D&D General Replacing 1d20 with 3d6 is nearly pointless

[Cadence]

DC 14 with a +4 bonus.

3d6 passes on an 10 or better. So does a d20. Simple. Easy. Clean. Which one passes more often?

d20 passes on 55% of rolls
3d6 passes on 62% of rolls.

Hmm... there seems to be a discrepancy, here.

How about DC18 with a +4 bonus? They both need a 14 or better!

d20 passes on 35% of rolls.
3d6 passes on 16% of rolls.

How can you look at these values, these significant differences in chance to land the hit, and say there's no difference?

I thought that throughout the entire thread they were comparing the 3d6 to the d20 with mods doubled, not to a raw d20 (post 1).

It sounded to me that the point they were trying to make was that switching to 3d6 effectively makes modifiers twice as important, and if you shift the target difficulty to 11 the probabilities all match really well, except at the very ends. (see posts 69, 70, 117, 123).

The bottom graph in 117 should be 3d6 vs. d20. I don't think they were every arguing there was no difference between those.

 

[JiffyPopTart]

DC 14 with a +4 bonus.

3d6 passes on an 10 or better. So does a d20. Simple. Easy. Clean. Which one passes more often?

d20 passes on 55% of rolls
3d6 passes on 62% of rolls.

Hmm... there seems to be a discrepancy, here.

How about DC18 with a +4 bonus? They both need a 14 or better!

d20 passes on 35% of rolls.
3d6 passes on 16% of rolls.

WILD.

How about a DC of 5 with a +2 bonus? Only need a 3 or better!

d20 is a 90%
3d6 is 100% (99.54 if a 3 is an automatic failure, 98.15 if a 3 and 4 are automatic failures)

Okay, okay. That one's a bit cheatsy. Let's bump it up to DC 7 with a +2 bonus.

d20 is 75%
3d6 is 98%

DC 20 with a +4 bonus?

d20 is 25%
3d6 is 4% Charitably we could round up to a 5%.

Now, of course, you can adjust all the DCs of 5e D&D to conform to a 3d6 system... but most people who use 3d6 change absolutely nothing whatsoever other than which dice are being rolled. And especially early game, it means greater competence for PCs and NPCs when DCs and bonuses are lowest.

And late game, when the enemy's AC is 20 and you've got a +13 to the roll? (+6 Proficiency, +5 Attribute, +2 Weapon)

d20 70%
3d6 91%

How can you look at these values, these significant differences in chance to land the hit, and say there's no difference?

This..plus...there hasn't been much discussion of opposed rolls which is where I feel the single die method feels wrong most often.

 

[JiffyPopTart]

I thought that throughout the entire thread they were comparing the 3d6 to the d20 with mods doubled, not to a raw d20 (post 1).

It sounded to me that the point they were trying to make was that switching to 3d6 effectively makes modifiers twice as important, and if you shift the target difficulty to 11 the probabilities all match really well, except at the very ends. (see posts 69, 70, 117, 123).

The bottom graph in 117 should be 3d6 vs. d20. I don't think they were every arguing there was no difference between those.

I'm confused. Much virtual ink has been spilled telling me that 3d6 (or 2d10) doesn't do what I think it does. For me that would be to make rare things rarer and average results more common.

This is a different point than 3d6 does what you want it to but doubling modifiers does the same thing with a single die.

 

[Steampunkette]

I thought that throughout the entire thread they were comparing the 3d6 to the d20 with mods doubled, not to a raw d20 (post 1).

It sounded to me that the point they were trying to make was that switching to 3d6 effectively makes modifiers twice as important, and if you shift the target difficulty to 11 the probabilities all match really well, except at the very ends. (see posts 69, 70, 117, 123).

The bottom graph in 117 should be 3d6 vs. d20. I don't think they were every arguing there was no difference between those.

But who doubles all their mods on a d20 roll?

Who rolls 1d10+5+Mods?

This is a thing no one does to play D&D.

It's mathematically sound but... what's the point of it? Just to say "You can get the same results by making significant changes"?

 

[Cadence]

But who doubles all their mods on a d20 roll?

Who rolls 1d10+5+Mods?

This is a thing no one does to play D&D.

It's mathematically sound but... what's the point of it? Just to say "You can get the same results by making significant changes"?

