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Aetis
2018-08-27, 08:35 AM
Hello, GITP Forum.

Our group is thinking about using 3d6 instead of d20 for rolls in our games. Has anyone done this? What were some of the pros and cons?

Thinker
2018-08-27, 08:43 AM
Hello, GITP Forum.

Our group is thinking about using 3d6 instead of d20 for rolls in our games. Has anyone done this? What were some of the pros and cons?

3d6 will make your rolls tend to fall more in the 8 - 13 range (~67% of your group's rolls will end up here). That makes it so you'll have far fewer criticals and that average challenges will be overcome with regularity, but more difficult successes will be harder to come by. Normally, you can calculate the benefit of bonuses and penalties as +1 = +5% (and vice versa), which makes it pretty easy to do in your head on the fly. With 3d6, every +1 moves the entire curve by 1. So, the benefits are more consistent rolls and skilled characters being more reliably skilled. The downsides are more difficult to evaluate what a bonus will do for a player and significantly harder to achieve high rolls.

Aetis
2018-08-27, 08:51 AM
Oh, I also forgot to mention that we were also considering using triples (same number three times) as criticals.

Minty
2018-08-27, 08:57 AM
My group tried a homebrew 3d6 system once, but gave up pretty quickly because a few players (including the GM) hated having to constantly add dice together.

We only tried 3d6 because our previous D100 systems were too linear and swingy. In the end, we found what we wanted with a d6 dice pool system with virtually no arithmetic at all, just counting successes, but I'm not sure that's something you could easily adopt if you're playing a D20/D&D type game.

So, I guess, in terms of cons: Some players hate arithmetic. Although this probably isn't an issue if you're coming from a system like D&D, which is like doing taxes.

Aetis
2018-08-27, 09:01 AM
We play on roll20, so dices should automatically add themselves.

DMThac0
2018-08-27, 10:12 AM
It used to be that wargames, survival games, and the first handful of iterations of D&D used only d6, it took a while for the multi-sided dice to come around. Your idea would work just fine, but you'd have to adapt some of the numbers to compensate for the slightly lower averages.

Calthropstu
2018-08-27, 10:26 AM
It used to be that wargames, survival games, and the first handful of iterations of D&D used only d6, it took a while for the multi-sided dice to come around. Your idea would work just fine, but you'd have to adapt some of the numbers to compensate for the slightly lower averages.

Actually, the average is exactly the same (10.5)
It just has a lower ceiling a d higher floor and a tendency to roll average on most rolls.

Thrudd
2018-08-27, 11:04 AM
Oh, I also forgot to mention that we were also considering using triples (same number three times) as criticals.
Triples on three dice is almost half as frequent as rolling 20 on d20 (1/36 instead of 1/20). You would also need to figure out how the Champion or any ability that affects critical chance will work. You may want to just do critical on 16+, which is almost 5%. When champion normally gets critical on 19+, change that to 15+(which is almost 10%).

Goaty14
2018-08-27, 11:14 AM
Also known as the Bell Curve Roll (http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm) (because if you plot out the x = number, y = probability for 3d6, it looks like a bell), you just get more average result, thus reducing the amount of 3's and 18's (replacing 1's and 20's), but makes it far more exhilirating when it does.

Triples will come up in your campaign once if you're lucky. My only commentary is that it benefits the DM/GM more than the PCs because the DM/GM usually makes more rolls against the PCs than the PCs make against the DM/GM, so you might consider only applying it to the PCs.

Red Bear
2018-08-27, 01:27 PM
I prefer to use 2d10

Aetis
2018-08-27, 01:40 PM
I prefer to use 2d10

Interesting. How does that work out for you, compared to 1d20?

CharonsHelper
2018-08-27, 01:45 PM
In general I like bell curves, but I don't think that slapping it onto any version of D&D which is built around a d20 will work well.

It makes fights against things which are already hard to hit much harder, and make getting your AC to the point where foes need a 12+ far more valuable since each point shift around the average of 10.5 has a much larger % swing.

If a system is designed around the bell curve from the ground up it can work great. D&D is not such a system.

Grod_The_Giant
2018-08-27, 01:50 PM
Interesting. How does that work out for you, compared to 1d20?
I've used 2d10 instead of 1d20 plenty of times. It works pretty nicely. You still get a trend towards middle values, but high and low rolls still pop up often enough to be exciting.

oudeis
2018-08-27, 02:02 PM
I have no understanding of statistics whatsoever, but these all seem like methods to reduce the randomness and range of combat resolution mechanics, making them less 'realistic', if the term has any meaning here. What's the benefit from these systems?

Nifft
2018-08-27, 02:25 PM
Oh, I also forgot to mention that we were also considering using triples (same number three times) as criticals.

This is kinda interesting.

You count 1-1-1 and 6-6-6 as critical rolls -- I assume this means both are equally good.

That means you'll have a range of (4,17) and 6 possible critical values outside the range, instead of 3-18.

Are there critical failures, too?

Aetis
2018-08-27, 02:37 PM
111 would be critical fail.

zlefin
2018-08-27, 03:06 PM
never have myself, but there's a short section in the srd which talks about this that has a few useful points
http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm

Minty
2018-08-27, 03:28 PM
I have no understanding of statistics whatsoever, but these all seem like methods to reduce the randomness and range of combat resolution mechanics, making them less 'realistic', if the term has any meaning here. What's the benefit from these systems?

The idea is to make it more realistic by increasing the frequency of average results, and decreasing the frequency of extreme results.

Anonymouswizard
2018-08-27, 03:31 PM
The short answer is that is increases the importance of character stats and reduces the importance of the die, because most rolls will be within a relatively small range. The game also becomes more predictable.

You can go into exactly how it affects things, but the short answer is that extreme results are less likely, so character stats are more important (although may have a lower 'effective' ceiling, depending on the game).

Mordar
2018-08-27, 03:32 PM
I have no understanding of statistics whatsoever, but these all seem like methods to reduce the randomness and range of combat resolution mechanics, making them less 'realistic', if the term has any meaning here. What's the benefit from these systems?

The benefit is actually increased realism. Decreasing the randomness of the system is one way to enhance the impact of skill on skill resolution, thus more often skillful people will succeed at their skilled tasks, and unskilled people will succeed less often at those same tasks. Sometimes you'll still be unlucky and fail (or lucky and succeed), but more often than under d20, you'll succeed or fail based on your skill, not the number that showed on the die.

