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Using 18 as your highest primary stat:
.
.
.
.
18 18 8 7 7 7
18 17 12 7 7 7
18 17 10 8 7 7
18 17 9 9 7 7
18 17 8 8 8 7
18 17 8 7 7 7
18 16 14 7 7 7
18 16 13 8 7 7
18 16 12 9 7 7
18 16 11 10 7 7
18 16 11 8 8 7
18 16 10 9 8 7
18 16 9 9 9 7
18 16 9 8 8 8
18 15 14 9 7 7
18 15 13 11 7 7
18 15 13 9 8 7
18 15 12 12 7 7
18 15 12 10 8 7
18 15 12 9 9 7
18 15 12 8 8 8
18 15 11 11 8 7
18 15 11 10 9 7
18 15 11 9 8 8
18 15 10 10 10 7
18 15 10 10 8 8
18 15 10 9 9 8
18 15 9 9 9 9
18 14 14 11 7 7
18 14 14 9 8 7
18 14 13 13 7 7
18 14 13 11 8 7
18 14 13 10 9 7
18 14 13 9 8 8
18 14 12 12 8 7
18 14 12 11 9 7
18 14 12 10 10 7
18 14 12 10 8 8
18 14 12 9 9 8
18 14 11 11 10 7
18 14 11 11 8 8
18 14 11 10 9 8
18 14 11 9 9 9
18 14 10 10 10 8
18 14 10 10 9 9
18 13 13 13 8 7
18 13 13 12 9 7
18 13 13 11 10 7
18 13 13 11 8 8
18 13 13 10 9 8
18 13 13 9 9 9
18 13 12 12 10 7
18 13 12 12 8 8
18 13 12 11 11 7
18 13 12 11 9 8
18 13 12 10 10 8
18 13 12 10 9 9
18 13 11 11 10 8
18 13 11 11 9 9
18 13 11 10 10 9
18 13 10 10 10 10
18 12 12 12 11 7
18 12 12 12 9 8
18 12 12 11 10 8
18 12 12 11 9 9
18 12 12 10 10 9
18 12 11 11 11 8
18 12 11 11 10 9
18 12 11 10 10 10
18 11 11 11 11 9
18 11 11 11 10 10

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Using 17 as your highest primary stat:
.
.
.
.
17 17 13 9 7 7
17 17 12 10 7 7
17 17 12 8 8 7
17 17 11 11 7 7
17 17 11 9 8 7
17 17 10 10 8 7
17 17 10 9 9 7
17 17 10 8 8 8
17 17 9 9 8 8
17 16 15 8 7 7
17 16 14 10 7 7
17 16 14 8 8 7
17 16 13 12 7 7
17 16 13 10 8 7
17 16 13 9 9 7
17 16 13 8 8 8
17 16 12 11 8 7
17 16 12 10 9 7
17 16 12 9 8 8
17 16 11 11 9 7
17 16 11 10 10 7
17 16 11 10 8 8
17 16 11 9 9 8
17 16 10 10 9 8
17 16 10 9 9 9
17 15 15 11 7 7
17 15 15 9 8 7
17 15 14 13 7 7
17 15 14 11 8 7
17 15 14 10 9 7
17 15 14 9 8 8
17 15 13 13 8 7
17 15 13 12 9 7
17 15 13 11 10 7
17 15 13 11 8 8
17 15 13 10 9 8
17 15 13 9 9 9
17 15 12 12 10 7
17 15 12 12 8 8
17 15 12 11 11 7
17 15 12 11 9 8
17 15 12 10 10 8
17 15 12 10 9 9
17 15 11 11 10 8
17 15 11 11 9 9
17 15 11 10 10 9
17 15 10 10 10 10
17 14 14 14 7 7
17 14 14 13 8 7
17 14 14 12 9 7
17 14 14 11 10 7
17 14 14 11 8 8
17 14 14 10 9 8
17 14 14 9 9 9
17 14 13 13 10 7
17 14 13 13 8 8
17 14 13 12 11 7
17 14 13 12 9 8
17 14 13 11 10 8
17 14 13 11 9 9
17 14 13 10 10 9
17 14 12 12 12 7
17 14 12 12 10 8
17 14 12 12 9 9
17 14 12 11 11 8
17 14 12 11 10 9
17 14 12 10 10 10
17 14 11 11 11 9
17 14 11 11 10 10
17 13 13 13 12 7
17 13 13 13 10 8
17 13 13 13 9 9
17 13 13 12 11 8
17 13 13 12 10 9
17 13 13 11 11 9
17 13 13 11 10 10
17 13 12 12 12 8
17 13 12 12 11 9
17 13 12 12 10 10
17 13 12 11 11 10
17 13 11 11 11 11
17 12 12 12 12 9
17 12 12 12 11 10
17 12 12 11 11 11

