3d6, re-roll 1's

[Finarvyn]

This is essentially a post I made on the TLG boards. A poster there was looking for an alternate to a 3d6 method for character creation. One popped into my head and so I had to do some number crunching. The more I look at it, the more I like it.

How about 3d6, re-roll 1's. This gives a minimum of 6, maximum of 18, average of 12.0 instead of 10.5, and tends to generally edge scores higher without being absurd.

Traditional 3d6:
Score Ways Percent
3 1 0%
4 3 1%
5 6 3%
6 10 5%
7 15 7%
8 21 10%
9 25 12%
10 27 13%
11 27 13%
12 25 12%
13 21 10%
14 15 7%
15 10 5%
16 6 3%
17 3 1%
18 1 0%

3d6, re-roll 1's:
Score Ways Percent
3 0 0%
4 0 0%
5 0 0%
6 1 1%
7 3 2%
8 6 5%
9 10 8%
10 15 12%
11 18 14%
12 19 15%
13 18 14%
14 15 12%
15 10 8%
16 6 5%
17 3 2%
18 1 1%

Just a thought....

Essentially, it gets rid of sucky numbers at the bottom but doesn't make the numbers at the top absurd.

[Sean Michael Kelly]

Me likes it. ;D

[Vile Traveller]

Yeah, we used to do this for a while in the late 80s / early 90s before moving on to 4d6 drop the lowest. I actually think I prefer 3d6 re-roll 1s now.

[Finarvyn]

Yeah, I've played that way before but had never actually calculated the numbers. The more I look at it, the more I like it better than other methods I've tried.

[kesher]

I love it when you guys crunch the numbers...

[cooper]

I'd rather give +1 to any stat each level than mess with the bell curve of 3d6. Words like exceptional and extraordinary stats lose their meaning when the 3d6 is tampered with and scores in 0d&d have so little impact on play that a persons desire not to have a low stat is more about their perception of themselves rather than the character.

It is the slow slouch toward the road of interactive fan fiction, rather than honest storytelling when players fret over imperfect and sometimes flawed characters. Flawed character can die, but how can a DM kill off my Adonis-like platonic ideal warrior???

[giantbat]

I think it's a bit extreme and inaccurate to burden how someone rolls dice with so much value judgement about their self-image and honesty.

[Edited: Originally I expressed my disagreement with sarcasm. In consideration of the tone of the forum I have redacted/amended this. Apologies for my negativity.]

[famouswolf]

This option was suggested by Newt Newport in Openquest, of all games, and we started using it when stats were rolled (the primary method was point buy). I liked it and started using it to generate characters for D&D type games and it works well. About four out of five sets are very playable, almost always with net positive bonuses. I usually only allow one re-roll, to keep the possibility of low scores. So the range is still 3-18, but with a very low chance of 3 to 5. When I ran Crypts and Things the group all used it and all four generated very playable, but not superhero, characters first try.

It's my go to chargen method now.

[cadriel]

Unless you are using Greyhawk or AD&D stat modifiers, I don't see why you would mess with 3d6 in order. Once you are in GH or AD&D territory, low-stat characters are just pathetic compared to their high-stat counterparts. The lack of stat inflation is a part of why I like LBB OD&D. Not sure how you can get "unplayable" characters in that.

[Finarvyn]

I agree on the stat inflation issue, but I also think that in general heroes shouldn't have stats too close to the "3" end of the scale. Having a range of 6-18 works fine for me.

Another add-on to this would be that "3d6, re-roll 1's" could be used for the first character of the campaign but standard 3d6 for any replacement characters. This would encourage players to take care of that first one a little more. (This is the way we did our Boot Hill games. BH has a special d% scale for PCs and a regular d% scale for NPCs, so we said if you died you had to use the regular scale for your replacement character.)

[Ynas Midgard]

I usually let the players roll two rows (both 3d6 in order) and choose whichever they like. For a first character, n may even consider letting them swap two scores (in a given row of stats), so that, as Finarvyn said, they feel encouraged to take care of their first characters.