Shifting to 2d10 or 3d6 decreases the chances of "outrageous fortune" on both ends. It makes it less likely that goblin with a sling will harm your level 10 fighter in full plate armor, or that the same fighter will miss the goblin standing right in front of him. It makes it less likely your Cleric will forget some key tenet of their God's scripture, but also less likely the cleric can accidentally pick the lock on the poor box (assuming the God isn't a God of Thieves, that is).

Chance still exists, but it is less impactful. Assuming a middle range on rolls represents an absence of luck, rolls of 9-12 rely most heavily on the skill of the actor. On a d20 the odds of rolling 9-12 are 20%. On 3d6 the odds of 9-12 are 48%. So, if you will, changing to 3d6 puts success or failure in the character's hands about half the time vs. 1/5th the time.

- M

Thrudd
2018-08-27, 03:47 PM
111 would be critical fail.
That is very low odds- less than half a percent chance to get one particular triple result (1/216). If critical fail or success only happens on one possible result, you are almost never going to see them. It is over ten times more rare than rolling 1s or 20s on ad20. That is ok for critical fails, maybe (they generally aren't a good idea anyway), but critical hits are sometimes factored into abilities of characters -because we're obviously talking about a D&D-type game, not GURPS or anything else that is designed to use 3d6. You want to look at the math.

AmberVael
2018-08-27, 04:34 PM
I do not advise replacing d20 with 3d6 for most existing games. The issue is simple: you're changing up the probability model significantly, and the rules probably aren't designed to handle it. You'd need to go through and alter roll modifiers and redetermine what are appropriate challenges for a party, because anything that was challenging before is going to be nearly impossible now.

Jama7301
2018-08-27, 05:08 PM
I do not advise replacing d20 with 3d6 for most existing games. The issue is simple: you're changing up the probability model significantly, and the rules probably aren't designed to handle it. You'd need to go through and alter roll modifiers and redetermine what are appropriate challenges for a party, because anything that was challenging before is going to be nearly impossible now.

This is what I was thinking about when it was proposed. While a straight switch can work, I feel like there's something that would go awry by messing with the underlying math. If you need a 12 to hit the the target, that's, what, a 45% chance on a d20? A 12+ on 3d6 is (if I did my math right) around 37.5%. It feels like you'd have to adjust a lot of ACs and saves, and attack rolls to make things fall in line.

Nifft
2018-08-27, 05:18 PM
111 would be critical fail. What about 2-2-2, 3-3-3, 4-4-4, and 5-5-5?


That is very low odds- less than half a percent chance to get one particular triple result (1/216). If critical fail or success only happens on one possible result, you are almost never going to see them. It is over ten times more rare than rolling 1s or 20s on ad20. That is ok for critical fails, maybe (they generally aren't a good idea anyway), but critical hits are sometimes factored into abilities of characters -because we're obviously talking about a D&D-type game, not GURPS or anything else that is designed to use 3d6. You want to look at the math.

Yeah.

It also means that critical success is less than the previously-assumed 1/36 chance.

(How much less depends on the answer to my question about the other triples.)

Jay R
2018-08-27, 05:37 PM
This system makes things variable in ways that don't necessarily make sense.

A +1 sword is worth an additional +0.5% to +12.5%, depending on the needed roll.
A +5 sword is worth an additional +0.5% to +57.9%, depending on the needed roll.

Similarly, a +2 circumstance bonus could be worth anywhere from +1.9% to +25%.

oudeis
2018-08-27, 06:03 PM
This system makes things variable in ways that don't necessarily make sense.

A +1 sword is worth an additional +0.5% to +12.5%, depending on the needed roll.
A +5 sword is worth an additional +0.5% to +57.9%, depending on the needed roll.

Similarly, a +2 circumstance bonus could be worth anywhere from +1.9% to +25%.

...what...

CharonsHelper
2018-08-27, 06:09 PM
...what...

It's how the probabilities work out due to being on a bell curve rather than the linear odds of a single d20.

As I said above, systems can work well if they're designed for such from the ground up, but D&D was not, so I consider 3d6 to be a bad fit for D&D.

(Though that's just the base %. If you start talking about the % increases in accuracy, both bell curve and linear odds start getting more complex.)

Nifft
2018-08-27, 06:31 PM
This system makes things variable in ways that don't necessarily make sense.

A +1 sword is worth an additional +0.5% to +12.5%, depending on the needed roll.
A +5 sword is worth an additional +0.5% to +57.9%, depending on the needed roll.

Similarly, a +2 circumstance bonus could be worth anywhere from +1.9% to +25%.

Using a d20 with a uniform distribution, a +2 bonus could increase your chance of success by +100%, depending on the needed roll.

Not making sense is a consequence of the framing language, not the dice.

3d6 makes perfect sense.

Saintheart
2018-08-27, 06:37 PM
...what...

Maybe try starting with the Angry DM's article on probability for gamers (https://theangrygm.com/probability-for-gamers/). I found it pretty enlightening. It also goes through the difference between 3d6 vs. d20 rolls.

Aetis
2018-08-27, 06:42 PM
What about 2-2-2, 3-3-3, 4-4-4, and 5-5-5?

They would threaten a crit.

Aetis
2018-08-27, 06:45 PM
Huh. Interesting side-effect of this switch is that "taking an 18" on a roll would actually approximately take 200 times the length of the action.

If you spend about 20 times the amount of time it takes to do the action, you would be "taking a 15" instead.

Red Bear
2018-08-27, 06:58 PM
I've used 2d10 instead of 1d20 plenty of times. It works pretty nicely. You still get a trend towards middle values, but high and low rolls still pop up often enough to be exciting.


The idea is to make it more realistic by increasing the frequency of average results, and decreasing the frequency of extreme results.

yeah what they said. In many situation I feel that 1d20 is too random compared to modifiers of around +3/+6 it feels too likely that the untrained person who does something for the first time does a better job than the person who basically devoted his entire career (and maybe build) to that. I fell 2d10 mostly works without reducing too much low rolls but it's also personal, I get more frustrated by missing unarmoured goblins some of the times than almost never hitting a monster with very high AC, because in those cases you can use other techniques anyway like spell with saving throws.
Also I have never played with a build optimized for critical so I never experienced the downside of having less critical hits.

Calthropstu
2018-08-27, 07:19 PM
Using a d20 with a uniform distribution, a +2 bonus could increase your chance of success by +100%, depending on the needed roll.

Not making sense is a consequence of the framing language, not the dice.

3d6 makes perfect sense.

You are wrong.

In d20 you never have worse than a 5% chance to hit. Now lets take a look at some scenarios.