I wonder if OP felt that when people explain why they switch from a d20 to 3d6, that a lot of them don't talk about how much the switch impacts what modifiers mean. That "When you switch from d20 to 3d6, the biggest thing you're doing is doubling the effect of the modifiers." is big, and if, for example, one thinks modifiers are being too impactful right now with a d20, going 3d6 effectively makes that a lot worse. And if you think the mods have just the right effect now with a d20, then you're going to make them much more impactful if you switch to a 3d6. (And of course, if you wish mods mattered more, then switching to 3d6 would do that).

A secondary point might be that, instead of rolling three dice and adding mods (or two sets of three dice with advantage I guess), one could just roll the d20 and add the doubled mods, or roll a single d10 and either add 5 or reduce the target base from 10 to 5.

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Is switching from d20 to 3d6 that much different in terms of process than keeping d20 and doubling the mods?

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I think for me and my mythical-in-the-back-of-my-head game that there are some skills where the mods don't matter as much and the d20 feels fine, but there are others where the skills feel a lot more important (chess?) and I was contemplating having the roll be 3d6 then. Knowing that d20 with doubled mods gives the same chance at success for much of it, with less chance of flukes at the ends, gives me more options to ponder.

 

[DND_Reborn]

Well, I guess since nothing was refuted in my last post, my point was made.

Wait... did I win the Internet again! Yeah, that is 2 points for me now. (j/k)

 

[FormerlyHemlock]

Use whatever such system you want. But, again, when I see people talking about using 3d6, they don't wax poetic about the crit fail/success system they have attached to it. They talk about the "Bell Curve".

Again, the fact the distribution is curved has nothing to do with the game properties that come out of it.

Of course it's relevant. Multiplicative difficulty is intuitive: if dodging a bullet while crawling is twice as difficult as dodging a bullet while standing, and dodging a bullet while nauseating and vomiting is also twice as difficult as dodging a bullet normally, then it makes sense that dodging a bullet while crawling and vomiting should be about four times as difficult as normal. The 3d6 curve has this property especially in the middle, around the 9-12 range. Every -2 roughly halves your probability of success.

This doesn't work on a d20. If you normally succeed on an 11+, then the penalty for crawling needs to be -5 in order to halve your success rate, and the penalty for vomiting also needs to be -5 to halve your success rate. And that means the penalty for crawling and vomiting is -10, so your success rate drops by a factor of 10 instead of 4.

And that's basically what's wrong with the d20 curve: it's too flat, so difficulty modifiers don't interact as you would intuitively expect.

 

[pemerton]

DC 14 with a +4 bonus.

3d6 passes on an 10 or better. So does a d20. Simple. Easy. Clean. Which one passes more often?

d20 passes on 55% of rolls
3d6 passes on 62% of rolls.

Hmm... there seems to be a discrepancy, here.

How about DC18 with a +4 bonus? They both need a 14 or better!

d20 passes on 35% of rolls.
3d6 passes on 16% of rolls.

WILD.

How about a DC of 5 with a +2 bonus? Only need a 3 or better!

d20 is a 90%
3d6 is 100% (99.54 if a 3 is an automatic failure, 98.15 if a 3 and 4 are automatic failures)

Okay, okay. That one's a bit cheatsy. Let's bump it up to DC 7 with a +2 bonus.

d20 is 75%
3d6 is 98%

DC 20 with a +4 bonus?

d20 is 25%
3d6 is 4% Charitably we could round up to a 5%.

Now, of course, you can adjust all the DCs of 5e D&D to conform to a 3d6 system... but most people who use 3d6 change absolutely nothing whatsoever other than which dice are being rolled. And especially early game, it means greater competence for PCs and NPCs when DCs and bonuses are lowest.

And late game, when the enemy's AC is 20 and you've got a +13 to the roll? (+6 Proficiency, +5 Attribute, +2 Weapon)

d20 70%
3d6 91%

How can you look at these values, these significant differences in chance to land the hit, and say there's no difference?

I'm not @NotAYakk, but I think you've misunderstood the claim.

NO ONE in this thread thinks that rolling 3d6 and rolling d20 produces the same likelihood of success against a given target number.

