D&D 5E How Many Point Buy Options

[Oofta]

EDIT
OK, so I shouldn't post and go to bed. Looks like I had a minor glitch (thanks m00) and missed a few entries. Updated below

On (yet) another thread about point buy vs rolling I made the claim that if you wanted to follow point buy but still be random, you could create a list of arrays that added up to 27 points. You could then roll to see which array you use. The counter claim was that it would be thousands of arrays, which i disagreed with.

Well, being the geek that I am I figured out all of the options using the 5E standard point buy for 27 points. There are 27 options, which I assume is just a weird coincidence. 64 options now that I fixed my code.

Here you go. I did some spot checking, let me know if I had a glitch in my calculation.

15, 15, 15, 8, 8, 8
15, 15, 14, 10, 8, 8
15, 15, 14, 9, 9, 8
15, 15, 13, 12, 8, 8
15, 15, 13, 11, 9, 8
15, 15, 13, 10, 10, 8
15, 15, 13, 10, 9, 9
15, 15, 12, 12, 9, 8
15, 15, 12, 11, 10, 8
15, 15, 12, 11, 9, 9
15, 15, 12, 10, 10, 9
15, 15, 11, 11, 11, 8
15, 15, 11, 11, 10, 9
15, 15, 11, 10, 10, 10
15, 14, 14, 12, 8, 8
15, 14, 14, 11, 9, 8
15, 14, 14, 10, 10, 8
15, 14, 14, 10, 9, 9
15, 14, 13, 13, 9, 8
15, 14, 13, 12, 10, 8
15, 14, 13, 12, 9, 9
15, 14, 13, 11, 11, 8
15, 14, 13, 11, 10, 9
15, 14, 13, 10, 10, 10
15, 14, 12, 12, 11, 8
15, 14, 12, 12, 10, 9
15, 14, 12, 11, 11, 9
15, 14, 12, 11, 10, 10
15, 14, 11, 11, 11, 10
15, 13, 13, 13, 11, 8
15, 13, 13, 13, 10, 9
15, 13, 13, 12, 12, 8
15, 13, 13, 12, 11, 9
15, 13, 13, 12, 10, 10
15, 13, 13, 11, 11, 10
15, 13, 12, 12, 12, 9
15, 13, 12, 12, 11, 10
15, 13, 12, 11, 11, 11
15, 12, 12, 12, 12, 10
15, 12, 12, 12, 11, 11
14, 14, 14, 13, 9, 8
14, 14, 14, 12, 10, 8
14, 14, 14, 12, 9, 9
14, 14, 14, 11, 11, 8
14, 14, 14, 11, 10, 9
14, 14, 14, 10, 10, 10
14, 14, 13, 13, 11, 8
14, 14, 13, 13, 10, 9
14, 14, 13, 12, 12, 8
14, 14, 13, 12, 11, 9
14, 14, 13, 12, 10, 10
14, 14, 13, 11, 11, 10
14, 14, 12, 12, 12, 9
14, 14, 12, 12, 11, 10
14, 14, 12, 11, 11, 11
14, 13, 13, 13, 13, 8
14, 13, 13, 13, 12, 9
14, 13, 13, 13, 11, 10
14, 13, 13, 12, 12, 10
14, 13, 13, 12, 11, 11
14, 13, 12, 12, 12, 11
14, 12, 12, 12, 12, 12
13, 13, 13, 13, 13, 10
13, 13, 13, 13, 12, 11
13, 13, 13, 12, 12, 12

 

[Tony Vargas]

I thought these were all already listed somewhere...?

... oh, no 27pts, guess not.

Nice to know, though, thanks for making the effort.

 

[Dan Chernozub]

This is quite useless as some are strictly better than others. If I want players to be unequal (which I usually do) - I have other options.

Ugh and randomizing through 27 options and without the chance to hit really high or low is just boooooring.

IMO.

PS. Math seems ok on the first glance.

 

[Ganymede81]

My current PC uses 15, 14, 14, 10, 10, 8, which is not in your chart.

 

[snickersnax]

Just a quick glance. I don't see

15,14,12,12,10,9
15,14,12,11,10,10

I'm fairly certain there are others, but I'll leave that to you

 

[bid]

My current PC uses 15, 14, 14, 10, 10, 8, which is not in your chart.

Yep.

Beside the 15 14 14 group missing, the 12 9 9 is not in order. Or 12 12 8 for that matter. This makes it hard to validate completion.

 

[cbwjm]

I think there may be quite a few missing, even without those already mentioned. I noticed that none of them were an array with 2 or more 14s like 14, 14, 13, 12, 10, 10 or 14, 14, 14, 10, 10, 10. A point buy with a double 14 is how I create Mountain dwarf warriors.

 

[m00]

For a point buy with 27 points, there turn out to be 65 different valid arrays. The easiest way to find these is to enumerate all possible arrays (all combinations of scores 8 through 15 each), and discard those whose point buy value is not 27 (using a computer of course).

