Bell Curve Die Rolls [Archive] - Wizards Community

Post/Author/DateTimePost
Boccaccio Barbarossa

07-05-05, 12:56 AM
I was wondering if anybody out there had given the concept a try. Myself, I am a big fan of "controlled randomness" in a agme, where 13th level Fighters don't just croack really easily from a Disintegrate because they rolled a 2 on their save, or whatever.

Any stories to share? Any suggestions? Opinions? I'm thinking of trying it out, but I need some sort of backing to sell my PCs on the idea.

Thanks!
weasel fierce

07-05-05, 03:27 AM
Your PC's are controlled by you. They are Player Characters after all.

You may be able to sell the idea to your players however.

Apart from that little nitpick, Bell curve rolls make the game a lot less random, which can be desirable. However, also be aware that hte really high, and really low, rolls will be less likely to happen.
I find that its more interesting though, in most cases
Greyman

07-05-05, 05:57 AM
Unlike the uniform distribution of the d20 roll, which is a straight 5% decrease in chance for each point higher the opposed DC becomes, the bell curve, by it's nature, clusters the die roll result around 10.5 more oftern than not, with high and low results being increasingly rare.

If the opposed armor class is somewhat higher than 11+attack bonus, it becomes increasingly difficult to hit. Conversely if the opposed armor class is somewhat less than 10+attack bonus, it becomes increasingly difficult to miss.

Depending on what are their character's AC and attack bonuses (and those of their opponents too), your players are either going to love or hate the 3d6 system.
BelZoradon

07-05-05, 12:16 PM
my players love 3d6, even when forced to invent new ways to kill things with retarded ACs... but im a nice DM i refuse to give them an encounter they cant win/overcome if they take the time to think about it and they love the challange of trying to get their charatures to out think me... its amusing watching my VERY smart players trying to role play 13int eheheheh
Boccaccio Barbarossa

07-05-05, 02:26 PM
my players love 3d6, even when forced to invent new ways to kill things with retarded ACs... but im a nice DM i refuse to give them an encounter they cant win/overcome if they take the time to think about it and they love the challange of trying to get their charatures to out think me... its amusing watching my VERY smart players trying to role play 13int eheheheh

Actually, the fact that they won't be able to kill things "normally" (certain things, anyways) is possibly the exact reason for which they may like the system. I run a Ravenloft/Gothic Horror game, which rewards thinking and role-playing over die rolls, so this is sounding better and better... Hmmm... And by the same token, you're fairly certain that, pound for pound, whoever has the better modifiers will win, unless they come up with a great strategy to turn the tides...

I guess we're looking at a system that generates more "close calls" rather than shining successes. I think that's a good thing, in most of the games I run.

Wow! It just occured to me: in most games, the golden DM rules of "give them a +2/-2 modifier when you're not certain of what the modifier should be" really doesn't significantly impact the PC's chances all that much. With this system, it moves the average result to 12.5, and you can be reasonably certain that most rolls fall within this range, so consequently, you can plan "tighter-feeling" encounters,... I like, I like...

...now will my players like it...
BelZoradon

07-05-05, 05:04 PM
get them to test it one day... just play that day/encounter to feel very heroic and the "close" calls with make it feel more drimatic
Gilean

07-06-05, 03:48 AM
Just for reference, the likelyhood of getting specific results with 3d6.
3: 1 /216
4: 3 /216
5: 6 /216
6: 10 /216
7: 15 /216
8: 21 /216
9: 25 /216
10: 27 /216
11: 27 /216
12: 25 /216
13: 21 /216
14: 15 /216
15: 10 /216
16: 6 /216
17: 3 /216
18: 1 /216
Greyman

07-06-05, 07:22 AM
Also, the likelyhood of getting or exceeding specific results with 3d6. Included for further reference are the chances of doing the same with 1d20.

3 or less: 216/216 = 100% (vs 90%)
(NB: for attack and save checks, this is actually 99.5%, as a natural 3 is an automatic failure on 3d6.)
4: 215/216 = 99.5% (vs 85%)
5: 212/216 = 98.1% (vs 80%)
6: 206/216 = 95.4% (vs 75%)
7: 196/216 = 90.7% (vs 70%)
8: 181/216 = 83.8% (vs 65%)
9: 160/216 = 74.1% (vs 60%)
10: 135/216 = 62.5% (vs 55%)
11: 108/216 = 50% (vs 50%)
12: 81/216 = 37.5% (vs 45%)
13: 56/216 = 25.9% (vs 40%)
14: 35/216 = 16.2% (vs 35%)
15: 20/216 = 9.26% (vs 30%)
16: 10/216 = 4.63% (vs 25%)
17: 4/216 = 1.85% (vs 20%)
18: 1/216 = 0.463% (vs 15%)
(NB: skill checks do not auto succeed on a natural 18 on 3d6, so skill checks needing a roll of 19 or 20 cannot be made.)
19: 1/216 = 0.463% (vs 10%)
20 or more: 1/216 = 0.463% (vs 5%)