I also use a unified table for determining modifiers (and everything else based on ability scores):
3 -2
4-6 -1
7-14 no adjustment
15-17 +1
18 +2

I also experimented with 8-13 being the "no modifier" range, and even giving -2 and +2 for 3-4 and 17-18, respectively (about 1.5% chance of each extreme occurring); not liking many modifiers, however, I ended up with the table above.

[Finarvyn]

Ynas, I use the same attribute bonus chart you mentioned. I think it's from B/X D&D or something like that. I grew up with the OD&D chart but like the bell-curve style shape of the newer chart.

[badger2305]

What I do is fairly simple. Players get to roll 3d6 in order for six stats. Then they get a seventh roll, which may be used to substitute for one of the six. Doesn't mess with the distribution, but it does remedy a really bad roll for one stat.

[waysoftheearth]

I don't mind Fin's chart at all, but I think it worthwhile mentioning that a low roll is waaay more interesting that an average roll in terms of role playing. E.g., It's much more fun to play a PC with a critical flaw than one who is monotonously average.

The worst PCs (IMO) are those that have either all low scores, all high scores, or all average scores. What is ideal as far as role playing opportunity goes, is a PC with strengths and weaknesses.

It would be neat to speculate about how these kinds of PCs could be generated...


That aside, it's true that many players are discouraged by low rolls and encouraged by high rolls. This is in part because even the OD&D game mechanics favour high ability scores.

However, a critical distinction between the old and new styles of play is that new school D&D caters more to "character builds" where the player works at maximising the adjustments his PC has, while old school D&D doesn't so much. The old school player, therefore, has to manufacture his advantages by in-game scheming of one kind or another.


Regarding generating abilities, I've tried a number of things since retreating from "new school" and coming to "old school" gaming...

I've let players roll 3d6 six times, in order, and then replace any one die (of the 18 rolled) with a 6.

I've let players roll 3d6 seven times, in order, and then choose which roll is their starting money. The others, still in order, are their abilities.

I've let players roll two green dice and a red die. The numbers 1 to 6 indicate the six abilities, in order. Each green die indicates an advantaged ability (a 14, or a 17 if both green die are the same). The red dice indicates a disadvantaged ability (a 6). This method is quick, but gives less variation.


FWIW -- I also like a universal table of ability modifiers, because it's simple.

I like the +1 advantage to kick in at 14+ because there is very nearly a 1 in 6 chance of rolling a 14+ on 3d6.

I like an 18 to have a +2 advantage, cos an 18 is special (in fact I can't remember anyone ever rolling one up in play, so it's kinda a theoretical "Holy Grail").

[aher]

Dec 11, 2012 0:14:08 GMT -6 waysoftheearth said:

a low roll is waaay more interesting that an average roll in terms of role playing. E.g., It's much more fun to play a PC with a critical flaw than one who is monotonously average.

The worst PCs (IMO) are those that have either all low scores, all high scores, or all average scores. What is ideal as far as role playing opportunity goes, is a PC with strengths and weaknesses.

I totally agree. I once rolled a PC with INT 5 and DEX 18. So I developed the following backstory:

INT 5. He suffers from Tuberous Sclerosis Complex. This genetic disease causes autism and epilepsy in half its victims and retardation in a fifth of its victims. His IQ is roughly 10*INT, corresponding to mild mental retardation on the Wechsler Adult Intelligence Scale. Such a person has trouble speaking, remembering things, understanding social rules, discerning cause and effect, and problem solving. Criminologists tell us those with IQs below 90 are 7 times more likely to be jailed than those with IQs above 110. So it's no wonder he fell into a life of crime and became a Thief. This career choice works well with his high DEX.

DEX 18. The PC has Ehlers-Danlos Syndrome, a genetic disease which causes defective collagen production. The result is loose, stretchy ligaments (the things that hold joints in their place). People with EDS tend to be more flexible than the general population. Some people with EDS exhibit extreme flexibility. Such people can perform joint dislocations at will. This made my Thief into an amazing contortionist and escape artist.

Dec 11, 2012 0:14:08 GMT -6 waysoftheearth said:

It would be neat to speculate about how these kinds of PCs could be generated...