Here they are:

15,15,15,8,8,8
15,15,14,10,8,8
15,15,14,9,9,8
15,15,13,12,8,8
15,15,13,11,9,8
15,15,13,10,10,8
15,15,13,10,9,9
15,15,12,12,9,8
15,15,12,11,10,8
15,15,12,11,9,9
15,15,12,10,10,9
15,15,11,11,11,8
15,15,11,11,10,9
15,15,11,10,10,10
15,14,14,12,8,8
15,14,14,11,9,8
15,14,14,10,10,8
15,14,14,10,9,9
15,14,13,13,9,8
15,14,13,12,10,8
15,14,13,12,9,9
15,14,13,11,11,8
15,14,13,11,10,9
15,14,13,10,10,10
15,14,12,12,11,8
15,14,12,12,10,9
15,14,12,11,11,9
15,14,12,11,10,10
15,14,11,11,11,10
15,13,13,13,11,8
15,13,13,13,10,9
15,13,13,12,12,8
15,13,13,12,11,9
15,13,13,12,10,10
15,13,13,11,11,10
15,13,12,12,12,9
15,13,12,12,11,10
15,13,12,11,11,11
15,12,12,12,12,10
15,12,12,12,11,11
14,14,14,13,9,8
14,14,14,12,10,8
14,14,14,12,9,9
14,14,14,11,11,8
14,14,14,11,10,9
14,14,14,10,10,10
14,14,13,13,11,8
14,14,13,13,10,9
14,14,13,12,12,8
14,14,13,12,11,9
14,14,13,12,10,10
14,14,13,11,11,10
14,14,12,12,12,9
14,14,12,12,11,10
14,14,12,11,11,11
14,13,13,13,13,8
14,13,13,13,12,9
14,13,13,13,11,10
14,13,13,12,12,10
14,13,13,12,11,11
14,13,12,12,12,11
14,12,12,12,12,12
13,13,13,13,13,10
13,13,13,13,12,11
13,13,13,12,12,12

EDIT: in case it's of interest, there are a total 1716 unique arrays (before sorting them into 6 ability scores). The number of arrays per point buy value is distributed like this:

value: #
0: 1
1: 1
2: 2
3: 3
4: 5
5: 7
6: 10
7: 13
8: 17
9: 22
10: 27
11: 32
12: 39
13: 44
14: 51
15: 56
16: 62
17: 66
18: 72
19: 73
20: 77
21: 77
22: 79
23: 76
24: 77
25: 72
26: 71
27: 65
28: 63
29: 56
30: 55
31: 46
32: 45
33: 37
34: 36
35: 28
36: 28
37: 21
38: 21
39: 15
40: 15
41: 10
42: 11
43: 6
44: 7
45: 4
46: 5
47: 2
48: 3
49: 1
50: 2
52: 1
54: 1

 

[cbwjm]

For a point buy with 27 points, there turn out to be 65 different valid arrays. The easiest way to find these is to enumerate all possible arrays (all combinations of scores 8 through 15 each), and discard those whose point buy value is not 27 (using a computer of course).

Here they are:

15,15,15,8,8,8
15,15,14,10,8,8
15,15,14,9,9,8
15,15,13,12,8,8
15,15,13,11,9,8
15,15,13,10,10,8
15,15,13,10,9,9
15,15,12,12,9,8
15,15,12,11,10,8
15,15,12,11,9,9
15,15,12,10,10,9
15,15,11,11,11,8
15,15,11,11,10,9
15,15,11,10,10,10
15,14,14,12,8,8
15,14,14,11,9,8
15,14,14,10,10,8
15,14,14,10,9,9
15,14,13,13,9,8
15,14,13,12,10,8
15,14,13,12,9,9
15,14,13,11,11,8
15,14,13,11,10,9
15,14,13,10,10,10
15,14,12,12,11,8
15,14,12,12,10,9
15,14,12,11,11,9
15,14,12,11,10,10
15,14,11,11,11,10
15,13,13,13,11,8
15,13,13,13,10,9
15,13,13,12,12,8
15,13,13,12,11,9
15,13,13,12,10,10
15,13,13,11,11,10
15,13,12,12,12,9
15,13,12,12,11,10
15,13,12,11,11,11
15,12,12,12,12,10
15,12,12,12,11,11
14,14,14,13,9,8
14,14,14,12,10,8
14,14,14,12,9,9
14,14,14,11,11,8
14,14,14,11,10,9
14,14,14,10,10,10
14,14,13,13,11,8
14,14,13,13,10,9
14,14,13,12,12,8
14,14,13,12,11,9
14,14,13,12,10,10
14,14,13,11,11,10
14,14,12,12,12,9
14,14,12,12,11,10
14,14,12,11,11,11
14,13,13,13,13,8
14,13,13,13,12,9
14,13,13,13,11,10
14,13,13,12,12,10
14,13,13,12,11,11
14,13,12,12,12,11
14,12,12,12,12,12
13,13,13,13,13,10
13,13,13,13,12,11
13,13,13,12,12,12

EDIT: in case it's of interest, there are a total 1716 unique arrays (before sorting them into 6 ability scores). The number of arrays per point buy value is distributed like this:

value: #
0: 1
1: 1
2: 2
3: 3
4: 5
5: 7
6: 10
7: 13
8: 17
9: 22
10: 27
11: 32
12: 39
13: 44
14: 51
15: 56
16: 62
17: 66
18: 72
19: 73
20: 77
21: 77
22: 79
23: 76
24: 77
25: 72
26: 71
27: 65
28: 63
29: 56
30: 55
31: 46
32: 45
33: 37
34: 36
35: 28
36: 28
37: 21
38: 21
39: 15
40: 15
41: 10
42: 11
43: 6
44: 7
45: 4
46: 5
47: 2
48: 3
49: 1
50: 2
52: 1
54: 1

I knew it wouldn't be long before someone would come up with something like this.

 

[Krachek]

Poing buy options?
Allow only 24,25,26, or give a bonus to 28,29,30 could be nice options.