D20 your opponent has ac 25 and you have +5 to hit with a normal sword. You have 5% chance to hit.
You have a magic sword that hasn't been identified so an unspecified bonus. You grab it and swing.

We know each +1 will increase your chance to hit by 5% up to a maximum of +25%

But what if it were 3d6 instead.

To make this easier we will reduce the monster's ac by 2.
So we need an 18 to hit, which is a 1/216 chance. Less than .5%
Now we add +1 weapon. Now we need a 17. We can get 17 with: 6-6-5, 6-5-6, 5-6-6 and an 18 also hits for a total of 4 permutations or 4/216 or 1/54 for a total of 2℅
Now we have a +2 weapon. Now we need 16 to hit. We have the 4 from 17+ to hit as well as 6-6-4, 6-5-5, 6-4-6, 5-6-5, 5-5-6, 4-6-6 for total of 6 chances added to our 4 from 17+ which makes 10/216 or 5/108

We finally came close to the 5% mark needed to make a 20.

Let's keep going. Now our sword is a +3
We need 15+ to hit.now our permutations are getting much more numerous. 6-6-3, 6-5-4, 6-4-5, 6-3-6, 5-6-4, 5-5-5, 5-4-6, 4-6-5, 4-5-6
So added to the 10 chances from 16+ we now have 19 total chances. So now we are at 19/216

Are you starting to see the issue here?

Now let's raise the fighters bonus to +10. He now starts needing a 13+ to hit. Odds are about 40% on a d20 while it's 25% on 3d6. But what happens with a +5 sword? You need an 8 to hit.
Obviously with the d20 you get 65%. With the 3d6 you now have an 83% chance to hit. Yes, +5 from needing 13 to hit goes from 25% to hit to an 83% chance.
As to hit climbs your chance to hit eventually rises to 99.537%
That skewering of the odds means a +1 is either MASSIVE or utterly useless.

Nifft
2018-08-27, 07:53 PM
Using a d20 with a uniform distribution, a +2 bonus could increase your chance of success by +100%, depending on the needed roll.

Not making sense is a consequence of the framing language, not the dice.

3d6 makes perfect sense.


You are wrong.

In d20 you never have worse than a 5% chance to hit. Now lets take a look at some scenarios. Heh, as expected, someone didn't understand the framing language.

If you start with a 10% chance to hit, and you get +2 -> 20% chance, your chance to hit has increased by 100%.

Next time, read a bit more carefully, and don't assume that other people are wrong when they say something you don't immediately understand.


So yeah, I'm right and d20 can be framed in confusing ways -- in this example, the volunteer who got confused was Calthropstu, but it's the sort of thing that could catch anyone. 3d6 can be framed in confusing ways, too. That's not a problem with either dice mechanism.

Thrudd
2018-08-27, 08:27 PM
You are wrong.

In d20 you never have worse than a 5% chance to hit. Now lets take a look at some scenarios.

D20 your opponent has ac 25 and you have +5 to hit with a normal sword. You have 5% chance to hit.
You have a magic sword that hasn't been identified so an unspecified bonus. You grab it and swing.

We know each +1 will increase your chance to hit by 5% up to a maximum of +25%

But what if it were 3d6 instead.

To make this easier we will reduce the monster's ac by 2.
So we need an 18 to hit, which is a 1/216 chance. Less than .5%
Now we add +1 weapon. Now we need a 17. We can get 17 with: 6-6-5, 6-5-6, 5-6-6 and an 18 also hits for a total of 4 permutations or 4/216 or 1/54 for a total of 2℅
Now we have a +2 weapon. Now we need 16 to hit. We have the 4 from 17+ to hit as well as 6-6-4, 6-5-5, 6-4-6, 5-6-5, 5-5-6, 4-6-6 for total of 6 chances added to our 4 from 17+ which makes 10/216 or 5/108

We finally came close to the 5% mark needed to make a 20.

Let's keep going. Now our sword is a +3
We need 15+ to hit.now our permutations are getting much more numerous. 6-6-3, 6-5-4, 6-4-5, 6-3-6, 5-6-4, 5-5-5, 5-4-6, 4-6-5, 4-5-6
So added to the 10 chances from 16+ we now have 19 total chances. So now we are at 19/216

Are you starting to see the issue here?

Now let's raise the fighters bonus to +10. He now starts needing a 13+ to hit. Odds are about 40% on a d20 while it's 25% on 3d6. But what happens with a +5 sword? You need an 8 to hit.
Obviously with the d20 you get 65%. With the 3d6 you now have an 83% chance to hit. Yes, +5 from needing 13 to hit goes from 25% to hit to an 83% chance.
As to hit climbs your chance to hit eventually rises to 99.537%
That skewering of the odds means a +1 is either MASSIVE or utterly useless.

yes, you can't just replace the d20 with 3d6 in a system designed for a d20. It's going to create some wacky results if you try to use the same target numbers. The whole system needs to be revised to account for the new probabilities, especially how you estimate challenge levels. You need to think about every single sort of roll, and decide how often you think such a thing ought to succeed, taking into account the type of bonuses you might expect characters to have and/or t get, and reassign DCs according to the dice system being used.

Nifft
2018-08-27, 08:33 PM
yes, you can't just replace the d20 with 3d6 in a system designed for a d20. It's going to create some wacky results if you try to use the same target numbers. The whole system needs to be revised to account for the new probabilities, especially how you estimate challenge levels. You need to think about every single sort of roll, and decide how often you think such a thing ought to succeed, taking into account the type of bonuses you might expect characters to have and/or t get, and reassign DCs according to the dice system being used.

Yes.

Also it's interesting to note that all the criticisms -- "a +1 is either MASSIVE or utterly useless" -- also apply to d20, since a +1 when you would succeed on a 1 is useless, and a +1 when you would otherwise need a 19 is "MASSIVE".

Calthropstu
2018-08-27, 09:53 PM
Yes.

Also it's interesting to note that all the criticisms -- "a +1 is either MASSIVE or utterly useless" -- also apply to d20, since a +1 when you would succeed on a 1 is useless, and a +1 when you would otherwise need a 19 is "MASSIVE".

Increasing odds by 5% isn't exactly massive. Even 25% from a +5 sword isn't that huge considering the investment required.

But going from needing an 11 to hit to a 10 for the cost of a +1 weapon is the same as getting a +3 weapon for a d20. Conversely, going from needing an 18 to a 17 or anything 5 or higher to 4+ is less than 1/4 as effective.