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Using 16 as your highest primary stat:
.
.
.
.
16 16 16 8 7 7
16 16 15 11 7 7
16 16 15 9 8 7
16 16 14 13 7 7
16 16 14 11 8 7
16 16 14 10 9 7
16 16 14 9 8 8
16 16 13 13 8 7
16 16 13 12 9 7
16 16 13 11 10 7
16 16 13 11 8 8
16 16 13 10 9 8
16 16 13 9 9 9
16 16 12 12 10 7
16 16 12 12 8 8
16 16 12 11 11 7
16 16 12 11 9 8
16 16 12 10 10 8
16 16 12 10 9 9
16 16 11 11 10 8
16 16 11 11 9 9
16 16 11 10 10 9
16 16 10 10 10 10
16 15 15 12 8 7
16 15 15 11 9 7
16 15 15 10 10 7
16 15 15 10 8 8
16 15 15 9 9 8
16 15 14 13 9 7
16 15 14 12 10 7
16 15 14 12 8 8
16 15 14 11 11 7
16 15 14 11 9 8
16 15 14 10 10 8
16 15 14 10 9 9
16 15 13 13 11 7
16 15 13 13 9 8
16 15 13 12 12 7
16 15 13 12 10 8
16 15 13 12 9 9
16 15 13 11 11 8
16 15 13 11 10 9
16 15 13 10 10 10
16 15 12 12 11 8
16 15 12 12 10 9
16 15 12 11 11 9
16 15 12 11 10 10
16 15 11 11 11 10
16 14 14 14 9 7
16 14 14 13 11 7
16 14 14 13 9 8
16 14 14 12 12 7
16 14 14 12 10 8
16 14 14 12 9 9
16 14 14 11 11 8
16 14 14 11 10 9
16 14 14 10 10 10
16 14 13 13 13 7
16 14 13 13 11 8
16 14 13 13 10 9
16 14 13 12 12 8
16 14 13 12 11 9
16 14 13 12 10 10
16 14 13 11 11 10
16 14 12 12 12 9
16 14 12 12 11 10
16 14 12 11 11 11
16 13 13 13 13 8
16 13 13 13 12 9
16 13 13 13 11 10
16 13 13 12 12 10
16 13 13 12 11 11
16 13 12 12 12 11
16 12 12 12 12 12

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Using 15 as your highest primary stat:
.
.
.
.
15 15 15 15 7 7
15 15 15 14 8 7
15 15 15 13 10 7
15 15 15 13 8 8
15 15 15 12 11 7
15 15 15 12 9 8
15 15 15 11 10 8
15 15 15 11 9 9
15 15 15 10 10 9
15 15 14 14 10 7
15 15 14 14 8 8
15 15 14 13 12 7
15 15 14 13 10 8
15 15 14 13 9 9
15 15 14 12 11 8
15 15 14 12 10 9
15 15 14 11 11 9
15 15 14 11 10 10
15 15 13 13 12 8
15 15 13 13 11 9
15 15 13 13 10 10
15 15 13 12 12 9
15 15 13 12 11 10
15 15 13 11 11 11
15 15 12 12 12 10
15 15 12 12 11 11
15 14 14 14 12 7
15 14 14 14 10 8
15 14 14 14 9 9
15 14 14 13 12 8
15 14 14 13 11 9
15 14 14 13 10 10
15 14 14 12 12 9
15 14 14 12 11 10
15 14 14 11 11 11
15 14 13 13 13 9
15 14 13 13 12 10
15 14 13 13 11 11
15 14 13 12 12 11
15 14 12 12 12 12
15 13 13 13 13 11
15 13 13 13 12 12

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Kyle
Interesting posting. I tried to go one step further based on your math. No gurantee I'm correct - was a quick Excel I did on your numbers.
As we have 6 different stats, this allows for many more combinations. It is simplest for all Singletons. There are 28 combinations with 6 different values. This results in 6*5*4*3*2*1 = 720 possible stat combinations.
So doing similar math for the other combinations I get
Array/occurence/Stat Combinations/Total
All Singletons/28/720/20160
One Duplicate/107/360/38520
Two Duplicates/56/360/20160
One Triplicate/42/120/5040
Three Duplicates/8/90/720
Duplicate/Triplicate/23/60/1380
Quartett/11/30/330
Duplicate/Quartett/3/15/45
Quintett/2/6/12
86367 different legal stat combinations for PFS.
Thod

