Can someone explain to me why the d20 is broken?

[Snowbluff]

Why is 3d6 supposed to be better? Why do people on the WotC forum report that that math is more balanced that way.

I mean, if you are at a disadvantage (you have to roll over 11 to succeed), wouldn't it be more fair you had a better chance at succeeding. which you would with a d20?

[Raven777]

1d20 is a flat destribution, each result having an equal 1 in 20 chance to happen.

3d6 is a bell curve, with average results more likely than extremes. For exemple, an 11 can come from many combinations : 6-4-1, 6-3-2, 5-5-1, 4-5-2, 5-3-3, etc... On the other hand, extremes like 3 (1-1-1) or 18 (6-6-6) are rarer.

Some believe a bell curve favoring average results feels more representative or reality / less gamey / more predictable.

[Jeraa]

With the d20, you have exactly the same change to roll average (10-11) as you do excellent (20) or horrible (1). So, every time you attempt something, you have the same chance to get an average result as you do an exceptional success or an exceptional failure.

However, real life tells us it doesn't work that way. You are far more likely to get an average result over one of the extremes. By rolling 3d6 instead of 1d20, you are far more likely to roll an average result then a really good or really bad one.

d20 - every result is equally likely
3d6 - average results (10-11) far more likely then extremes
3d6 is more reliable then 1d20, though 1d20 gives a bigger chance of an exceptional roll (while also giving a bigger chance of an exceptional failure).

[TheSunKing]

I'm not entirely certain what exactly you are referring to, so I apologize if I start speaking off-topic.

A d20 has a 5% chance to roll a 1, 2, 3,... 19, and 20, and on average rolls 10.5.

3d6 cannot roll 1, 2, 19, or 20. It also has an average of 10.5, but has a much higher chance of being near 10.5. This is due to the fact that there are many more ways to roll near 10 and 11 than there are to roll near 3 and 18.

I'm not sure why it would be considered "balanced", but it has a more natural curve of probability than the d20 does (I apologize for the slightly inaccurate terminology here).

Edit: Ninja'd, I knew it would happen!

[Phelix-Mu]

While I accept the logic regarding probability, I think it also prudent to note that, especially as any campaign progresses, only certain rolls that allow critical failures (rolls that always fail on a roll of 1) will actually fail reliably. Because most of the game's mechanics involve improving bonuses to one roll or another, there are about a million ways to mitigate the poorly modeled probability of the d20.

This is pretty much completely clear from the fact the actual number rolled on any die is less relevant as time goes on. Bonuses to rolls, re-rolls, methods to avoid critical fails, and substituting one roll for another type of roll are legion.

If I were to switch to 3d6, I'd also want to tone down the regime of easy-to-acquire bonuses (I think spells are some of the biggest offenders here).

Also, it is probably much easier to just implement some kind of "Take 10 on an Attack" or the like. I kind of feel that bell curves aren't as crucial for saves, so I'd probably keep that little bit of stubborn bad luck (especially as there are already forms of mitigation for it).

[navar100]

It's not broken, merely a matter of taste. Despite the even chance of rolling a 1, 10, or 20 on a d20, you're not trying to roll a specific number. You're trying to roll a target number or higher. It doesn't matter if you would succeed on a 19 if you roll a 7 and succeed anyway. The extremes do matter depending on the cause of making the roll - critical hit, autosave, autofailsave. Whether you like the 5% of a 1 or 20 over the less percentage of 3 or 18 on 3d6 is only dependent upon your particular taste, not objective superiority.

[137beth]

Maybe because some people prefer predictability? I don't know, I haven't seen many people say that 3d6 is inherently "better" or "more balanced". I guess it could be better for people who own more d6s than d20s, but I can't think of anything that would make one inherently better than the other other than preference.

I will say, however, that 3d6 tends to favor the players more than 1d20, since the players are expected to win more often against similar-level monsters. BUT it likely affects martial classes more than casters: most of the time, when I play a T3+ character, I try to avoid techniques which depend to heavily on die rolls, because I know those can be unreliable. If you are a fighter, you're stuck, though--a monster can always roll high, and you can always roll low and miss. A wizard, on the other hand, has a ton of no-save spells and spells which target touch-AC, so they can do well no matter what rolling mechanism is used. So I would presume that switching to a more consistent rolling mechanic like 3d6 would help martials, blasters, and save-or-lose casters without really affecting buff/debuff/BC/utility casters, so I can see the potential benefit. On the other hand, 3d6 has the (for me) undesirable effect of really hurting critical-hit-based builds.

