Quote from: Pat on July 03, 2021, 02:27:44 PMAD&D1e has some complex lower bounds as well, when you consider all the maximums and minimums for classes and races. But I was mostly just pointing out that when using Monte Carlo simulations like this, the outer bounds tend to be a bit swingy. The 1 in 100,000 characters will vary a lot more than the 90% characters, or even the 1 in 10,000 characters.

If I'm reading it right, both AD&D and Basic D&D expect you to roll your stats before you choose your character race / class. AD&D doesn't appear to have any rules about unplayable characters (before choose race and class) except an implication that you should keep rolling until you get an acceptable character. I guess the hope is that the various rolling methods I to IV should avoid the need for that.

Quote from: mightybrain on July 04, 2021, 07:23:25 PM

Quote from: Pat on July 03, 2021, 02:27:44 PMAD&D1e has some complex lower bounds as well, when you consider all the maximums and minimums for classes and races. But I was mostly just pointing out that when using Monte Carlo simulations like this, the outer bounds tend to be a bit swingy. The 1 in 100,000 characters will vary a lot more than the 90% characters, or even the 1 in 10,000 characters.

If I'm reading it right, both AD&D and Basic D&D expect you to roll your stats before you choose your character race / class. AD&D doesn't appear to have any rules about unplayable characters (before choose race and class) except an implication that you should keep rolling until you get an acceptable character. I guess the hope is that the various rolling methods I to IV should avoid the need for that.

The AD&D PHB was released a year prior, to the release of the DMG; so the game was played for a year, prior to any additional methods spelled out in the DMG.

Quote from: mightybrain on July 04, 2021, 07:23:25 PM

Quote from: Pat on July 03, 2021, 02:27:44 PMAD&D1e has some complex lower bounds as well, when you consider all the maximums and minimums for classes and races. But I was mostly just pointing out that when using Monte Carlo simulations like this, the outer bounds tend to be a bit swingy. The 1 in 100,000 characters will vary a lot more than the 90% characters, or even the 1 in 10,000 characters.

If I'm reading it right, both AD&D and Basic D&D expect you to roll your stats before you choose your character race / class. AD&D doesn't appear to have any rules about unplayable characters (before choose race and class) except an implication that you should keep rolling until you get an acceptable character. I guess the hope is that the various rolling methods I to IV should avoid the need for that.

AD&D has implicit rules. Each of the races has stat mins and maxes, though since (male) humans don't have any restrictions, human can always serve as a fall back. But each of the classes have stat minimums, and it's possible to roll a character who doesn't qualify for any class. For instance a character with S 5 and I 8. The reason that doesn't work is because you need at least an I 9 to play a magic-user, but characters with S 5 or less are only allowed to be magic-users. This being AD&D, which arrays don't qualify for any class cam get fairly complex, but in practice it doesn't come up that often.

I don't know if anyone has an accurate number for the total D&D players in the world. I've seen ~10,000,000 used. Given that, and assuming they each make one character using 4d6 and drop the lowest, here's what the top ten rolled characters would look like:
[18, 18, 17, 18, 16, 16] total = 103
[18, 18, 17, 18, 16, 16] total = 103
[17, 18, 17, 18, 16, 17] total = 103
[18, 17, 17, 17, 17, 17] total = 103
[16, 18, 18, 16, 18, 17] total = 103
[16, 18, 16, 18, 17, 17] total = 102
[16, 17, 17, 17, 17, 18] total = 102
[18, 17, 18, 14, 17, 18] total = 102
[17, 17, 18, 18, 16, 16] total = 102
[17, 18, 17, 15, 18, 17] total = 102

Whereas with 3d6 they would look more like this:
[17, 17, 15, 17, 16, 17] total = 99
[16, 15, 15, 18, 17, 17] total = 98
[14, 18, 17, 18, 15, 15] total = 97
[13, 18, 17, 17, 16, 16] total = 97
[16, 11, 18, 16, 18, 17] total = 96
[18, 15, 15, 16, 16, 16] total = 96
[17, 17, 15, 16, 17, 14] total = 96
[17, 14, 16, 15, 17, 17] total = 96
[16, 17, 17, 18, 12, 15] total = 95
[17, 15, 16, 17, 13, 17] total = 95

Those top results are crazy.

Quote from: mightybrain on July 04, 2021, 08:13:24 PM
I don't know if anyone has an accurate number for the total D&D players in the world. I've seen ~10,000,000 used. Given that, and assuming they each make one character using 4d6 and drop the lowest, here's what the top ten rolled characters would look like:
[18, 18, 17, 18, 16, 16] total = 103
[18, 18, 17, 18, 16, 16] total = 103
[17, 18, 17, 18, 16, 17] total = 103
[18, 17, 17, 17, 17, 17] total = 103
[16, 18, 18, 16, 18, 17] total = 103
[16, 18, 16, 18, 17, 17] total = 102
[16, 17, 17, 17, 17, 18] total = 102
[18, 17, 18, 14, 17, 18] total = 102
[17, 17, 18, 18, 16, 16] total = 102
[17, 18, 17, 15, 18, 17] total = 102

Whereas with 3d6 they would look more like this:
[17, 17, 15, 17, 16, 17] total = 99
[16, 15, 15, 18, 17, 17] total = 98
[14, 18, 17, 18, 15, 15] total = 97
[13, 18, 17, 17, 16, 16] total = 97
[16, 11, 18, 16, 18, 17] total = 96
[18, 15, 15, 16, 16, 16] total = 96
[17, 17, 15, 16, 17, 14] total = 96
[17, 14, 16, 15, 17, 17] total = 96
[16, 17, 17, 18, 12, 15] total = 95
[17, 15, 16, 17, 13, 17] total = 95

I assume you ran 10,000,000 trials. How many replicates did you run?

