Dice math help needed

[Zombimode]

My next campaign is based arround the standart 28 point buy.

But since rolling for stats has a long tradition in this group, I want to provide an option for rolling stats, but one that is fair alongside 28 pb. Now, I suck at math and have no idea how to come up with a rolling method more or less equal to 28 pb.

Any suggestions?

[Darth_Versity]

Something simple that still provides a slightly better average. Something like roll 4d6 seven times dropping the lowest, and then take the six highest results.

Another one I do is 4d6 six times, but you have a single bonus d6 you can use at any time. So if you end up rolling 1,1,2,4 giving a 7 on your third roll, you can roll the extra die and hopefully get a higher number to replace the 1 thats currently lowering the total.

[Zombimode]

Something simple that still provides a slightly better average. Something like roll 4d6 seven times dropping the lowest, and then take the six highest results.

Providing slightly higher avarages is fine. It only helps MAD people, and SAD charecters probaly wont trust the dice to produce an 18 anyway.

Thanks :smallsmile:

[Golden Ladybug]

Well, a 'standard' 28 Point Buy is 16, 14, 14, 10, 10, 10. Now, if we set it to an average ability score, we'd get 12.33

So, we need something that averages around that.

Here are some things that come close, die roll wise. Be warned, I'm not a mathmetician, so how I'm doing this might be incredibly flawed. I just rolled 20 times for each, and took the average from there. These are also just some decent ideas to try out for stat rolling.

Prepare for some fruity ideas for rolling stats

3d6+3 averaged at 11.75

3d6+3
4,2,3+3 = 12

3d6+3
2,3,6+3 = 14

3d6+3
6,2,6+3 = 17

3d6+3
3,1,2+3 = 9

3d6+3
1,5,6+3 = 15

3d6+3
2,4,2+3 = 11

3d6+3
5,1,2+3 = 11

3d6+3
2,6,5+3 = 16

3d6+3
3,3,5+3 = 14

3d6+3
1,4,5+3 = 13

3d6+3
3,1,2+3 = 9

3d6+3
1,4,3+3 = 11

3d6+3
4,5,2+3 = 14

3d6+3
3,3,5+3 = 14

3d6+3
5,2,1+3 = 11

3d6+3
3,6,4+3 = 16

3d6+3
5,3,2+3 = 13

3d6+3
3,5,4+3 = 15

3d6+3
3,6,4+3 = 16

3d6+3
6,3,1+3 = 13



4d4+4 averaged at 15. Bit of an outlier, but it could work out.