The 3d6 exacarbates all the issues of d20 and skews the results so greatly.

Lunali
2018-08-27, 10:56 PM
My advice would be instead of trying to force D&D to use a radically different probability distribution, check out other RPGs that already use them and adapt them to your tastes. The results of changing the core odds are far more difficult to predict than the results of altering other rules to suit your tastes.

VincentTakeda
2018-08-28, 12:38 AM
In the battle between the cognitive dissonance of failing an easy task 5% of the time (d20 model) vs the everything happens the way it should model of the 3d6 bell curve (easy things are amazingly common, difficult things can be made amazingly common with a very small amount of bonuses, and nearly impossible things can be modified to become coin tosses) I vote for d20 hands down full stop 100 percent of the time.

I became a gamer because i like flat probabilities. The swinginess is a feature not a bug for me. Failures create excitement and the flatness and reliability that 3d6 gaming makes inherently quickly became fantastically dull. Over time (and increasingly over increasing time), if you only fail an easy task one time out of 200 you violate the 'why bother rolling at all when the outcome isn't interesting' trope. Similarly if the party can get a few paltry bonuses together and are suddenly accomplishing the amazingly difficult half the time... They're still succeeding at amazing things 50 percent of the time where a d20 party does something amazing 1 time out of 20. It's like gaming with training wheels.

3d6 with bonuses takes the amazing out of amazing and makes the simple tasks not even rollworthy.

Even if you guarantee the sanctity of the bell curve function by taking away the possibility of bonuses it's still bad. Lets say your players are fighting thanos and in a bonus free system they need an 18 to hit him. They will statistically miss 108 times before anyone even touches him, only statistically to fail another 108 times after that. To quote Thanos... 'all that for one drop of blood'... your players will not enjoy failing 108 rolls in a row even if that's a 'more satisfyingly realistic representation of the curve of probabilities.'

They could be making one attack roll per second for nearly a minute and a half with not a single hit, celebrate the amazing statistically accurate single success, only to start the minute and a half of misses over again. Narratively it feels like proper statistical representation, but when the rubber hits the road, it ain't gonna be fun for anyone. 90 seconds of miss rolls will start to seem like an eternity.

Far too easy for 3d6 to become either so easy that its boring or so difficult that its boring. Swinginess is your friend.

5a Violista
2018-08-28, 04:46 AM
In the battle between the cognitive dissonance of failing an easy task 5% of the time (d20 model) vs the everything happens the way it should model of the 3d6 bell curve (easy things are amazingly common, difficult things can be made amazingly common with a very small amount of bonuses, and nearly impossible things can be modified to become coin tosses) I vote for d20 hands down full stop 100 percent of the time.

I became a gamer because i like flat probabilities. The swinginess is a feature not a bug for me. Failures create excitement and the flatness and reliability that 3d6 gaming makes inherently quickly became fantastically dull. Over time (and increasingly over increasing time), if you only fail an easy task one time out of 200 you violate the 'why bother rolling at all when the outcome isn't interesting' trope. Similarly if the party can get a few paltry bonuses together and are suddenly accomplishing the amazingly difficult half the time... They're still succeeding at amazing things 50 percent of the time where a d20 party does something amazing 1 time out of 20. It's like gaming with training wheels.

3d6 with bonuses takes the amazing out of amazing and makes the simple tasks not even rollworthy.

[...]


On the other hand, I prefer 3d6 because it keeps the amazing things amazing and the trivial things trivial.
Creating tactical advantages and properly using your resources in a way to set up bonuses means a lot more with 3d6 than 1d20, and it makes you feel amazing because it was your cleverness and tactics and strategy that set up the win, not a swingy random chance. The bonus for taking advantage of terrain or map layout or abilities means a lot more for a 3d6 than a 1d20, and so if you set up a good strategy then the amazing thing happened because you set it up to be amazing.

Of course, whether something is reliable and dull or strategic and fun entirely depends on what DC the DM/the game set up. Sure, with a DC of 3 or 4 you'll only fail 1 in 200-ish times but if the DM thinks about the probabilities and what advantages/disadvantages/bonuses/detriments are available, then they can easily set up the scenario such that poor tactics leads to a longshot gamble, but a little bit of player-planning and tactics can turn it into a high-tension scene where the players need to find one or two more tactical bonuses and remove one disadvantage before the Big Bad's plans come through. As a result, the 3d6 feels more like actually playing a strategy game compared to the d20's gambling-feeling.

1d20 makes the amazing trivial and makes you wish you hadn't rolled for simple tasks.

...
My point is, if the game is designed around 3d6-with-bonuses then 3d6 rolls can be made to have high stakes and high tension (but if the game is designed around 1d20, a 3d6 would lose its main benefits). TBH, the only intrinsic benefit I can see to a 1d20 is that it makes the statistical-math easy, while 3d6's big intrinsic benefit is that, with liberal enough bonuses available, the game depends more on player skill and strategy than the d20's chancey results.

DaveOTN
2018-08-28, 08:10 AM
What D&D system are you using? Although they all use d20 rolls for most actions, they deal with the probabilities in different ways. In 3.5, there's a tendency for the game to become a race of bonuses - so a 1st level fighter fighting a 1st level goblin, both of whom have AC 15 and a +3 to attack, play out more or less identical to a 12th level fighter fighting a fiendish minotaur, both of whom have AC 35 and +23 to attack. In 5th edition, bonuses are much harder to come by, and the even spread of the die rolls thus becomes much more important - the system is really based around getting 17-20s on that d20 about a fifth of the time. Also you'll have to deal with advantage and disadvantage and nobody wants to roll three blue d6s and three red d6s and decide whether the blues or the reds add up to more :)

DeTess
2018-08-28, 09:06 AM
What D&D system are you using? Although they all use d20 rolls for most actions, they deal with the probabilities in different ways. In 3.5, there's a tendency for the game to become a race of bonuses - so a 1st level fighter fighting a 1st level goblin, both of whom have AC 15 and a +3 to attack, play out more or less identical to a 12th level fighter fighting a fiendish minotaur, both of whom have AC 35 and +23 to attack. In 5th edition, bonuses are much harder to come by, and the even spread of the die rolls thus becomes much more important - the system is really based around getting 17-20s on that d20 about a fifth of the time. Also you'll have to deal with advantage and disadvantage and nobody wants to roll three blue d6s and three red d6s and decide whether the blues or the reds add up to more :)

If I where to try to convert 5e to 3d6, I'd probably make advantage 4 or 5d6 keep the best 3, and disadvantage make it 4 or 5d6 keep the worst 3. I agree that its probably better to pick a system based around rolling d6's, rather than trying to fit dnd to this system though. If a group really wanted a more consistent roll, I'd probably use 2d10, as that's still somewhat manageable when converting.