My first thought was simply to cut the 3d6 bell-shaped curve down the middle and flip it inside out to get a symmetrical U-shaped distribution:

x:= sum 3d6; if x <= 10 then 13 - x else 29 - x
Range is 3 to 18 (same as 3d6)
Mean is 10.5 (same as 3d6)
Standard deviation is 5.83809329605 (vs 2.95803989155 for 3d6)

You get 3s and 18s with the same probablitties you used to get 10s and 11s and vice versa. See it here, using the Troll dice roll probability calculator.

But this was a little too extreme. To moderate it a bit, start with 2d6 -- a triangular distribution -- cut it between the 6 and 7 and flip it inside out. Then add a d6. The result is

x:= sum 2d6;
y:= if x <= 6 then 8 - x else 19 - x;
d6 + y

Range is 3 to 18 (same as 3d6)
Mean is 10.9166666667 (vs 10.5 for 3d6)
Standard deviation is 4.09522079177 (vs 2.95803989155 for 3d6)

You can see it here using the Troll dice roll probability calculator.

[waysoftheearth]

Umm, sure but I find that simplicity tends to fly.

What about just sum 3d6 and half it. If there is any fraction round up, otherwise add 10.

If you end up with 2 (because you rolled a 3) then it makes a 10 instead. If you end up with 19 (because you rolled an 18) then it makes an 11 instead.

I.e., do this:
3 (0%) --> 10
4 (1%)--> 12
5 (3%)--> 3
6 (5%)--> 13
7 (7%)--> 4
8 (10%)--> 14
9 (12%)--> 5
10 (13%)--> 15
11 (13%)--> 6
12 (12%)--> 16
13 (10%)--> 7
14 (7%)--> 17
15 (5%)--> 8
16 (3%)--> 18
17 (1%)--> 9
18 (0%)--> 11

So then, the distribution of ability scores would look like this:

3 (3%)
4 (7%)
5 (12%)
6 (13%)
7 (10%)
8 (5%)
9 (1%)
11 (0%)
10 (0%)
12 (1%)
13 (5%)
14 (10%)
15 (13%)
16 (12%)
17 (7%)
18 (3%)

10 and 11 would be the least likely scores, while 6 and 15 would be the most likely scores.

Hmm. Why haven't I thought of that before??


Aher, if you can figure a "neat" (i.e., usable at the table) method with 3d6 of "flipping" the distribution around each of the bi-model peaks to get this:

3 (0%)
4 (1%)
5 (5%)
6 (10%)
7 (13%)
8 (12%)
9 (7%)
11 (3%)
10 (3%)
12 (7%)
13 (12%)
14 (13%)
15 (10%)
16 (5%)
17 (1%)
18 (0%)

Then I'll be using it

[verhaden]

You could find an ugly way to easily generate arrays following that distribution, put them into a table, and have players roll a d100 to determine their stats.

[giantbat]

Dec 11, 2012 4:49:41 GMT -6 waysoftheearth said:

if you can figure a "neat" (i.e., usable at the table) method with 3d6 of "flipping" the distribution around each of the bi-model peaks to get this:

3 (0%)
4 (1%)
5 (5%)
6 (10%)
7 (13%)
8 (12%)
9 (7%)
11 (3%)
10 (3%)
12 (7%)
13 (12%)
14 (13%)
15 (10%)
16 (5%)
17 (1%)
18 (0%)

Then I'll be using it

Use a table:

roll	value
3	3
4	4
5	10
6	5
7	9
8	6
9	8
10	7
11	14
12	13
13	15
14	12
15	16
16	11
17	17
18	18

[verhaden]

I edited a PHP script from Stack Overflow to represent ways' distribution, generated six numbers, and then randomly sorted each row in excel.

[kesher]

how can a DM kill off my Adonis-like platonic ideal warrior???

Save vs. Poison, Adonis!

* edited to point out that I obviously have nothing to add to all the math flying around in here, but I find it fascinating to read...

[waysoftheearth]

@giantbat: Simplicity shines ;D

verhaden: I don't quite understand what you mean... are you saying that your table shows some sample ability score sets rolled up according to the distribution I proposed?