[AmberVael]

The idea is that the results are less swingy. In practice, the results are less swingy.

Also in practice, systems not carefully set up for it handle bell curved results really badly. I elaborated on this a few days ago, here. (http://www.giantitp.com/forums/showpost.php?p=15597323&postcount=9)

Edit: In short, I am inclined to say that if either of the two is 'broken,' its 3d6, because it will quite likely mess up the game.

[Snowbluff]

Yeah, guys, I know the math. I just wanted a look into the minds of the people who thought it was a good idea. :smalltongue:

How is 3d6 more predictable? I guess if you are guessing you are getting an 11 it's right, but I know when I have a d20 I can predict I have 5% chance of getting any single number.

Phelix Mu, you are right that only certain rolls give a critical success/failure.

[TheSunKing]

Yeah, guys, I know the math. I just wanted a look into the minds of the people who thought it was a good idea. :smalltongue:

How is 3d6 more predictable? I guess if you are guessing you are getting an 11 it's right, but I know when I have a d20 I can predict I have 5% chance of getting any single number.

Phelix Mu, you are right that only certain rolls give a critical success/failure.

You are far more likely to get near 10 & 11, so you can predict "meh" results. With a little googling/stats you can know the percentage chance of each results like you know the results of the d20.

[Snowbluff]

You are far more likely to get near 10 & 11, so you can predict "meh" results. With a little googling/stats you can know the percentage chance of each results like you know the results of the d20. Well, yeah, but that's besides the point.

Jeraa ascribed this as reliability. He will have fun reliably being reliably bad when outmatched, I guess.

[Kane0]

I wouldn't say the d20 is broken. If it was, it wouldn't be as popular in RPGs and such as it is.

But anyway, I find that people prefer 3d6 for two main reasons:
1. 3d6 gives you more average results more often, as opposed to the d20 being able to 'swing' higher or lower more often. People that like consistency tend to prefer the idea of 3d6 where those that like chance lean towards the d20.
2. They are more likely to have and are more comfortable with d6s rather than d20s. Also your average person will think of a d6 when someone says 'dice', your average gamer has a good chance to think of a d20, a d6 or some other kind of die depending on what he plays.

[Friv]

Well, yeah, but that's besides the point.

No, it's not beside the point, it's the entire point. If a system tilts towards average results, it delivers more average results.


Jeraa ascribed this as reliability. He will have fun reliably being reliably bad when outmatched, I guess.

Well, yes, that's what reliability means. It means you have a good idea about what the outcome of an event will be.

[lsfreak]

How is 3d6 more predictable? I guess if you are guessing you are getting an 11 it's right, but I know when I have a d20 I can predict I have 5% chance of getting any single number.

Right, which isn't predictable at all. The entire range of numbers has an equal chance. Meanwhile, with 3d6, you can predict you will, 50% of the time, roll between 9 and 12, and you only have a 1:6 chance of rolling 3-7 and a 1:6 chance of rolling 14-18. Before you drop the dice, you have a very clear idea of what your roll is likely to end up, so you can predict what actions are likely to do well or which ones are going to be impossibly difficult. If you're as likely to roll a 1 as a 10 as a 20, you have no basis for predicting the outcome of your roll.

[TheSunKing]

Well, yeah, but that's besides the point.

How so? I was responding to this:


How is 3d6 more predictable?

The 3d6 is more predictable because it tends towards 10 and 11.

[Snowbluff]

No, it's not beside the point, it's the entire point. If a system tilts towards average results, it delivers more average results.
We were discussing memorizing percentages.



Well, yes, that's what reliability means. It means you have a good idea about what the outcome of an event will be.

The 2 have the same average. You can just as easily assume 10.5 on either roll.

[Studoku]

Jeraa ascribed this as reliability. He will have fun reliably being reliably bad when outmatched, I guess.
Or have fun being reliably good if he manages to secure a slight advantage.

I'm not sure where you're getting the idea that more chance to succeed equals fairer, more fun or better. If you genuinely believe that, I suggest eschewing the dice entirely and playing a freeform game where everyone always succeeds at everything they do.

[JusticeZero]

An optimization expert will stack high natural ability with a lot of small easy to acquire bonuses from different sources to get, say, a high AC. In D20, that makes them annoyingly hard to hit. In a system with a bell curve, that character is now virtually impervious to being harmed in melee. If you thought having the fighter stand completely surrounded by enemies and only getting hit slightly less than every other round was obnoxious, imagine how bad it is for him to do that and only be hit once out of 216 swings, so he only gets hit every 27th round on average.