Notice how the odds of equalling or exceeding a number lower than 11 is much higher using 3d6 than 1d20. Conversely the odds of equalling or exceeding a number greater than 11 is much lower using 3d6 than 1d20.

So compare your character's attack bonuses to the AC of the creatures placed in opposition to them (and vice versa). If a 12 or more is needed to hit, it will not happen anywhere near as often using 3d6 as with 1d20. Be very aware of this when designing challenges and distributing magic items.
Paul Hopebringer

07-06-05, 04:37 PM
I'm planning on using the 3d6 method for my next campaign as well, but I've heard of a varient 2d10... that produceds a slightly more predictable role than d20, but still more random that d20...

I personally really like 3d6, but does anybody have... I don't know... Maybe a mathematical breakdown of what 2d10 really *does*, sort of like what Greyman did? Or at least give an idea of what "problems" would come up with it, in comparison to the other systems?
srkingdavy

07-06-05, 04:41 PM
a mathematical breakdown of what 2d10 really *does*, sort of like what Greyman did? Or at least give an idea of what "problems" would come up with it, in comparison to the other systems?
I just posted this in another thread.

edit: here it is. http://boards1.wizards.com/showthread.php?t=459066

I don't like using bellcurve rolls. It's a maxim of game theory that randomness favors the underdogs. the PCs are expected to "win" the majority of all encounters, making the NPCs (monsters) the underdogs, therefore using bell curve rolls favors PCs.
Greyman

07-06-05, 08:52 PM
3d6 2d10 1d20
1: never never 100%
2: never 100% 95%
3: 100% 99% 90%
4: 99.5% 97% 85%
5: 98.1% 94% 80%
6: 95.4% 90% 75%
7: 90.7% 85% 70%
8: 83.8% 79% 65%
9: 74.1% 72% 60%
10: 62.5% 64% 55%
11: 50% 55% 50%
12: 37.5% 45% 45%
13: 25.9% 36% 40%
14: 16.2% 28% 35%
15: 9.26% 21% 30%
16: 4.63% 15% 25%
17: 1.85% 10% 20%
18: 0.463% 6% 15%
19: 0.463% 3% 10%
20: 0.463% 1% 5%
Boccaccio Barbarossa

07-07-05, 03:42 AM
I just posted this in another thread.

edit: here it is. http://boards1.wizards.com/showthread.php?t=459066

I don't like using bellcurve rolls. It's a maxim of game theory that randomness favors the underdogs. the PCs are expected to "win" the majority of all encounters, making the NPCs (monsters) the underdogs, therefore using bell curve rolls favors PCs.


I hear that. I think that's what I'm getting at. It's kind of a grand deception I'm playing on my players, really. They think the deck is heavily stacked against them, while it's the opposite.

I run a high role-playing, high-drama, high-story-telling game, where combat tends to be against creatures where head on confrontation is almost always a bad idea. I run and play Ravenloft quite a bit, and many of the monsters there are best defeated by the application of some special circumstance or item or resource, which is related to the personal history of the creature. And ioften, without this "secret weapon" (of a sorts) beating the creature is VEY difficult, and rarely succeeds, until the PCs reach a certain level anyways. Often, the enemies are underdogs because the DM scales encounters like in the DMG - which is fine, but in a game where there's maybe 1 combat every, maybe, 3 session, maybe 2 if we're being generous, you can really "let 'em have it" with the monster. My PCs are in the habit of runnign away from fights - fighting just enough to "test" a creature's weaknesses, so they can plan a better encounter later.

So, really, combat is something I need most of my PCs to survive almost all of the time, the reasons being very simple - while in many games I have played, PC backgrounds are very important, in most of the games my friends and I tend to play, you expect your character to die, not as a result of die rolls (generally, though it does, of course, happen) but as a result of some character flaw that you have built into him. Dying, just like killing a monster, should advance the sotry in a concret and real way, not just be a hurdle that needs to be surmounted. (And I've seen some beauties! Inclusding a friend of mine whose character was at 1 or 2 hp following an encounter, but had a dirty little secret. He told the DM "I choose this moment to die", just so, poeticallly, his secret would never see the light of day...)