MoiMagnus
2018-08-28, 09:58 AM
Using 3d6 mean more works for the DM. Why? Because if the DM fails to balance correctly the game, or if one player exploit too much a feature, or at the contrary if a player is just less skilled than the other players, you will ends up with test of DC (after subtracting every bonus to the roll) of 5 or 15 instead of 10.

If your are playing with a d20, it will just double your chances of success/failure. The game will feel a little unbalanced, but will still be playable. If you are playing with 3d6, the system will just break since test become impossible or auto-success.

Which mean that the DM has to make even more work to ensure that the game is balanced. (Particularly, making sure he/she does not give too much magic weapons to the players)

Assuming you do manage to maintain a balanced game, it will result into a game rewarding skill and strategy much more significantly. Which is good if that's what your players want, but make sure all of them is ok with that. Moreover, the more you play strategically, the less the game advance quickly, so expect longer encounters.

Segev
2018-08-28, 11:33 AM
When people suggest using 3d6 to replace 1d20, I like to suggest adding 2 Fudge Dice to it. Fudge Dice have two +1s, two -1s, and two 0 sides, and are cubes. Adding these restores the potential range to being 1-20, while keeping the general bell curve of 3d6. (Three 1s and two -1s leads to a 1; three 6s and two +1s leads to a 20.) The odds are vanishingly small for either of the extreme results, though.


For D&D, I generally recommend against going for the bell curve, anyway. It is balanced around the flat probability curve of the d20. 3e and PF introduced taking 10 to eliminate the swing where it shouldn't be there. 5e instead just tells the DM not to ask for a roll if there shouldn't be a swing, and grant more auto-successes (and auto-fails).

Aetis
2018-08-28, 12:20 PM
I've heard the arguments before, but has anyone actually tried using the 3d6 at their table?

I'm hoping to hear more about some first-hand experiences.

Aetis
2018-08-28, 12:25 PM
When people suggest using 3d6 to replace 1d20, I like to suggest adding 2 Fudge Dice to it. Fudge Dice have two +1s, two -1s, and two 0 sides, and are cubes. Adding these restores the potential range to being 1-20, while keeping the general bell curve of 3d6. (Three 1s and two -1s leads to a 1; three 6s and two +1s leads to a 20.) The odds are vanishingly small for either of the extreme results, though.

This is interesting, and I have never heard of this before.

Have you seen this in action?

Mastikator
2018-08-28, 12:40 PM
You are wrong.

[math]
That skewering of the odds means a +1 is either MASSIVE or utterly useless.

Take a scenario from D&D.

The enemy's "to hit" bonus is +10

Your AC is 20, there's a 50% chance to hit. Increase it by 1 and now it's 45% chance to hit, it's not utterly useless but it is below the very subjective "who cares" limit.

If your AC is 28 then that +1 extra armor would take you from 10% chance of being hit to 5%, that's actually half DPS you're receiving.

This skewing only happens when you're at the edge and it means you wanna stack up all the bonuses or skip them completely, a 3d6 means this skewing happens across the entire range and you always want bonuses. I'd say 3d6 is too much though and 2d10 is preferred.

CharonsHelper
2018-08-28, 12:59 PM
When people suggest using 3d6 to replace 1d20, I like to suggest adding 2 Fudge Dice to it. Fudge Dice have two +1s, two -1s, and two 0 sides, and are cubes. Adding these restores the potential range to being 1-20, while keeping the general bell curve of 3d6. (Three 1s and two -1s leads to a 1; three 6s and two +1s leads to a 20.) The odds are vanishingly small for either of the extreme results, though.


It seems that it would also slow down play substantially.

Segev
2018-08-28, 01:00 PM
This is interesting, and I have never heard of this before.

Have you seen this in action?

I have not. But the odds are easy enough to calculate, especially with tools like Anydice.com. All it does is smear out the distribution enough to open back up 1,2,19, and 20 as possibilities.

Mordar
2018-08-28, 01:12 PM
Heh, as expected, someone didn't understand the framing language.

If you start with a 10% chance to hit, and you get +2 -> 20% chance, your chance to hit has increased by 100%.

Next time, read a bit more carefully, and don't assume that other people are wrong when they say something you don't immediately understand.

Legitimate, and exactly the kind of language trick used by pharma to hype their products.

Drug X reduces the mortality rate of Disease from 1.5% to 1.0%. Drug X has other good effects and is probably a useful and valuable product. Now...will MegaPharma say "Drug X is linked to a mortality rate reduction of 0.5%" or will they say "Drug X could cut your risk of dying from Disease by a third!"?

Technically true but intentionally misleading.

How did GURPS handle all of this sort of thing? Didn't it use a 3d6 resolution system back in the day?

- M

Aetis
2018-08-28, 01:23 PM
I have not. But the odds are easy enough to calculate, especially with tools like Anydice.com. All it does is smear out the distribution enough to open back up 1,2,19, and 20 as possibilities.

Actually, you gave me a great idea. I have no reason to limit myself to nice looking dice combinations, since my table just plays on roll20 and our dice are calculated automatically at a click of a button.

I agree 3d6 is steep and its steepness gives me heebie jeebies, and after some experimentation, I present you, 1d2+2d10-2.

This frankenstein monstrosity of a roll gives me 1-20 range with nice linear slopes that are much softer than the 3d6. I have big hopes for this distribution, but I will be trying out other combinations before settling on this one.

Segev
2018-08-28, 01:25 PM
Actually, you gave me a great idea. I have no reason to limit myself to nice looking dice combinations, since my table just plays on roll20 and our dice are calculated automatically at a click of a button.

I agree 3d6 is steep and its steepness gives me heebie jeebies, and after some experimentation, I present you, 1d2+2d10-2.

This frankenstein monstrosity of a roll gives me 1-20 range with nice linear slopes that are much softer than the 3d6. I have big hopes for this distribution, but I will be trying out other combinations before settling on this one.
I wish you luck, sir!

Might I ask why you want the non-flat distribution? Are you seeing too many crits? Too many fails-where-they-should-succeed?