[Snowbluff]

Or have fun being reliably good if he manages to secure a slight advantage.

This is sad.


I'm not sure where you're getting the idea that more chance to succeed equals fairer, more fun or better. If you genuinely believe that, I suggest eschewing the dice entirely and playing a freeform game where everyone always succeeds at everything they do.

You should probably stop.

You actually have an equal chance to get every number on a d20. That's called being fair. While guessing odds you should assume you are getting 10.5, the truth is if you need an extreme value to succeed or fail, the d20 is more appropriate for use.

See JusticeZero for a logical response.

[eggynack]

The 2 have the same average. You can just as easily assume 10.5 on either roll.
No, you can't. If you roll the dice sets an infinite number of times, you'll get a 10.5 both ways, but the individual rolls have different distributions. With 3d6, you'd be more likely to hit stuff that require rolls that are close to 10.5. In particular, the percentages divide evenly around the median point, but around different points, the averages change. The chance of hitting an enemy that requires a 12 with a d20 is a straight 45%, while hitting an enemy that requires a 12 with 3d6 is a 37.5. However, the odds of hitting an enemy that requires a 10 on a d20 is a 55%, while the odds on a 3d6 is 62.5%. You're more likely to hit numbers that are below your to hit, while you're less likely to hit numbers that are above it. The average is the same, but the standard deviation is different.

[Snowbluff]

And in that case you would be wise to decide not to act/ do it, since you are less than likely to succeed.

[Lapak]

An optimization expert will stack high natural ability with a lot of small easy to acquire bonuses from different sources to get, say, a high AC. In D20, that makes them annoyingly hard to hit. In a system with a bell curve, that character is now virtually impervious to being harmed in melee. If you thought having the fighter stand completely surrounded by enemies and only getting hit slightly less than every other round was obnoxious, imagine how bad it is for him to do that and only be hit once out of 216 swings, so he only gets hit every 27th round on average.The flip side of this is that 3d6 (which I don't use, though I see the appeal) does mitigate the problem with skills. Taking two level 1 people, one a highly-trained specialist and one a total total novice.

Expert: 4 skills ranks, +2 ability mod, something else adding up to +2 more. (More skill ranks, masterwork tools, whatever.) Skill check: +8.

Novice: No skill ranks, no ability mod, no benefits. Skill check: +0.

With each rolling 1d20, the utter novice will at least match the expert 20% of the time. He'll flat beat him 16.5% of the time. At his area of specialty. So an untalented novice should be an expert at their own game a little better than one time in seven tries. That seems... odd.

With 3d6, the novice will only match him around 4% of the time, actually beating him less than 2% of the time. 1-in-25 or 1-in-50 reflects what we'd expect of such an opposed check more than the d20 roll does.

So yeah, I can see the appeal of a bell curve.

[TheSunKing]

We were discussing memorizing percentages.

When I mentioned memorizing percentages I was trying (probably poorly) to say that describing the d20 as "predictable" through these words


I know when I have a d20 I can predict I have 5% chance of getting any single number.

is a tad silly when that is just knowing the random chance of a d20, something that can be done for 3d6 as well :P.

If this above isn't exactly the point you were attempting to make, I apologize.

In short (sort of), I was saying your point about being able to predict what a d20 gets by the fact is has an even distribution doesn't make it predictable through the use of saying you can know what the 3d6 results are

[Phelix-Mu]

I think people are ascribing too much significance to the rolling of the dice.

If you have a good Hide check, you can be good at hiding on a regular basis (particularly if you are better much better than the people looking for you). This is true with d20. It will be blatantly so with 3d6.

Now, with d20, there is a chance that you roll quite low and the enemy rolls quite high. This only comes up with opposed rolls and checks, but I find that some luck in the game is desirable, purely from a dramatic perspective.

Modifiers and bonuses mitigate most rolls at all but the lowest levels and the lowest of op-levels.

Some rolls, as I mentioned, have more import than others (save vs death), and some predictability in these matters is comforting; but why on Earth is the system trying to comfort the players? I'm kind of old school in this matter, but I like to have my characters rise up above the odds, not corner the table and beat the house at its own game.

Taking 10 or 20 on some rolls is, I think, plenty of predictability. If you want to instill more of this into the game, I'd advise broadening the use of taking 10/20 and using "checks without rolling dice" and other variants/optional rules, rather than changing the assumed mathematical basis of the game mechanics.