[verhaden]

Yes. I used a PHP script to generate the scores given your stated probability distribution. However, because I just edited an existing script, it spits out results as such:

4 was picked 0 times...
5 was picked 0 times...
6 was picked 1 times...
7 was picked 2 times...
8 was picked 1 times...
9 was picked 1 times...
10 was picked 0 times...
11 was picked 0 times...
12 was picked 1 times...
13 was picked 0 times...
14 was picked 0 times...
15 was picked 0 times...
16 was picked 0 times...
17 was picked 0 times...

I recorded the results as 6, 7, 7, 8, 9, 12 into rows in excel, used =Rand() to generate random numbers in the neighboring column, and used sort to shuffle them accordingly.

***

There are much, much better ways to go about it.

stackoverflow.com/questions/13105417/generate-a-random-number-from-a-given-set-of-numbers-and-chances

Statistics isn't my strong suit, though, so those more able than I feel free to point out any problems.

[aher]

Dec 11, 2012 4:49:41 GMT -6 waysoftheearth said:

Aher, if you can figure a "neat" (i.e., usable at the table) method with 3d6 of "flipping" the distribution around each of the bi-model peaks to get this:

3 (0%)
4 (1%)
5 (5%)
6 (10%)
7 (13%)
8 (12%)
9 (7%)
11 (3%)
10 (3%)
12 (7%)
13 (12%)
14 (13%)
15 (10%)
16 (5%)
17 (1%)
18 (0%)

Then I'll be using it

The only way I could possibly improve on giantbat's superb idea of using a permutation π ∈ S₁₆ (relabeled 3 to 18) would be to re-write his table a bit more concisely using cycle notation:

π = (10 7 9 8 6 5) (11 14 12 13 15 16)

[giantbat]

Dec 13, 2012 3:15:45 GMT -6 @aher said:

The only way I could possibly improve on giantbat's superb idea of using a permutation π ∈ S₁₆ (relabeled 3 to 18) would be to re-write his table a bit more concisely using cycle notation:

π = (10 7 9 8 6 5) (11 14 12 13 15 16)

Exalt for concision and teaching!

[Sean Michael Kelly]

Quite a digital orgy this is. ;D

[Finarvyn]

Yeah, and it looks almost nothing like my original concept. :-)

[waysoftheearth]

Sorry for hijacking your thread Fin your original idea (and the following discussion) inspired new ideas


The other issue, in my mind, is how to create "reasonably equal" PCs for each of the players.

It's all well and good to promote a crappy roll as an opportunity to role play, but it can be perceived as unfair when some guys at the table "roll up" and others roll poor.

I'm not saying it's necessarily a bad thing, just that the idea is for everyone to enjoy their D&D experience.

A notion I was toying with was; rather than rolling six abilities, roll only three. The other three would then be calculated as the inverse of the three rolled scores.

Thus, if a player rolled an 18, he also gets a 3.
If the player rolls a 5, then he also gets a a 16. And so on.

This way, each PC would theoretically be on an equal footing, but exactly how the opposing ability scores would be allocated is open for discussion...

[Finarvyn]

Dec 14, 2012 20:53:17 GMT -6 waysoftheearth said:

Sorry for hijacking your thread Fin your original idea (and the following discussion) inspired new ideas

That's okay. I appreciate the enthusiasm around this place!

[waysoftheearth]

Thinking on the "inverse" idea some more, perhaps an easier option would be to:

1) have the players roll six abilities exactly as per usual.

2) allow the player to keep the rolls they made OR the exact inverse of the rolls they made.

Therefore, if a player rolled poorly, he could instead take the "inverse PC" which would (in theory) be as "good" as the original was "bad".

I.e., if you happened to roll up 11, 5, 8, 10, 12, 9 then the you could choose the inverse result which would instead be: 10, 16, 13, 11, 9, 12.

11 --> 10
5 --> 16
8 --> 13
10 --> 11
12 --> 9
9 --> 12

[famouswolf]

Really, the only way to make the characters 'reasonably equal' is probably by using point buy and making sure the 'dump stats' are useful enough to not be dumped on. Newt Newport in Crypts and Things made Wisdom more useful by making it the sanity points and a WIS 13+ granting an exp. point bonus, for instance. That way everyone would have to make a sacrifice or three for an eighteen score depending on the size of the point pool.

Number crunching aside, it's probably the only way to be sure. It's not as much fun as rolling, though.