Thoughts on using 1d20 instead of 3d6?

[Super Squirrel]

Re: Thoughts on using 1d20 instead of 3d6?

 

I should note here that I'm not wed to 3d6; I'm wed to the bell curve. A 5d6 or 6d6 method would probably work too' date=' but it would change the probabilities of success markedly and +1 would have a whole different meaning within the context of a campaign using such a method.[/quote']

Actually only 3d6 and 4d6 as far as d6 go retain the normal distrubution aspect of a bell curve. The 4d6 has a larger standard deviation meaning that the normal range encompasses more but the expert range encompasses less. Meaning a +1 means less to an average joe.

 

http://tft.brainiac.com/archive/0401/msg00008.html

[Super Squirrel]

Re: Thoughts on using 1d20 instead of 3d6?

 

Remember, the more dice you roll, the tighter to the average you will be. You need more +1's to get outside of the normal range or more -1's to hit under a target.

[TaxiMan]

Re: Thoughts on using 1d20 instead of 3d6?

 

No, you're absolutely right... as the discussion has progressed, my understanding of how 3d6 and d20 compare progressed as well, and some original assumptions I had made turned out to be wrong.

 

Now THAT'S a mature, intelligent and honest post! Repped with my measely 3 - Anyone else want to join in?

[Sean Waters]

Re: Thoughts on using 1d20 instead of 3d6?

 

Now THAT'S a mature' date=' intelligent and honest post! Repped with my measely 3 - Anyone else want to join in?[/quote']

 

Yes, I do.

 

Can I also commend Trebuchet:

 

Thanks for starting an interesting topic, even if I didn't agree with you hardly at all. That's what these boards are for.

 

This thread is in danger of becoming a model of decorum...someone get Vorsch over here (only kidding, buddy!)

[Sean Waters]

Re: Thoughts on using 1d20 instead of 3d6?

 

Actually only 3d6 and 4d6 as far as d6 go retain the normal distrubution aspect of a bell curve. The 4d6 has a larger standard deviation meaning that the normal range encompasses more but the expert range encompasses less. Meaning a +1 means less to an average joe.

 

http://tft.brainiac.com/archive/0401/msg00008.html

 

 

I made up a little game that worked using (just) 4d6 for everything. Whilst I know that the results ought to be reasonably tight to the mid-point, it is astonishing how much variation you get in practice. That's the difference between probablity theory and real dice: with the latter, you tend to remember the really good and really bad rolls, which always seems to come at some pre-destined moment

[McCoy]

Re: Thoughts on using 1d20 instead of 3d6?

 

All of this has brought me one question.... why don't more people take a ton of combat levels? Heck, for 10 points you get +5 OCV with one attack.... screw an extra 2d6 on your EB, spend the points on combat levels and you'll pretty much never miss.

 

-Nate

Primary character concept. About tht only time I buy a ton od combat levels is for bricks. Below average DEX and DCV, but enough levels with HTH, OCV only, that their OCV is double their DCV.

[Sean Waters]

Re: Thoughts on using 1d20 instead of 3d6?

 

Many games (quite rightly IMO) have caps on CV, but not all. You can certainly become the ultimate one-trick-pony with lots of 2 point levels, but, as McCoy says, it is really a question of balance and building a character in concept, not just munchkining your way through the rulebook, fun as that can be on occasion

 

I have to say I'd be wary of a brick with a lot of OCV levels, but it's a big universe.

[Dr. Anomaly]

Re: Thoughts on using 1d20 instead of 3d6?

 

Now THAT'S a mature' date=' intelligent and honest post! Repped with my measely 3 - Anyone else want to join in?[/quote']

I got him yesterday for something else, so I won't be able to do so for a while yet, sadly enough...

[Warp9]

Re: Thoughts on using 1d20 instead of 3d6?

 

Now THAT'S a mature' date=' intelligent and honest post! Repped with my measely 3 - Anyone else want to join in?[/quote']

Yes

[Cancer]

Re: Thoughts on using 1d20 instead of 3d6?

 

I've played a lot of systems, in my decades with the dice,

And in all those years I've never had polyhedra without lice.

But the jinxes when they come, it's never all at once,

Unless you're only rolling one of 'em, and then it's

you

being the dunce.

 

I really hate flat probability density distributions; no matter how skilled the character, he'll always have abject rookie pratfall failures whenever there's a roll to be made. And no matter how absurdly impossible the task cooked up by the munchkin with the trained die, he can succeed.