Aetis
2018-08-28, 01:35 PM
I wanted a bit more emphasis on strategy and skill over luck. I understand that high variance is what makes the game fun, but I'm tired of "the lv 1 goblin hits you 5% of the time, even though you have epic gear and numerous buffs". I don't think I necessarily wanted a 3d6 distribution because my goodness that distribution has steep slopes, but I wanted something more bell-curvy than the flat d20.

Segev
2018-08-28, 01:39 PM
I wanted a bit more emphasis on strategy and skill over luck. I understand that high variance is what makes the game fun, but I'm tired of "the lv 1 goblin hits you 5% of the time, even though you have epic gear and numerous buffs". I don't think I necessarily wanted a 3d6 distribution because my goodness that distribution has steep slopes, but I wanted something more bell-curvy than the flat d20.

As alternative thoughts - not saying "don't try your thing," just pointing out some options - consider that the level 1 goblin is doing next to no damage compared to the hp total, and against many PCs may do zero damage entirely thanks to DR from buffs and gear. Additionally, if the foes in question are meant to be no threat, you don't have to roll combat at all; just ask the players to narrate how they defeat them.

Thrudd
2018-08-28, 01:46 PM
Legitimate, and exactly the kind of language trick used by pharma to hype their products.

Drug X reduces the mortality rate of Disease from 1.5% to 1.0%. Drug X has other good effects and is probably a useful and valuable product. Now...will MegaPharma say "Drug X is linked to a mortality rate reduction of 0.5%" or will they say "Drug X could cut your risk of dying from Disease by a third!"?

Technically true but intentionally misleading.

How did GURPS handle all of this sort of thing? Didn't it use a 3d6 resolution system back in the day?

- M

GURPS works in reverse from D&D. You have a skill or attribute number (like melee combat or shooting or car driving) that you are trying to roll under in order to succeed at any task the skill or attribute pertains to. Modifiers are assigned to your skill to reflect different conditions, then you try to roll under the modified (effective) skill. So you want a high skill number, things that make a task easier add to your skill, things that make it harder subtract from the skill.

Assigning your attributes and skills at character creation cost differing amounts of points, the cost for higher skills increases in proportion to the probability curve. There is no rolling for anything, and the cost of increasing your scores with experience are equally weighted according to the curve, so going up from 14 to 15 costs way more than going from 11 to 12.

Anonymouswizard
2018-08-28, 04:32 PM
I've heard the arguments before, but has anyone actually tried using the 3d6 at their table?

I'm hoping to hear more about some first-hand experiences.

I've note bolted it onto D&D, because I don't need all the work :smallyuk:

However I have played and run 3d6 systems. It works much better for 'roll over difficulty' than 'roll under stat' systems, but it still works even then. It makes rolls a lot more predictable, extreme results unlikely, and all those other things, but it also lowers the minimum investment for those '80% success on standard difficulty tasks' due to the huge increase in probability of average numbers.

In addition in a system that is based around more than just hitting the more reliable results allow you to focus on how well or what else much more, although that can also be said of lower difficulty numbers.

The short reason for why 3d6 seems to be popular is that many systems seem to be designed so you'll hit people not specced for defence on a result somewhere between eight and twelve, which is the common range in 3d6 throws. This can boost hit rate from every other attack to over one attack in four.

On the other hand you also have dice pool systems, which tend to give each die an X% chance of success, and tends towards even more reliable results than 3d6 if your dice pool is big enough (while rolling big pools of dice is good I've seen a tendency for systems to try to keep it under ten dice), while small pools with exploding dice can be more swingy. I like dice pools almost as much as I like d% roll under systems, the only downside for me is shared by non-d% roll under (that it's kind of hard to guage your chances of success from ratings).

Koo Rehtorb
2018-08-28, 06:04 PM
Legitimate, and exactly the kind of language trick used by pharma to hype their products.

It's not a trick at all. If you go from being hit on a 19-20 to being hit on a 20 you have literally halved the damage you're taking. This is a big deal in a game that involves rolling lots of dice.

Mordar
2018-08-28, 06:35 PM
It's not a trick at all. If you go from being hit on a 19-20 to being hit on a 20 you have literally halved the damage you're taking. This is a big deal in a game that involves rolling lots of dice.

Only because this is fun...

(Assuming every hit does equal damage, and assuming normal distribution) Yes, you have reduced the amount of damage you take per successful attack by 50%. That is maximizing the appearance of impact, and is great for hyping a product/item/whatever. But the successful attacks causing that damage are few and far between given the 19-20 are the only successful hits. You have halved the number of attacks that hit you, but you also have really only reduced that number by an absolute 5%.

It is an improvement but it is only noticeable 5% of the time - when the bad guy rolls a 19. Anything less misses anyway, anything more hits anyway.

You couldn't say that +1 halved the damage you're taking if the target number to hit you used to be 12-20 and now it is only 13-20.

That's why I say it is a legitimate trick - advertisers can use which ever magnitude looks better to sell their product so long as they can justify the number.

- M

Koo Rehtorb
2018-08-28, 07:41 PM
Only because this is fun...

(Assuming every hit does equal damage, and assuming normal distribution) Yes, you have reduced the amount of damage you take per successful attack by 50%. That is maximizing the appearance of impact, and is great for hyping a product/item/whatever. But the successful attacks causing that damage are few and far between given the 19-20 are the only successful hits. You have halved the number of attacks that hit you, but you also have really only reduced that number by an absolute 5%.

It is an improvement but it is only noticeable 5% of the time - when the bad guy rolls a 19. Anything less misses anyway, anything more hits anyway.

The issue is you are downplaying the significance of this. Yes, the odds of it mattering for any given attack are 5%. But you don't have one attack rolled at you over the course of your career. A roleplaying game involves literally hundreds of dice being rolled at you over the course of your career and the difference between needing a 19 and needing a 20 will, over time, be massively impactful.


You couldn't say that +1 halved the damage you're taking if the target number to hit you used to be 12-20 and now it is only 13-20.

Well yes. This is one of the big flaws with d20 based systems. That's sort of the point. The fact that the point of AC that makes them go from needing a 19 to needing a 20 to hit you is massively more impactful than making them go from a 10 to 11 is a glaring design flaw.

Kyrell1978
2018-08-28, 09:50 PM
Triples on three dice is almost half as frequent as rolling 20 on d20 (1/36 instead of 1/20). You would also need to figure out how the Champion or any ability that affects critical chance will work. You may want to just do critical on 16+, which is almost 5%. When champion normally gets critical on 19+, change that to 15+(which is almost 10%).

It's actually even worse than that. You have a 1 in 36 chance to roll two sixes on two dice it's a 1 in 216 chance to get all three.