Whatever. I think all I'm saying is that it sounds interesting as a concept, and at least when you have a monster with a special attack that asks for a Will Save DC 15 (say) and your party has on average a +5 to that savem, you can fel a LOT safer sending the PCs against it, becasue, one iis likely to fail , and make the creature seem fearsome, but it's not likely to charm the whole group! :)

I'm LESS concerned, personally, with PCs being able to hit and MORE concerned with PCs being able to survive saving throws which are sometimes the biggest of plot breakers...
Gilean

07-10-05, 11:26 AM
Greyman, just curious, how did you get the results? I have a spreadsheet that usually works, and a method of noting when it doesn't. Works off of Pascal's triangle.
Millennium

07-11-05, 09:51 AM
I hear that. I think that's what I'm getting at. It's kind of a grand deception I'm playing on my players, really. They think the deck is heavily stacked against them, while it's the opposite.
That depends. If you're using this system, you need to be careful to make sure the encounters are evenly balanced (unless, of course, you don't want them to be), because it will be much more difficult for the PCs to beat a foe which is stronger than they are. Then again, you might consider this to be a Good Thing, in which case go right ahead.
Loren Pechtel

07-11-05, 10:52 PM
That depends. If you're using this system, you need to be careful to make sure the encounters are evenly balanced (unless, of course, you don't want them to be), because it will be much more difficult for the PCs to beat a foe which is stronger than they are. Then again, you might consider this to be a Good Thing, in which case go right ahead.

While I haven't tried it I would think the effect of bell curve rolls is more predictable results. You won't have the PC's stomping on something they shouldn't be able to and you won't be nearly as likely to have a TPK from bad rolls.
Paul Hopebringer

07-12-05, 08:40 AM
Yeah, I say TPK's should only happen from player stupidity. I don't mind folling up actions with appropriate results, but when the players make a tactically sound desision to go into a fight, I'd rather not have them die...

I suggest the use of action points. Liberal use of action points gives the same exitment as the randomness of d20, but you can control it, making it all the more satisfying. Luck still has it's place, but where is the fun in rolling a vorpal hit on a sewer rat? Splat factor aside, I'd rather have *some* control over my resources. "Make your own luck" can be a theme running through the campain, It makes you feel more like a hero.
Greyman

07-12-05, 10:38 AM
Greyman, just curious, how did you get the results? I have a spreadsheet that usually works, and a method of noting when it doesn't. Works off of Pascal's triangle.Then it's probably the same technique I used.
Boccaccio Barbarossa

07-12-05, 01:29 PM
Yeah, I say TPK's should only happen from player stupidity. I don't mind folling up actions with appropriate results, but when the players make a tactically sound desision to go into a fight, I'd rather not have them die...

I suggest the use of action points. Liberal use of action points gives the same exitment as the randomness of d20, but you can control it, making it all the more satisfying. Luck still has it's place, but where is the fun in rolling a vorpal hit on a sewer rat? Splat factor aside, I'd rather have *some* control over my resources. "Make your own luck" can be a theme running through the campain, It makes you feel more like a hero.

Yeah, I agree comletely. As for action points - I've been trying to get my players in on that as well, but I haven't had the chace to present it to them properly yet. I think it's a good idea as well - at least when it REALLY counts, you can tip the odds in your favour, and quite a bit, in fact, when the levels start to add up.
CaptainNifty

07-16-05, 09:29 PM
We introduced 3d6 into our campaigns as well as fractional base and saves. The 3d6 allows the merit of your character to shine through. A character with good stats benefits the most from this. My players tend to produce characters with high stats (we play heroes--not just adventurers). I'll encourage any group I play with to use both of these house rules.
Salla

07-17-05, 08:44 PM
A friend of mine once played in a game using what was termed a 'Gaussian d20' (how it got that name, I don't know), where the d20 was replaced by 2d8+1d6-2, giving a combination of a bell curve and a 20 point spread, at the expens of some math (and risking players forgetting the -2 at the end). I never got the chance to find out how it turned out.

But I do often feel really annoyed, both as a player and a GM, when the dice simply turn brown (as we call it), because there's as good a chance of rolling 1 as anything else.
Mind Rogue

07-17-05, 11:21 PM
A friend of mine once played in a game using what was termed a 'Gaussian d20' (how it got that name, I don't know), where the d20 was replaced by 2d8+1d6-2, giving a combination of a bell curve and a 20 point spread, at the expens of some math (and risking players forgetting the -2 at the end). I never got the chance to find out how it turned out.