 

Quite possibly this distaste is the result stumbling into poor GMing with some of those flat-distribution systems, but it's there and no arguing with it. I'm not wedded to 3d6 per se, but there should be some mechanism for producing reasonable expectations of success -- or more properly, assurance against the same failure a completely unskilled individual should suffer -- for routine tasks by skilled individuals. A peaked p.d.f. is a natural way to do this, especially when combined with Hero-style skill adds naturally giving you successively larger probabilistic payoff as you buy more of them.

[The Souljourner]

Re: Thoughts on using 1d20 instead of 3d6?

 

Thanks for the repping, guys. I do eventually come around to the side of reason

[Ura-Maru]

Re: Thoughts on using 1d20 instead of 3d6?

 

‘Taking 10’ and ‘taking 20’ aren’t dependant on which die you’re using.

 

“You don’t have to roll for doing an everyday task†was a pretty common house rule in a lot of games using various systems I’ve been involved in over the years.

 

An interesting alternate ‘curve’ model is the one used in Dream Pod Nine’s Silhouette games.

 

Roll a number of d6s equal to the skill level (these get expensive real fast)

Take the highest number of all the dice

For every extra six, add +1

If ALL the dice come up 1, you fumble.

 

So, fumbles come up pretty commonly if you’re just a beginner (+1), rarely if you’re competent (+2), and almost never if you’re better than that. Extraordinary successes become more and more possible as you get better, but are still never assured.

 

--

Vaguely similar to those ‘dice pool’ games that I hate, but don’t let that fool you.

[prestidigitator]

Re: Thoughts on using 1d20 instead of 3d6?

 

There's nothing wrong with you using a d20 to replace the 3d6 roll. The average is the same so it isn't going to change the average game dynamic. It wil probably have quite a profound effect on individuals though. It suddenly becomes much more difficult to protect yourself with DEX and skills as the chance of hitting, say, even if you have OCV 5 and the target is OCV 13 is 15% as opposed to the current 1 in 216. Moreover, the game becomes less tactical: on a bell curve, suprise manaouvres and small bomuses beceome important: on a straight line, less so.

 

I don't intend to change, but if you try it I'd be interested to know how it went.

I think this is why armor in D20 will never be able to get away from modifying the chance to hit. Their Star Wars system tried to change this, with the result that everyone gets hit all the time and people drop like flies until they are really high level (level and, "profession," do affect Armor Class). How they get to be high in level is beyond me.... Anyway, I think the reason Hero can handle characters like Spiderman nicely in the comic genre and light fighters nicely in the fantasy genre is largely due to the 3d6 distribution.

 

Differing levels of skill should be significant but not totally insurmountable given circumstances. D20 has just never done this well. I had a very competent 9th level Ranger in D20 sneaking around behind cover a quarter mile from a bunch of fully occupied and uncaring, light-blinded, first level orcs in full noon-time daylight, and he technically should have been spotted because he rolled something like a 3 on his Move Silently check (and believe me, we triple-checked all the applicable modifiers). The GM, however, just decided to ignore the result. In Hero, such a circumstance would have been darn near impossible, and I actually would have been okay with him being spotted if he had been so darned unlucky as to roll an 18 (provided a roll was even deemed necessary). Now things would have been very different if he had been underground in near or total darkness with alert and motivated orc guards on duty. Then the unskilled orcs might even have had the edge. Hero, all the way!

[prestidigitator]

Re: Thoughts on using 1d20 instead of 3d6?

 

Actually only 3d6 and 4d6 as far as d6 go retain the normal distrubution aspect of a bell curve. The 4d6 has a larger standard deviation meaning that the normal range encompasses more but the expert range encompasses less. Meaning a +1 means less to an average joe.

 

http://tft.brainiac.com/archive/0401/msg00008.html

Actually, the more dice you roll the closer you will approximate a normal distribution. That actually turns out to be one of the fundamental theorems of statistics. However, that doesn't mean it does what we want it to. A normal distribution with a very small standard deviation (which is perfectly possible) just isn't all that useful or fun for roleplaying, even if it is a , "perfectly shaped," distribution. We could have a computer generate a result that is very, very close to a, "perfect," normal distribution without worrying about the discrete nature of the result nearly so much as with dice, and we still wouldn't be happy if the standard deviation were too small.