Thrudd
2018-08-28, 10:11 PM
It's actually even worse than that. You have a 1 in 36 chance to roll two sixes on two dice it's a 1 in 216 chance to get all three.

Yeah, and it's 1/36 to get any triple number. That's what was originally proposed, crits on triples, not just triple 6's. I wasn't confused w/two dice odds.

Knaight
2018-08-29, 04:25 AM
This is kinda interesting.

You count 1-1-1 and 6-6-6 as critical rolls -- I assume this means both are equally good.

That means you'll have a range of (4,17) and 6 possible critical values outside the range, instead of 3-18.


I'm reading this the same way you are, and this does interesting things to the probability distribution.

Most notably, you get a surprisingly decent curve - the reduction in probabilities for 6,9,12, and 15 slightly offsets their probabilities, but because they're symmetrical it barely shows up in the curve. The two points of oddity are that the critical chance is exactly equal to the odds of getting a 5 or 16 (individually) and the extent to which the probabilities are weirdly linear. There are four line segments of constant slope* that cross 14 points, instead of 15 for 16. In play it should be a total non issue, but it's a weird little pattern in and of itself.

*Obviously it's discrete math, so there aren't, but it explains the appearance.


I've heard the arguments before, but has anyone actually tried using the 3d6 at their table?

I'm hoping to hear more about some first-hand experiences.
I've played GURPS, and used it elsewhere (incidentally in the d6 system, in that while it isn't a 3d6 system specifically it is an Xd6 system with a variable X, and 3 shows up kind of a lot in my experience). It works just fine, though I wouldn't recommend using it as a d20 replacement in systems built around a d20.

johnbragg
2018-08-29, 05:51 AM
Something I've kicked around, but never gotten to playtest, is having a class or set of classes where the player can choose to roll 3d6 instead of d20, and can spend resources (of some kind) to roll 4d6 or 5d6). Rogue-types, tightly bound to the principles of chance and luck that govern the universe, and able to manipulate them the way spellcasters manipulate the Weave or whatever.

Mordar
2018-08-29, 04:58 PM
The issue is you are downplaying the significance of this. Yes, the odds of it mattering for any given attack are 5%. But you don't have one attack rolled at you over the course of your career. A roleplaying game involves literally hundreds of dice being rolled at you over the course of your career and the difference between needing a 19 and needing a 20 will, over time, be massively impactful.

I think I must be missing something...I'm not undercutting the value of a +1 shield, for instance (level issues aside). Just that it is easy to spin the value as being greater than it really is. In both cases (11>12 and 19>20) over 100 attacks from the respective enemies, 5 fewer attacks will hit (yes, I know...let's just assume perfect distribution for the sake of the argument). The greatest combat outcome impact would be at the high end, but in the sense of fewer deaths of level 5s from housecats, not necessarily from trolls.

I don wonder what the actual level of impact would be over the course of say 10 levels. How many times would that +1 in a d20 system "save" the character (from being hit, and from being killed)? In 3.x vs 4?


Well yes. This is one of the big flaws with d20 based systems. That's sort of the point. The fact that the point of AC that makes them go from needing a 19 to needing a 20 to hit you is massively more impactful than making them go from a 10 to 11 is a glaring design flaw.

Were it not for enemies scaling with heroes, anyway, yes - at least as concerns damage reduction. But shouldn't the peons who already only had a 10% chance to hit you not be a grave concern in any event? The onslaught of goblins versus the armored knight of the realm, if you will. I'm legitimately struggling with that idea (kind of "Supers" fantasy versus "Gritty" fantasy).

- M

Knaight
2018-08-29, 05:18 PM
I think I must be missing something...I'm not undercutting the value of a +1 shield, for instance (level issues aside). Just that it is easy to spin the value as being greater than it really is. In both cases (11>12 and 19>20) over 100 attacks from the respective enemies, 5 fewer attacks will hit (yes, I know...let's just assume perfect distribution for the sake of the argument). The greatest combat outcome impact would be at the high end, but in the sense of fewer deaths of level 5s from housecats, not necessarily from trolls.

However, in terms of incoming damage going from 11-12 means you take 90% as much damage, on average. Going from 19-20 means you take 50% as much damage, on average. That's not "spinning the value as being greater than it really is", that's "using a metric that's more relevant to the actual value".


Well yes. This is one of the big flaws with d20 based systems. That's sort of the point. The fact that the point of AC that makes them go from needing a 19 to needing a 20 to hit you is massively more impactful than making them go from a 10 to 11 is a glaring design flaw.
It's a distinct design trait, but I wouldn't call it a flaw. The decision to have small variations in ability have the smallest effect when up against tasks or opponents very near that ability and the largest effect when vastly distant is a bit weird, but there are reasonable cases for it.


It's actually even worse than that. You have a 1 in 36 chance to roll two sixes on two dice it's a 1 in 216 chance to get all three.
Which goes back to 1/36 if any triple works.

Anonymouswizard
2018-08-29, 05:26 PM
Honestly, I like the idea of all triples being a critical success, and a set of critical benefits that you can spend points on. Like 111 would give one Crit Point and 666 would give six, and you'd have a bunch of effects costing one or more points (with seperate combat and noncombat effects). Bit then you're just doing 'Fantasy AGE Stunts, but rarer'.

Mordar
2018-08-29, 05:50 PM
However, in terms of incoming damage going from 11-12 means you take 90% as much damage, on average. Going from 19-20 means you take 50% as much damage, on average. That's not "spinning the value as being greater than it really is", that's "using a metric that's more relevant to the actual value".

20 perfectly distributed attacks coming in at our sample warriors, each attack does 4 hp if it hits.

The AC 11 character takes 40hp. He bumps his AC to 12, now he takes 36hp. Net real effect = -4hp.
The AC 19 character takes 8hp. She bumps her AC to 20, now she takes 4hp. Net real effect = -4hp.

Putting it in terms of percentage damage reduced doesn't make it more relevant. It arguably makes it less relevant because example 1 is in greater trouble in the first place, and 36hp vs 40hp is more likely to be a difference maker than 4hp vs 8hp for someone with that kind of AC. Again, assumptions abound (such as starting the combat with full or even half hp).

- M

Jama7301
2018-08-29, 05:50 PM
Honestly, I like the idea of all triples being a critical success, and a set of critical benefits that you can spend points on. Like 111 would give one Crit Point and 666 would give six, and you'd have a bunch of effects costing one or more points (with seperate combat and noncombat effects). Bit then you're just doing 'Fantasy AGE Stunts, but rarer'.