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Kyle
Interesting posting. I tried to go one step further based on your math. No gurantee I'm correct - was a quick Excel I did on your numbers.
As we have 6 different stats, this allows for many more combinations. It is simplest for all Singletons. There are 28 combinations with 6 different values. This results in 6*5*4*3*2*1 = 720 possible stat combinations.
So doing similar math for the other combinations I get
Array/occurence/Stat Combinations/Total
All Singletons/28/720/20160
One Duplicate/107/360/38520
Two Duplicates/56/360/20160
One Triplicate/42/120/5040
Three Duplicates/8/90/720
Duplicate/Triplicate/23/60/1380
Quartett/11/30/330
Duplicate/Quartett/3/15/45
Quintett/2/6/1286367 different legal stat combinations for PFS.
Thod
Thod, the issue is that you need to only consider unique combinations. 17 16 14 10 7 7 is the same as 16 17 14 7 10 7
280 is the number of unique combinations that add up to exactly 20. You could also consider not spending all 20 points if you wished.
For an excel spreadsheet, just do this:
Copy/Paste the lists above into Word
Ctrl+H and replace " " with ^t
Select All, Copy/paste into Excel. Voila!

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Thod, the issue is that you need to only consider unique combinations. 17 16 14 10 7 7 is the same as 16 17 14 7 10 7280 is the number of unique combinations that add up to exactly 20. You could also consider not spending all 20 points if you wished.
Kyle
I'm aware of that. There are only 280 different combinations of absolute stats.
If you regard 17 16 14 10 7 7 and 16 17 14 7 10 7 the same depends. If my first value is Str, then Con, etc (not sure what the official order should be) then you get 360 combinations of 17 16 14 10 7 7 - or more genral - 360 combinations for each of you 280 stats that have a single duplicate stat.
I write 360 above as in principal you can have 720 - but half the combinations are redundant in this case.
It is a question how far you want to enumerate the combinations:
280 different stat combinations.
86367 combinations
The next step would be to combine this with the core classes.
And one step further you can multiply with the races.
If you want, add male/female to double the number.
Now you have all possible starting characters (awaiting equipment options for give even more choice).
Thod

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Stuff
Thod you're absolutely correct, except that the purpose of the stats I presented was to help people pick stats by deciding on the number they wanted for their best stat.
Your point was well made in regards to the diversity allowed by the 20 point buy system, although we should probably throw out any combinations with a 7 for Constitution. ;-)

Enevhar Aldarion |
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I just want to say that you are both right, just in different ways. Kyle, you are right when people are assigning numbers to the stats in the order they want them, while Thod, you are right when people are generating stats randomly or if they are having to pick a list of numbers and assign them in the order written rather than getting to place them as they see fit.

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Hello, could someone point out where the rules are for the point buy system in Society play? I can't seem to find how this is done.
Ability score costs are on pg. 16 of the core rulebook. The rule on how many points to create a character is in the Guide to Pathfinder Society Organized Play in chapter 4, step 2:abilities. That's pg 13 of my older version of the document(haven't printed the latest version due to no ink for my printer and no extra money in budget to get some). Hope this helps.

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Ok, so 6 abilities at 10 = 60 +20 to mess with = 80
This isn't quite right, this will probably help it make sense.

Enevhar Aldarion |

Ok, so 6 abilities at 10 = 60 +20 to mess with = 80
All of your number combinations do not add up to 80.
15 15 15 15 7 7= 74
18 18 8 7 7 7= 65Why not 18 17 18 9 9 9= 80? for instance?
They do not add up to 80 because the point buy scale is not a one for one cost, but rather increases in cost in steps. Here is the chart in case you do not have the Core Book available to look at:
7: -4 points
8: -2 points
9: -1 points
10: no cost
11: +1 point
12: +2 points
13: +3 points
14: +5 points
15: +7 points
16: +10 points
17: +13 points
18: +17 points
You have 20 points total, not 80, to buy the stats you want.

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Since a few have asked for something, I figured since I threw it together for myself, might as well share in case someone else wants it.
http:// jstockmann.com /pfrpg/20_Point_Buys.xlsx
Wanted to keep out any bots, so just copy, paste, and remove the space before the "j" and after "com" and you'll be good to go. I may move change the link later when I have access to a shared space, but can't right now.
Thanks again Kyle for putting all that out there.