[eggynack]

And in that case you would be wise to decide not to act/ do it., since you are less than likely to succeed.
Sure. That's how it works. You're also much less likely to get a critical hit or critical failure. You've only got a .5% chance of hitting either one. It regulates numbers away from the edges, which is generally more reflective of real life. that's the claim at least. If you usually jump ten feet, it makes more sense that you'd have a higher chance of jumping ten feet than jumping twenty or one feet (The numbers are probably a little off, but just substitute actual skill check stuff in your brain). Folks tend to have skills that approximate bell curves rather than linear progressions.

[Snowbluff]

Sure. That's how it works. You're also much less likely to get a critical hit or critical failure. You've only got a .5% chance of hitting either one. It regulates numbers away from the edges, which is generally more reflective of real life. that's the claim at least. If you usually jump ten feet, it makes more sense that you'd have a higher chance of jumping ten feet than jumping twenty or one feet (The numbers are probably a little off, but just substitute actual skill check stuff in your brain). Folks tend to have skills that approximate bell curves rather than linear progressions.

Eggynack, assuming that was sarcasm, you are smarter than this...

Case study.
Citation needed.

Then there is the assumption we are simulating real life, with knights encumbered by armor, locks that can be picked with fingers, zweihanders without reach, and the average man not knowing bears live in caves.

[Phelix-Mu]

The flip side of this is that 3d6 (which I don't use, though I see the appeal) does mitigate the problem with skills. Taking two level 1 people, one a highly-trained specialist and one a total total novice.

So an untalented novice should be an expert at their own game a little better than one time in seven tries. That seems... odd.

With 3d6, the novice will only match him around 4% of the time, actually beating him less than 2% of the time. 1-in-25 or 1-in-50 reflects what we'd expect of such an opposed check more than the d20 roll does.

So yeah, I can see the appeal of a bell curve.


Sure. That's how it works. You're also much less likely to get a critical hit or critical failure. You've only got a .5% chance of hitting either one. It regulates numbers away from the edges, which is generally more reflective of real life. that's the claim at least. If you usually jump ten feet, it makes more sense that you'd have a higher chance of jumping ten feet than jumping twenty or one feet (The numbers are probably a little off, but just substitute actual skill check stuff in your brain). Folks tend to have skills that approximate bell curves rather than linear progressions.

For skills, the area where 3d6 is, I think, most persuasive, there already is a mechanic for achieving an average result, Take 10. If you think that this should be more available, then just adjust the rules to allow it to be used under stress, or add in an ability at level x in any class that someone of that level can start to Take 10 on all class skills, even under pressure or when rushing, etc. Change classes that grant some form of Skill Mastery to Take 12 or 15 or some such.

Take 10 can also be extended to other types of rolls, should you think this necessary.

Seems much easier than just re-writing dice rolls the game over.

[Raven777]

bears live in caves.

Wait, what?!? ALL THIS TIME I LIVED A LIE!

[JusticeZero]

Most ordinary people, when making skill checks, will either Take 10 or Take 20. Doesn't get much more predictable than a fixed number.

[Snowbluff]

Wait, what?!? ALL THIS TIME I LIVED A LIE!
Don't worry, some of them live on ice. :smalltongue:

Most ordinary people, when making skill checks, will either Take 10 or Take 20. Doesn't get much more predictable than a fixed number.

I am going to have to ask you and Phelix to stop making sense.

[limejuicepowder]

There's another funny thing to consider as well when it comes to bonuses to the roll. Because the 3d6 is weighed to middle of the road rolls, bonuses that bring you below that middle roll are less useful.

Ex: fighter A has an attack bonus of +8. Fighter B has an AC of 18, meaning fighter A needs a 10 to hit (62.5%). If fighter A's attack was only +7, he'd need have a 50% chance. If it was +9, he'd have a 73%. Thus, going from 7 to 8 is a +12%, but 8 to 9 is only +11%. The diminishing returns drop off quite quickly as well - 16 to 17 is only +3%. Something as simple as flanking or shaken could swing the character's chance of success by as much as 23%.

With the d20, each bonus or penalty is worth the same 5% (until you get to the upper and lower limits).

[eggynack]

Eggynack, assuming that was sarcasm, you are smarter than this...

Case study.
Citation needed.