This sounds kiiiiinda rad.

Knaight
2018-08-29, 06:10 PM
20 perfectly distributed attacks coming in at our sample warriors, each attack does 4 hp if it hits.

The AC 11 character takes 40hp. He bumps his AC to 12, now he takes 36hp. Net real effect = -4hp.
The AC 19 character takes 8hp. She bumps her AC to 20, now she takes 4hp. Net real effect = -4hp.

Putting it in terms of percentage damage reduced doesn't make it more relevant. It arguably makes it less relevant because example 1 is in greater trouble in the first place, and 36hp vs 40hp is more likely to be a difference maker than 4hp vs 8hp for someone with that kind of AC. Again, assumptions abound (such as starting the combat with full or even half hp).

- M

Treating the number of attacks as a constant is incredibly dubious - fights usually go until they end (in escape or incapacitation), and it's a matter of who goes down first. Taking half as much damage means you have twice as long to take down your opponent, which makes those incoming attacks suddenly a variable.

Mordar
2018-08-29, 06:58 PM
Treating the number of attacks as a constant is incredibly dubious - fights usually go until they end (in escape or incapacitation), and it's a matter of who goes down first. Taking half as much damage means you have twice as long to take down your opponent, which makes those incoming attacks suddenly a variable.

How else to model it then? Take the same 20 housecats/kobolds/whatever and work though the fight? Give each hero 20 or 30 or 40 hits before they fall, and assume they can take out one or two housecats per round?

20 hits
AC11: Kills 6, drops in round 3 after taking 27.0 hits.
AC12: Kills 6, drops in round 3 after taking 24.3 hits.

AC19: Kills 20, took 11 hits.
AC20: Kills 20, took 5.5 hits.

For 30 hits it is again equivalent, with our low AC versions killing 8 housecats and lasting 4 rounds (differential 34.0 vs 30.6 taken) . At 40 hits the AC12 version makes it to 12 killed before falling at the 6th round, while the AC11 only got 10 in 5 rounds (differential at round 5 40 vs 36).

So the 19>20 does see a greater net reduction in damage based on surviving all 10 rounds (if our 11>12 survived all 10 rounds there is a 55.0 vs 49.5 differential, exactly the same), it made no difference in the fight. The 19 was going to win anyway...the 20 is just in better shape to handle the next group of 20 housecats. The 11 and 12 are neck and neck until a certain point at which we see the 12 actually make a round of suvivability difference.

Basically the risk posed by low skill attackers (needing a 19 or 20) is already too low to matter, and for the 11>12 AC characters the difference may make 1 round somewhere along the line.

It looks like it would take larger and larger numbers of low level attackers to make a difference, or potentially attackers that do damage out of "normal line" with their skill.

Please help me understand what I am missing.

- M

Knaight
2018-08-29, 07:42 PM
How else to model it then? Take the same 20 housecats/kobolds/whatever and work though the fight? Give each hero 20 or 30 or 40 hits before they fall, and assume they can take out one or two housecats per round?

You could just use the extremely standard DPR models, but for incoming damage - which is basically what I've been saying all along, among others.

Calthropstu
2018-08-29, 07:48 PM
You could just use the extremely standard DPR models, but for incoming damage - which is basically what I've been saying all along, among others.

Omg...

Bonded accuracy
Housecats.

How many housecats does it take to bring down a lvl 20 fighter?

*Messenger approaches king obviously distressed*
"Sire, terrible news. The country's greatest warrior has been killed."
"What? Who could do such a thing? He was a 20th lvl fighter."
"Someone rubbed cat pheremones into his codpiece. He was mauled by thousands of cats."
King:...

5a Violista
2018-08-29, 07:53 PM
Please help me understand what I am missing.

This is the point, and I'm going to give a similar example you did:

Our character has 100hp and deals 10 damage per turn.

With AC 11, the character takes 40hp per turn.
With AC 12, the character takes 36hp per turn.

With AC 19, the character takes 8hp per turn.
With AC 20, the character takes 4hp per turn.

AC 11, the character dies on the 3rd turn (100/40=2.5) and deals 30 damage.
AC 12, the character dies on the 3rd turn (100/36=2.78) and deals 30 damage.
Net difference: 0 damage, or 0.28 turns

AC 19, the character dies on the 13th turn (100/8=12.5), dealing 130 damage.
AC 20, the character dies on the 25th turn (100/4=25), dealing 250 damage.
Net difference: 120 damage, or 12.5 turns.

At "low" AC, there was almost no difference at all.
At "high" AC, the character's damage output doubled and survivability doubled (well, because damage output per damage received is higher, the character is more than double able to defeat the opponent before being defeated, unless the battle is specifically designed such that the damage you do doesn't make the battle end sooner or easier over time) (but, really, since this is a team game, these are increased even further because then the rest of the team has time to put into place better tactics).

MrSandman
2018-08-30, 07:20 AM
This is the point, and I'm going to give a similar example you did:

Our character has 100hp and deals 10 damage per turn.

With AC 11, the character takes 40hp per turn.
With AC 12, the character takes 36hp per turn.

With AC 19, the character takes 8hp per turn.
With AC 20, the character takes 4hp per turn.

AC 11, the character dies on the 3rd turn (100/40=2.5) and deals 30 damage.
AC 12, the character dies on the 3rd turn (100/36=2.78) and deals 30 damage.
Net difference: 0 damage, or 0.28 turns

AC 19, the character dies on the 13th turn (100/8=12.5), dealing 130 damage.
AC 20, the character dies on the 25th turn (100/4=25), dealing 250 damage.
Net difference: 120 damage, or 12.5 turns.

At "low" AC, there was almost no difference at all.
At "high" AC, the character's damage output doubled and survivability doubled (well, because damage output per damage received is higher, the character is more than double able to defeat the opponent before being defeated, unless the battle is specifically designed such that the damage you do doesn't make the battle end sooner or easier over time) (but, really, since this is a team game, these are increased even further because then the rest of the team has time to put into place better tactics).

But then again, that's only a benefit if you're going to be fighting without magical healing for over thirteen rounds. Otherwise there's hardly any noticeable improvement.

The thing is that it is highly dependent on the context. Does going from 19 to 20 mean that you'll get half of the damage? Yes. Is it such a big deal? Maybe, it depends on your adventuring routine. Can you find examples where going from 12 to 13 gives you a more noticeable improvement than going from 19 to 20? Probably. Can you find examples where the opposite is true? Probably.