But I do often feel really annoyed, both as a player and a GM, when the dice simply turn brown (as we call it), because there's as good a chance of rolling 1 as anything else.
This is an interesting one. It has the proper minimum and maximum, something the standard 3d6 lacks, and it has the proper median (which is missing from the 2d10 method). I don't have the time right now for a statistical analysis of it, but I suspect that it will be a little more random than the 3d6 method, but not nearly so much as the 1d20.

That said, it seems that about the only thing it has going against it is that certain tendancy to not subtract the 2 at the end. Of course, you could always put that in as a standard penalty to all your skills and such, so a 1st level fighter with weapon focus and a str 15 only has a +2 attack bonus instead of +4. Otherwise, you could simply bump the DCs up by 2.
Laszlo Koller

10-17-05, 11:27 PM
Our group played with the following:

We rolled three d20s, and kept the median value. This provided us with the bell curve-style result that you're looking for.

You can still roll 1's and 20's but they're a lot harder to get. In order to roll a "20" for example, at least two of the three dice need to be 20's. Consequentially, critical hits (and misses) are much, much rarer.

All-in-all, this system worked quite well for us, and it was quite an easy system to implement. All that everyone needed were three 20-sided dice (as opposed to only one).

I was wondering if anybody out there had given the concept a try. Myself, I am a big fan of "controlled randomness" in a agme, where 13th level Fighters don't just croack really easily from a Disintegrate because they rolled a 2 on their save, or whatever.

Any stories to share? Any suggestions? Opinions? I'm thinking of trying it out, but I need some sort of backing to sell my PCs on the idea.

Thanks!
Jaxgaret

10-18-05, 01:06 AM
Great suggestions guys! The Gaussian system and the three-d20 median system both seem workable and interesting... i'll run 'em by my playgroup. I never liked the 3d6 system, it's too much of a departure from d20.
Mirage_1

10-18-05, 05:49 AM
we used 3d6, and found the lack of variance a bit too much (high BAB guys always hit, lower BAB never hit). We changed to 2d10 and have been rather happy. A bit more of a bell, but not as much as the 3d6
Millennium

10-18-05, 10:54 AM
While I haven't tried it I would think the effect of bell curve rolls is more predictable results. You won't have the PC's stomping on something they shouldn't be able to and you won't be nearly as likely to have a TPK from bad rolls.
Exactly, but once again, this is a double-edged sword. When encounters become less random, you can plan them with more precision, but you must plan them more carefully. If, due to some oversight or miscalculation, the encounter isn't balanced just the way you want it, you could be in trouble. Although a TPK resulting from bad rolls is less likely, so is escaping a TPK through good rolls.

People are right that TPKs should only happen through player stupidity. However, that doesn't always happen. DMs are not infallible, and it's possible to make a mistake when planning an encounter. You can minimize this risk by being careful, but being careful becomes that much more important when using the 3d6 system.
Longarms

10-27-05, 12:12 AM
"People are right that TPKs should only happen through player stupidity. However, that doesn't always happen. DMs are not infallible, and it's possible to make a mistake when planning an encounter. You can minimize this risk by being careful, but being careful becomes that much more important when using the 3d6 system."

This poster makes a good point.

Has anyone considered using 3d6 or 2d10 ONLY for ability checks and skill checks? Keep the d20 for attacks rolls. I find that ability and skill checks seem to random. Like someone with the jump skill can frequently jump 20 feet horizontally and then another time only jump 5'. I would like to reduce the chance of those freak occurances.


One effect this would have is to make ability score bonuses a bigger deal. Also, someone who trained in a skill could get more predictable results.

Not sure where saving throws would fall. Probably would have to stay d20.

Thought on the effects this would have to my game?
Gilean

10-27-05, 12:47 PM
Increased complexity, at least, when the rolling method isn't universal. Not necessarily a bad thing.

One option might be to allow characters with high base save/skill/BAB to select how they roll, but keep ability checks 3d6.
Jaxgaret

10-27-05, 04:53 PM
Increased complexity, at least, when the rolling method isn't universal. Not necessarily a bad thing.

One option might be to allow characters with high base save/skill/BAB to select how they roll, but keep ability checks 3d6.

Gilean! I think you might have hit on an awesome idea - what if you let your players decide to roll d20 OR 2d10 OR Gaussian for attack rolls, whenever they want? And you do the same as the DM.