[Duke Bushido]

Re: Thoughts on using 1d20 instead of 3d6?

 

Besides, what fun is anything without the DICE?!

 

;D

 

Duke

[Trebuchet]

Re: Thoughts on using 1d20 instead of 3d6?

 

Now THAT'S a mature' date=' intelligent and honest post! Repped with my measely 3 - Anyone else want to join in?[/quote']Beat you to it - I repped him this morning when I thanked him for starting the thread.

[prestidigitator]

Re: Thoughts on using 1d20 instead of 3d6?

 

I suggested d20 because it has a higher resolution than 3d6... +1 is 5% instead of up to 12%. However, its resolution comes at a price - randomness. The maximum value comes up 10 times as often as the maximum value of 3d6. Two successive rolls are likely to have wildly different results...

 

So I don't know that there is a solution to the problem that doesn't cause problems of its own, if you even think there's a problem in the first place.

Well, if all you are worried about is the granularity, roll 3d12 instead of 3d6. The average and overall spread will be doubled, and the standard deviation is (very very nearly) doubled as well. The general shape of the curve is almost exactly the same (except for the discrete nature of the dice). A +1 on 3d6 is amost exactly equivalent to a +2 on 3d12. Here is a direct comparison:

 3d12             3d6
result prob      result prob
------ ----      ------ ----
3-    0.058%
4-    0.23%
5-    0.58%      3-    0.46%
6-    1.2%
7-    2.0%       4-    1.9%
8-    3.2%
9-    4.9%       5-    4.6%
10-    6.9%
11-    9.5%       6-    9.3%
12-    12.7%
13-    16.6%      7-    16.2%
14-    21.1%
15-    26.2%      8-    25.9%
16-    31.7%
17-    37.6%      9-    37.5%
18-    43.8%
19-    50.0%     10-    50.0%
20-    56.3%
21-    62.4%     11-    62.5%
22-    68.3%
23-    73.8%     12-    74.1%
24-    78.9%
25-    83.4%     13-    83.8%
26-    87.3%
27-    90.5%     14-    90.7%
28-    93.1%
29-    95.1%     15-    95.4%
30-    96.8%
31-    98.0%     16-    98.1%
32-    98.8%
33-    99.4%     17-    99.5%
34-    99.8%
35-    99.9%     18-    100.0%
36-    100.0%

(Ignore the 100% value if you like--these are the straight probabilities of rolls on the dice, not those imposed by exceptions in the rules such as 18s always failing.)

 

All of this has brought me one question.... why don't more people take a ton of combat levels? Heck, for 10 points you get +5 OCV with one attack.... screw an extra 2d6 on your EB, spend the points on combat levels and you'll pretty much never miss.

Well, one reason is that most would like their characters to be able to do some things out of combat, like be persuasive and charismatic, or build things, or make money. It is all about balancing the points given a set number of base or total points and a set of Disadvantages that you are comfortable with for the character.

 

As for the tradeoff between OCV and damage, there is another key difference between Hero and D&D (most D20, in fact): in Hero, defenses decrease damage! In D&D, if you get hit, you take damage (and usually lots of it!). Period (well, okay, there are rare circumstances in which you have, "damage reduction," or, "hardness," in D&D/D20, but it is the exception rather than the rule, and by the time you have the potential for DR, you also typically have characters that can deal out such grossly huge amounts of damage that it makes relatively little difference anyway...). So in D20 it is all about not getting hit. In Hero it is about not getting hit, reducing damage, healing from the damage, etc. There are also many different attacks (HTH, Ranged, Mental, Physical, Energy, Flashes, etc.) to give you a variety of offenses and defenses. See the huge diversity in Hero that D20 lacks so drastically?

[The Souljourner]

Re: Thoughts on using 1d20 instead of 3d6?

 

Thanks for that chart, Pres, I was thinking 3d12 might make a nice spread with a good resolution, but didn't have the time to work it all out. Of course, it has a similar problem to d20 - in that +1 is now half as useful. It would be cool to use that and just double all bonuses... then you could allow for what would be half bonuses in 3d6, to allow for better granularity.

 

I'd actually love to see a reworking of Hero using 3d12, since I think it gives the best of both worlds - a nice granularity but still with the sweet bell curve so average is really average.

 

Maybe that'll be a project I'll take up at some point. And besides, it would be nice to make those d12s feel useful for once...