The absoukte best roll ive seen a player get was 4 18s and 2 17s, and whats crazy is she's dine this twice, only the 2nd time one if the 17s was a 16.

Quote from: mightybrain on July 04, 2021, 08:13:24 PM
I don't know if anyone has an accurate number for the total D&D players in the world. I've seen ~10,000,000 used. Given that, and assuming they each make one character using 4d6 and drop the lowest, here's what the top ten rolled characters would look like:
[18, 18, 17, 18, 16, 16] total = 103
[18, 18, 17, 18, 16, 16] total = 103
[17, 18, 17, 18, 16, 17] total = 103
[18, 17, 17, 17, 17, 17] total = 103
[16, 18, 18, 16, 18, 17] total = 103
[16, 18, 16, 18, 17, 17] total = 102
[16, 17, 17, 17, 17, 18] total = 102
[18, 17, 18, 14, 17, 18] total = 102
[17, 17, 18, 18, 16, 16] total = 102
[17, 18, 17, 15, 18, 17] total = 102

Whereas with 3d6 they would look more like this:
[17, 17, 15, 17, 16, 17] total = 99
[16, 15, 15, 18, 17, 17] total = 98
[14, 18, 17, 18, 15, 15] total = 97
[13, 18, 17, 17, 16, 16] total = 97
[16, 11, 18, 16, 18, 17] total = 96
[18, 15, 15, 16, 16, 16] total = 96
[17, 17, 15, 16, 17, 14] total = 96
[17, 14, 16, 15, 17, 17] total = 96
[16, 17, 17, 18, 12, 15] total = 95
[17, 15, 16, 17, 13, 17] total = 95

Of course - that's assuming that dice are totally random. Even the best dice will slant a bit - and some dice are pretty badly weighted.

So - I'd assume that more extreme rolls would be more common than that simply due to improperly weighted dice.

Quote from: dkabq on July 04, 2021, 09:20:56 PM
I assume you ran 10,000,000 trials. How many replicates did you run?

Only one.

Here's a second run with 3d6:
[16, 18, 16, 18, 13, 17] total = 98
[17, 17, 18, 18, 11, 17] total = 98
[17, 16, 15, 18, 16, 16] total = 98
[17, 18, 16, 12, 17, 17] total = 97
[12, 18, 16, 18, 16, 17] total = 97
[17, 13, 18, 17, 16, 16] total = 97
[15, 17, 15, 17, 14, 18] total = 96
[17, 11, 17, 18, 17, 16] total = 96
[18, 15, 17, 17, 14, 15] total = 96
[15, 16, 17, 13, 17, 18] total = 96

Not vastly different.

Quote from: Slambo on July 04, 2021, 10:15:37 PM
The absoukte best roll ive seen a player get was 4 18s and 2 17s, and whats crazy is she's dine this twice, only the 2nd time one if the 17s was a 16.

Was that with 4d6 drop the lowest, or 3d6?

I think the highest I've seen is one 18 and one 17. And I thought that was pretty lucky even with 4d6 and drop the lowest.

Straight down the line gives the representation, that these are the cards you were dealt at birth.  This is what you started out with.  You're just playing the hand that you were dealt.  It offers an insight into who exists in your setting.  I don't mind a person rolling up 3 or 4 characters, and choosing one to play first; but those other characters they rolled, also exist in the setting.  They just aren't part of the adventuring party, yet.

I'd note here two things. The best stat rolls in terms of total number of points does not necessarily generate the best character for a particular class. And your party is unlikely to be made up entirely out of such one in a million characters.

Here, for example, is the best party in terms of total points from 2 million parties of 5:
[15, 12, 15, 14, 6, 12]
[12, 16, 12, 14, 11, 13]
[10, 13, 16, 17, 10, 14]
[14, 16, 7, 15, 13, 17]
[12, 14, 14, 13, 10, 17]

I'm sure there are many better parties in that mix, but I won't find them using a pure points criteria.

Quote from: mightybrain on July 05, 2021, 07:52:14 AM
I'd note here two things. The best stat rolls in terms of total number of points does not necessarily generate the best character for a particular class. And your party is unlikely to be made up entirely out of such one in a million characters.

Here, for example, is the best party in terms of total points from 2 million parties of 5:
[15, 12, 15, 14, 6, 12]
[12, 16, 12, 14, 11, 13]
[10, 13, 16, 17, 10, 14]
[14, 16, 7, 15, 13, 17]
[12, 14, 14, 13, 10, 17]

I'm sure there are many better parties in that mix, but I won't find them using a pure points criteria.

FWIW, another metric of "goodness" to consider would be the sum of the stat bonuses/penalties.

Quote from: dkabq on July 05, 2021, 08:20:12 AM

FWIW, another metric of "goodness" to consider would be the sum of the stat bonuses/penalties.

That's less universal, because it varies by edition. Point totals are the most broadly applicable standard.

Another option is some kind of point buy total, like third edition's, which would favor exceptional scores combined with poor scores over consistently high scores. But again, this should be tweaked by edition.

Quote from: mightybrain on July 05, 2021, 02:43:48 AM

Quote from: Slambo on July 04, 2021, 10:15:37 PM
The absoukte best roll ive seen a player get was 4 18s and 2 17s, and whats crazy is she's dine this twice, only the 2nd time one if the 17s was a 16.

Was that with 4d6 drop the lowest, or 3d6?

I think the highest I've seen is one 18 and one 17. And I thought that was pretty lucky even with 4d6 and drop the lowest.

Its been a while but i think it was 4d6 drop lowest.  Though...she did 3d6 in order for out swords and wizardry game and her lowest stat there are really good and those were digital dice. I think she's just lucky.