Rather, the claim is that there is a simple single-die roll that produces much-the-same likelihood of success against a given target number as 3d6 does. Hence changing the spread of results from a linear distribution (which is what a single-die roll gives) to a curved distribution (which is what 3d6 does) has no real relevance to game play. Because you can get almost identical play with a single die roll.

One simple single-die roll that will produce much the same likelihoods as 3d6 is 1d10+5 - in the following list, the values are Target Number, percentage likelihood of meeting or exceeding that target number rolling 3d6, percentage likelihood of meeting or exceeding that target number rolling 1d10+5:

3 or lower	100			100
4			99.5		100
5			98.1		100
6			95.4		100
7			90.7		90
8			83.8		80
9			74.1		70
10			62.5		60
11			50			50
12			37.5		40
13			25.9		30
14			16.2		20
15			9.3			10
16			4.6			0
17			1.9			0
18			0.5			0

There is a marked difference only at the extremes, that is the results that are less than 5% likely on 3d6 (ie rolls of 3, 4 5 on 3d6, which fail against target numbers of 4, 5 and 6 respectively; and rolls of 16, 17, and 18 which succeed against those target numbers respectively).

As was noted in the OP, and has been reiterated since, these correspond (roughly) to the 1 and 20 results on a d20, which in D&D games are often given special treatment in any event (eg auto-fail or auto-success). You could get much the same result as this in play using some sort of exploding-dice-on-a-10 result.

 

[FormerlyHemlock]

One simple single-die roll that will produce much the same likelihoods as 3d6 is 1d10+5 - in the following list, the values are Target Number, percentage likelihood of meeting or exceeding that target number rolling 3d6, percentage likelihood of meeting or exceeding that target number rolling 1d10+5:

3 or lower    100            100
4            99.5        100
5            98.1        100
6            95.4        100
7            90.7        90
8            83.8        80
9            74.1        70
10            62.5        60
11            50            50
12            37.5        40
13            25.9        30
14            16.2        20
15            9.3            10
16            4.6            0
17            1.9            0
18            0.5            0

There is a marked difference only at the extremes, that is the results that are less than 5% likely on 3d6 (ie rolls of 3, 4 5 on 3d6, which fail against target numbers of 4, 5 and 6 respectively; and rolls of 16, 17, and 18 which succeed against those target numbers respectively).

As was noted in the OP, and has been reiterated since, these correspond (roughly) to the 1 and 20 results on a d20, which in D&D games are often given special treatment in any event (eg auto-fail or auto-success). You could get much the same result as this in play using some sort of exploding-dice-on-a-10 result.

As your table shows, every -2 penalty on 3d6 roughly doubles the difficulty of the task, not just at the extreme ends. If you think of a difficulty modifier, like trying to resist falling down while poisoned, as representing the fraction of universes where an average PC's chance of success turns to failure, then you can pick a modifier (or visualize the severity of an existing modifier) by asking what proportion of successes turn to failures under that modifier. If bad footing is a -2 to dodging, then that means it's quite a severe penalty because in half of all possible universes where you would otherwise dodge, you fail. In half of THOSE universes, being nauseated for -2 makes you fail anyway. The penalties stack nicely and intuitively.

Expertise (such as +4 to Dodge) either offsets penalties, or if you have no penalties, starts halving your failure rate instead.

There's no way to choose difficulty modifiers on a d20 which nicely represent multiplicative difficulty this way. On a d20, halving the number of possible successes for an average person requires a -5, and then halving it again requires a -2.5, and then -1.25. A difficulty modifier has no fixed meaning, and rules writers often seem to default to low penalties like -1 or -2 which are fairly meaningless unless you are already penalized. In a 3d6 system like Dungeon Fantasy though, taking a -2 for bad footing has a consistent meaning, and you can meaningfully decide whether buying hobnails for your boots is a good tradeoff ($25; avoids the -2 to attack/-1 to defend for bad footing; basically imposes -1 on your stealth attempts, so the entire party has worse odds of being able to surprise monsters).

Nobody writes or is proposing to write multiplicative difficulty modifiers for d20 ("-5 if your target number otherwise is under 15, otherwise -2") because it's too much of a hassle.

 

[pemerton]

As your table shows, every -2 penalty on 3d6 roughly doubles the difficulty of the task, not just at the extreme ends.

That’s pretty approximate, though I do follow the overall thrust of your post.