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"18 11 11 11 10 10" has to the be the best one. There should be a challenge on the boards using it. Make a spellcasting character with that array, dropping the 18 in your casting stat, and see how long the character lasts.
NEW CHALLENGER:
Thx for the list. It's nice to see how many min/max suicidal options I have. I am sure that some point along the line someone took that wonderful 18 18 8 7 7 7 for a synthesis summoner.
18 8 18 7 7 7 down the line, play human and take
Dual Talent: Some humans are uniquely skilled at maximizing their natural gifts. These humans pick two ability scores and gain a +2 racial bonus in each of those scores. This racial trait replaces the +2 bonus to any one ability score, the bonus feat, and the skilled traits.For:
STR 20
DEX 8
CON 20
INT 7
WIS 7
CHA 7
AM BARBARIAN!

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2, 3, 5, 8, 13, 21, might be the closest subset of fibonacci numbers, but you'd have to suffer permanent drain to a stat, and really boost one stat a lot. Maybe you can pick a significantly large # in the sequence as a stat block [ 10946, 17711 ] is close. 10 / 9 / 4/ 6/ 17/ 7 / 11. drop the lowest? =D

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Bump! ;-)
So, I wonder how player stats compare to randomly picking a stat array...
94 combinations with 1 stat < 10 (33.6%)
92 combinations with 2 stats < 10 (32.9%)
39 combinations with 3 stats < 10 (13.9%)
7 combinations with 4 stats < 10 (2.5%)

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Someone needs to make a random pfs character generator which picks one of the valid spreads, class, race, faction, and perhaps core only traits/feats.
Or at least tables that one can roll on to ditermine their next PC.
STATS:
1. Roll 2d6+6. This is one of your stats. Calculate remaining points. Repeat until you have 10 or fewer points left.2. Find your points among the following:
• If you have 5+ points left, roll 2d4+7 for this stat.
• If you have 0 points left and this is your last stat, it's 10.
• If you have 0-1 points left and it's not your last stat, this stat is 8.
• If you have 1 point left and it's your last stat, it's 11.
• If you have 2-4 points left, this stat is a 12.
3. Repeat step 2 until you have all your stats. Verify your point total, and if it's off, raise or lower your lowest stat(s) to comply with 20pt buy.
RACE:
Roll d%.
01-40: Human
41-55: Half-elf
56-65: Dwarf
66-75: Halfling
76-85: Elf
86-95: Half-orc
96-00: Gnome
CLASS:
Roll d%.
01-05: Barbarian
06-20: Bard
21-30: Cleric
31-35: Druid
36-45: Fighter
46-50: Monk
51-55: Paladin
56-65: Ranger
66-75: Rogue
76-85: Sorcerer
86-00: Wizard
I advise against rolling randomly for feats and traits. Have fun!

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To try out what I just suggested...
STATS
2d6 + 6 ⇒ (6, 4) + 6 = 16
That's 10 points, which means I have 10 or fewer left, and 5+ left, so...
2d4 + 7 ⇒ (3, 4) + 7 = 14
Which leaves me with 5 points, therefore I repeat...
2d4 + 7 ⇒ (2, 3) + 7 = 12
Which leaves me with 3 points, therefore my 4th stat is a 12.
Which leaves me with 1 point and not looking at my last stat, which means this one's an 8.
Which leaves me with 3 points for my final stat, so it's a 12. Since I have a point left over, I adjust my lowest stat to compensate, changing the 8 to a 9.
This makes my final spread (before race) look like this: 16/14/12/12/12/9.
Now, race:
1d100 ⇒ 39
Human, by a hair.
Class:
1d100 ⇒ 87
And it's a wizard.
So I have a human wizard. Stats are probably thus:
STR 9
DEX 12
CON 14
INT 18 (racial bonus)
WIS 12
CHA 12
Seems solid!

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STATS:
Stats: 2d6 + 6 ⇒ (3, 1) + 6 = 10 0
Stats: 2d6 + 6 ⇒ (4, 5) + 6 = 15 7
Stats: 2d6 + 6 ⇒ (5, 4) + 6 = 15 7
Stats: 2d4 + 7 ⇒ (4, 4) + 7 = 15 7
9 (originally 8) raised to satisfy 20 point buy -1
10
RACE:
race: 1d100 ⇒ 22 Human
CLASS:
class: 1d100 ⇒ 89 Wizard
Jiggy, clearly this is a plot to make more human wizards
str 9
Dex 15
Con 15
Int 17 (racial bonus)
Wis 10
Cha 10