Then there is the assumption we are simulating real life, with knights encumbered by armor, locks that can be picked with fingers, zweihanders without reach, and the average man not knowing bears live in caves.
Well, even if it's never going to happen, I've gotta figure that I'm more likely to jump twenty feet five percent of the time than that I'd be able to jump fifteen feet about nine percent of the time, and twenty feet none of the time. I guess I could jump repeatedly, and test whether I tend towards my average jump length and height, but I'm pretty sure that I will. If I jump a certain height once, I'm pretty likely going to jump that height most of the time. People are actually just more likely to get average results than extraordinarily bad or good results. I should probably do some actual checks for bell curve applications, but I'm pretty sure it'll work out. It's why we have bell curves in the first place, after all.

Edit: Actually, I think that average grades might provide a better example. In this case, it'd presumably correlate to knowledge checks. Grades distribute around a bell curve, rather than a linear d20 distribution. I can probably find statistics for that a lot easier.

[shadow_archmagi]

Most ordinary people, when making skill checks, will either Take 10 or Take 20. Doesn't get much more predictable than a fixed number.

To be fair though, taking 10 has its own issues.

[Snowbluff]

Well, even if it's never going to happen, I've gotta figure that I'm more likely to jump twenty feet five percent of the time than that I'd be able to jump fifteen feet about nine percent of the time, and twenty feet none of the time. I guess I could jump repeatedly, and test whether I tend towards my average jump length and height, but I'm pretty sure that I will. If I jump a certain height once, I'm pretty likely going to jump that height most of the time. People are actually just more likely to get average results than extraordinarily bad or good results. I should probably do some actual checks for bell curve applications, but I'm pretty sure it'll work out. It's why we have bell curves in the first place, after all.

Edit: Actually, I think that average grades might provide a better example. In this case, it'd presumably correlate to knowledge checks. Grades distribute around a bell curve, rather than a linear d20 distribution. I can probably find statistics for that a lot easier. Well, I don't know about you, but my standing just tends to vary rather wildly. Considering that the average man can JUMP 13 FEAT if they put any training into it, while the record is 29 feat, and I seem to recall most people don't even manage 5.

The problem is that you are using the premise of reality when nitpicking can destroy the reality of the game before we touch magic.

[Lapak]

For skills, the area where 3d6 is, I think, most persuasive, there already is a mechanic for achieving an average result, Take 10. If you think that this should be more available, then just adjust the rules to allow it to be used under stress, or add in an ability at level x in any class that someone of that level can start to Take 10 on all class skills, even under pressure or when rushing, etc. Change classes that grant some form of Skill Mastery to Take 12 or 15 or some such.

Take 10 can also be extended to other types of rolls, should you think this necessary.

Seems much easier than just re-writing dice rolls the game over.Opposed rolls (such as in the situation I'm suggesting) are specifically not take-10 situations for a reason; there IS supposed to be a chance that the novice can beat the expert, it should just be extremely remote. And I'm not even talking about high-level characters here, or even those with PC class levels that might have a Skill Mastery type ability, I'm just talking about two pretty ordinary characters. (Even if I was, requiring levels in a Skill Mastery class to perform better than untrained people on a consistent basis is as damaging to suspension of disbelief as the d20 roll is.)

As I said, I don't in fact USE 3d6 - I still do use d20. But a bell curve provides a much simpler and (I'd argue) more elegant fix for some specific issues than meddling with the rest of the mechanics around skill checks does.

[JusticeZero]

Rolls are made "under stress". Which ordinary people rarely experience. Randomness can indicate stumbling under a high adrenaline load or being aided by one. ("Until that animal came running out of the woods, I didn't even think I could climb a tree! Shut up and get me a ladder.. ") Take 10 works fine. If you really dislike it, have people Take 4d4 instead. You'll get similar results.

[eggynack]

Well, I don't know about you, but my standing just tends to vary rather wildly. Considering that the average man can JUMP 13 FEAT if they put any training into it, while the record is 29 feat, and I seem to recall most people don't even manage 5.

The problem is that you are using the premise of reality when nitpicking can destroy the reality of the game before we touch magic.
Yeah, jumping is weird. The test thing might work better. I'm pretty sure that most standardized tests have a results distribution that reflects a bell curve, and my personal performance generally remains pretty static. The latter is obviously anecdotal, but I doubt I'm going to get a perfectly even distribution of test results. The former thing can probably be looked up too, given my masterful having of the internet. There's a fancy graph hereabouts (http://en.wikipedia.org/wiki/SAT#Raw_scores.2C_scaled_scores.2C_and_percentiles ), and there's likely better data out there. Like, piles and piles of data, spanning back all the way to forever. Basically, it's usually going to look like a bell curve.