 

-Nate

[prestidigitator]

Re: Thoughts on using 1d20 instead of 3d6?

 

Thanks for that chart, Pres, I was thinking 3d12 might make a nice spread with a good resolution, but didn't have the time to work it all out. Of course, it has a similar problem to d20 - in that +1 is now half as useful. It would be cool to use that and just double all bonuses... then you could allow for what would be half bonuses in 3d6, to allow for better granularity.

 

I'd actually love to see a reworking of Hero using 3d12, since I think it gives the best of both worlds - a nice granularity but still with the sweet bell curve so average is really average.

 

Maybe that'll be a project I'll take up at some point. And besides, it would be nice to make those d12s feel useful for once...

Yep. And the point is that it really doesn't take much reworking at all. Nothing like what it would take to switch to a flat distribution, or even one with a drastically different width compared to the spread (and the discrete nature of our rolls and +1s). So switching to 3d12 would be much less of a change than even switching to 2d10 or 4d6 IMO.

[TaxiMan]

Re: Thoughts on using 1d20 instead of 3d6?

 

Re: 3d12 vs 3d6 vs 4d6 vs [other multi-die implementation] -

 

IMHO, 3d6 minimizes the "hassle" while retaining the bell curve. If you have a group that adds up 3d20 in the blink of an eye, go for it!

 

Me, I think it'd be cool if there were a d20 for Hero - but imprinted like so:

 

"3-5"

"6"

"7"

"8"

"8"

"9"

"9"

"9"

"10"

"10"

"11"

"11"

"12"

"12"

"12"

"13"

"13"

"14"

"15"

"16+"

 

Now that's the simplicity of a single die roll, with the bell curve built right in! I'd buy some just for the conversation value alone. Finally, a way to silence the critics of Hero because it isn't "D20"! I'd definitely use them as GM - as a player, I'd probably cling superstitiously to my "lucky dice".

[prestidigitator]

Re: Thoughts on using 1d20 instead of 3d6?

 

Re: 3d12 vs 3d6 vs 4d6 vs [other multi-die implementation] -

 

IMHO, 3d6 minimizes the "hassle" while retaining the bell curve. If you have a group that adds up 3d20 in the blink of an eye, go for it!

 

Me, I think it'd be cool if there were a d20 for Hero - but imprinted like so:

...

HAH! Good one!

 

I think 10s and 11s should be more frequent than 9s and 12s, but its a funny and interesting idea in general. Rep!

[TaxiMan]

Re: Thoughts on using 1d20 instead of 3d6?

 

I tried selecting numbers that matched the odds posted earlier. For every change of 5% from the previous value I assigned 1 of the 20-sider's faces.

 

Still, I think you're right. We should get rid of a "9" and a "12" and add in another "10" and "11".

 

Like this'll ever happen! But I own 18 Hero dice - I'd buy a half dozen of these too! Maybe replace the "3-5" with the Green Man . Oh yeah!

[PhilFleischmann]

Re: Thoughts on using 1d20 instead of 3d6?

 

I would be fine with a bell curve if it were flatter' date=' but 3d6 is crazy tight.[/quote']

If you want a flatter bell curve, you could try one of these dice combos:

 

d4+d6+d8 - gives the 3-18 results you're used to, but the curve isn't quite so steep, odds of a 3 are 1/192 instead of 1/216 - maybe not enough of a difference to notice.

 

2d4+d10 - also gives 3-18 results, with a flatter curve and a "plateau" in the middle covering 9-12, odds of a 3 are 1/160

 

You can also try weirder combos like d2+d4+d12, which creates an even larger plateau in the middle, or use some weird shaped (or weirdly numbered) dice like 2d5+d8 or d3+d6+d9.

 

I was at Origins this past June, and there was a booth selling strange dice, including d5's. "GameScience" IIRC.

 

I have also been playing around with the idea of using 3d12 for greater granularity, which I like. And as Presitidigitator pointed out, it has the same "shape" as 3d6, but a different size. Note that 4d6 does *not* produce the same shape of a bell curve - it's even steeper.

 

For a *really* steep bell curve, you can use 5d4-2 - giving 3-18 results with only a 1/1024 chance of a 3.

[Sean Waters]

Re: Thoughts on using 1d20 instead of 3d6?

 

Where can I get a 1d3to18, huh?

[Captain Obvious]

Re: Thoughts on using 1d20 instead of 3d6?

 

Or a properly marked d216...