If none do, then it's not an issue. Obviously, D&D falls into the former category.

I prefer midrange curves in general(ie, 2d10) as a general game design prinicple, as it gives more generally useful distributions. After all, as mentioned before, combinations that will probably never come up in a players career of playing can be effectively ignored. TN dice pool systems are also good when done right, for those who enjoy tossing a handful of dice.

Sophismata

2010-03-08, 11:39 PM

Naturally. I wasn't being serious. Hence the wink :smallsmile:

My apologies :smallredface:.

Unwitting Pawn

2010-03-09, 04:50 AM

My apologies :smallredface:.

None was necessary, but I'll accept it anyway :smallbiggrin:

Hmm, I'm interested in this, so I'll do some math:

We have three dice, Given that we always call the lowest one A, and the Highest one C, then what does the distribution of the middle die B (Such that A <= B <= C) look like?

After crunching some numbers (that I may of screwed up, a bit sleepy), we get a pdf of:

P(B) = (21b-b^2)/1560

This has an expected Value of 10.5, which means the mean is the same, and a variance of 21.85, compared to a d20's variance of 33.85

Math used:

Getting 1s: 20 possible rolls (1,1, X) (X >= 1)

Getting 2s: 19 possible rolls (1,2, X) (X >= 2) + 19 possible rolls (2, 2, X) (X >= 2)

Getting 3s: 18 possible rolls (1, 3, X) (X>=3) + 18 possible Rolls (2, 3, X) (X>=3) + 18 Possible Rolls (3, 3, X) (X>=3)

This is where I found I could generalize:

Getting n: n(20-n+1) = 21n-n^2 (Formula A)

Generate list from 1 to 10, double it: Get 1560 results. Divide Formula A by 1560, final PDF.

EX = Sum from n=1 to 20 of n((21n-n^2)/1560) = 1/1560 * Sum from n=1 to 20 (21n^2-n^3) = 10.5

E(X^2) = Sum from n=1 to 20 of n^2((21n-n^2)/1560) = 1/1560 * Sum from n=1 to 20 (21n^3-n^4) = 132.1

Variance = E(X^2) - E(X)^2 = 21.85

So its not a bell-curve: It is a perfect parabolic arc.

indeed, matches my research. the extrema (1 and 20) have a higher chance to be rolled than with 3d6 (3 and 18 in that case), but a much lower chance than with 1d20...

it's a compromise between randomness and predictability (and all those numbers don't have to be changed from the default d20 roll method)

If someone is interested, i may post the percentiles...

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