[Snowbluff]

Yeah, jumping is weird. The test thing might work better. I'm pretty sure that most standardized tests have a results distribution that reflects a bell curve, and my personal performance generally remains pretty static. The latter is obviously anecdotal, but I doubt I'm going to get a perfectly even distribution of test results. The former thing can probably be looked up too, given my masterful having of the internet. There's a fancy graph hereabouts (http://en.wikipedia.org/wiki/SAT#Raw_scores.2C_scaled_scores.2C_and_percentiles ), and there's likely better data out there. Like, piles and piles of data, spanning back all the way to forever. Basically, it's usually going to look like a bell curve.

Yeah, jumping is definitely weird.

As for those graphs, you might want to look at results of people with disabilities like ADHD. Most adventurers have it. Trust me. I am the Avatar of PC-dumb.

Additionally, keep in mind that results from nowadays might not correlate well to the medieval setting.

[navar100]

Right, which isn't predictable at all. The entire range of numbers has an equal chance. Meanwhile, with 3d6, you can predict you will, 50% of the time, roll between 9 and 12, and you only have a 1:6 chance of rolling 3-7 and a 1:6 chance of rolling 14-18. Before you drop the dice, you have a very clear idea of what your roll is likely to end up, so you can predict what actions are likely to do well or which ones are going to be impossibly difficult. If you're as likely to roll a 1 as a 10 as a 20, you have no basis for predicting the outcome of your roll.

But you do generally know the lowest number you need to succeed at a task, so you still know the percentage chance.

[Arcane_Snowman]

Whilst rolling 3d6 is more reliable in a mathematical sense, it does not lend itself well to standard D&D as it was never created with that kind of dice rolling mechanic in mind:
Whilst the rolling of multiple dice might help secure a more average result over multiple actions, it also greatly mucks with the challenge rating system (more so than the challenge rating system mucks with itself) as disparity between bonuses between combatants become more important, and thus making creatures of a higher CR compared to the player characters significantly stronger.

It helps inject some reality into the game, but D&D was never about reality.

That being said, I can see it making for an interesting E6/8 game, provided you fiddle with the armor numbers a bit.

[Drachasor]

Without heavily adjusting the game, I'd say that 3d6 is actually the broken mechanic. It's makes +1 bonuses and -1 penalties around the middle very strong and if you string a few +1's together then you are really, really good at hitting or avoiding to get hit. The game makes it pretty easy to do this too, because it wasn't designed with a 3d6 system.

It can also increases the difference between people with slight stat differences, especially early on. As someone said, it also affects martial characters more than casters.

[lsfreak]

Without heavily adjusting the game, I'd say that 3d6 is actually the broken mechanic. It's makes +1 bonuses and -1 penalties around the middle very strong and if you string a few +1's together then you are really, really good at hitting or avoiding to get hit. The game makes it pretty easy to do this too, because it wasn't designed with a 3d6 system.

Of course, you can go the other way too: the little +1's you get at lower levels are damned near meaningless with d20. With tweaking, I'd guess 3d6 is better than d20 in an E6 environment, where the DM can more closely balance encounters and before the level of ridiculous hits that would completely throw balance off in higher-level games.

[Snowbluff]

Of course, you can go the other way too: the little +1's you get at lower levels are damned near meaningless with d20. With tweaking, I'd guess 3d6 is better than d20 in an E6 environment, where the DM can more closely balance encounters and before the level of ridiculous hits that would completely throw balance off in higher-level games.

Every little +1 is worth as much as the previous with a d20.

[eggynack]

Every little +1 is worth as much as the previous with a d20.
This is true. I don't know if it's necessarily a good thing, but it's true. It's really a matter of preference. If you want a game to give greater incentives to boosting these rolls, 3d6 is better. If you want the game to not give greater incentives to boosting these rolls, d20 is better. There's no broken or unbroken about it.

Edit: I think anyways. boosting rolls on a d20 is probably better on the top edge, but I'm not sure if comparative rolls on the edge are as important. This is all complicated and stuff. I think that I'm saying that d20 is a higher variance system, while 3d6 is a lower variance system. As I said, it's a preference thing.

[Phelix-Mu]

Part of this just comes down to the classic and hard-to-generalize "is it fun?" issue.

If more realistic probabilites is what you find makes the game fun, then maybe 3d6 will be nice for you.

If you like a slightly less predictable, more dramatic style, then maybe stick with d20.

Either way, I think one should be careful about vivisecting major aspects of the game, changing them in isolation, and then sewing it back up and thinking it's all hunky-dory.