4d4+4
2,1,1,1+4 = 9

4d4+4
3,4,2,1+4 = 14

4d4+4
3,3,1,2+4 = 13

4d4+4
4,3,1,4+4 = 16

4d4+4
3,3,4,1+4 = 15

4d4+4
2,4,3,2+4 = 15

4d4+4
2,4,3,4+4 = 17

4d4+4
1,4,2,4+4 = 15

4d4+4
1,4,3,2+4 = 14

4d4+4
2,4,2,1+4 = 13

4d4+4
4,2,4,3+4 = 17

4d4+4
2,2,4,4+4 = 16

4d4+4
1,2,3,3+4 = 13

4d4+4
4,1,2,4+4 = 15

4d4+4
4,4,1,4+4 = 17

4d4+4
3,1,3,1+4 = 12

4d4+4
1,3,1,1+4 = 10

4d4+4
1,4,4,1+4 = 14

4d4+4
3,2,3,4+4 = 16

4d4+4
4,2,1,3+4 = 14



2d6+6 averaged at 11.9

2d6+6
1,4+6 = 11

2d6+6
4,1+6 = 11

2d6+6
5,5+6 = 16

2d6+6
2,1+6 = 9

2d6+6
1,5+6 = 12

2d6+6
4,5+6 = 15

2d6+6
6,2+6 = 14

2d6+6
3,2+6 = 11

2d6+6
3,4+6 = 13

2d6+6
1,6+6 = 13

2d6+6
6,1+6 = 13

2d6+6
3,6+6 = 15

2d6+6
2,3+6 = 11

2d6+6
3,2+6 = 11

2d6+6
3,1+6 = 10

2d6+6
3,4+6 = 13

2d6+6
3,6+6 = 15

2d6+6
6,5+6 = 17

2d6+6
6,5+6 = 17


And, finally, 2d8+2 averaged at 12.25

2d8+2
4,6+2 = 12

2d8+2
6,1+2 = 9

2d8+2
5,6+2 = 13

2d8+2
2,5+2 = 9

2d8+2
4,6+2 = 12

2d8+2
8,7+2 = 17

2d8+2
6,5+2 = 13

2d8+2
3,2+2 = 7

2d8+2
6,7+2 = 15

2d8+2
2,8+2 = 12

2d8+2
4,7+2 = 13

2d8+2
4,7+2 = 13

2d8+2
3,7+2 = 12

2d8+2
1,5+2 = 8

2d8+2
8,5+2 = 15

2d8+2
6,6+2 = 14

2d8+2
7,5+2 = 14

2d8+2
4,7+2 = 13

2d8+2
5,4+2 = 11

2d8+2
5,6+2 = 13



But, to be honest, if you prefer to roll dice, I'd just say go with that...or maybe you roll four of your Ability scores, and have two scores, one of 16 and the other 14, to place where you want. That might work.

[Feytalist]

Well. You want something that has a minimum of 3 and a maximum of 18. My guess is that's why they chose the 3d6 roll in the first place. The extra "higher" d6 just skews the results slightly in favour of larger numbers.

We already know the dice's standard distributions, so empirical testing isn't really necessary. A d4 averages on 2.5, a d6 on 3.5, and so on.

Honestly, 4d6 drop 1 should work fine. To skew it even more in your players' favour, you could even go 5d6 drop 2.


My old dm had his own weird little ways. He would let us roll 3d6, then reroll any result less than 4, and then reroll the lowest of the new scores. The results varied wildly, but it resulted in most scores over 10.

Edit: Actually, that 2d8+2 looks good. Results from 4 - 18, so it has a large variance, but its mean is 11, which is .5 more than a regular 3d6.

[Vladislav]

e roll wise. Be warned, I'm not a mathmetician, so how I'm doing this might be incredibly flawed. I just rolled 20 times for each, and took the average from there. These are also just some decent ideas to try out for stat rolling.

Prepare for some fruity ideas for rolling stats

3d6+3 averaged at 11.75

3d6+3
4,2,3+3 = 12

3d6+3
2,3,6+3 = 14

3d6+3
6,2,6+3 = 17

3d6+3
3,1,2+3 = 9

3d6+3
1,5,6+3 = 15

3d6+3
2,4,2+3 = 11

3d6+3
5,1,2+3 = 11

3d6+3
2,6,5+3 = 16

3d6+3
3,3,5+3 = 14

3d6+3
1,4,5+3 = 13

3d6+3
3,1,2+3 = 9

3d6+3
1,4,3+3 = 11

3d6+3
4,5,2+3 = 14

3d6+3
3,3,5+3 = 14

3d6+3
5,2,1+3 = 11

3d6+3
3,6,4+3 = 16

3d6+3
5,3,2+3 = 13

3d6+3
3,5,4+3 = 15

3d6+3
3,6,4+3 = 16

3d6+3
6,3,1+3 = 13



4d4+4 averaged at 15. Bit of an outlier, but it could work out.

4d4+4
2,1,1,1+4 = 9

4d4+4
3,4,2,1+4 = 14

4d4+4
3,3,1,2+4 = 13

4d4+4
4,3,1,4+4 = 16

4d4+4
3,3,4,1+4 = 15

4d4+4
2,4,3,2+4 = 15

4d4+4
2,4,3,4+4 = 17

4d4+4
1,4,2,4+4 = 15

4d4+4
1,4,3,2+4 = 14

4d4+4
2,4,2,1+4 = 13

4d4+4
4,2,4,3+4 = 17

4d4+4
2,2,4,4+4 = 16

4d4+4
1,2,3,3+4 = 13

4d4+4
4,1,2,4+4 = 15

4d4+4
4,4,1,4+4 = 17

4d4+4
3,1,3,1+4 = 12

4d4+4
1,3,1,1+4 = 10

4d4+4
1,4,4,1+4 = 14

4d4+4
3,2,3,4+4 = 16

4d4+4
4,2,1,3+4 = 14



2d6+6 averaged at 11.9

2d6+6
1,4+6 = 11

2d6+6
4,1+6 = 11

2d6+6
5,5+6 = 16

2d6+6
2,1+6 = 9

2d6+6
1,5+6 = 12

2d6+6
4,5+6 = 15

2d6+6
6,2+6 = 14

2d6+6
3,2+6 = 11

2d6+6
3,4+6 = 13

2d6+6
1,6+6 = 13

2d6+6
6,1+6 = 13

2d6+6
3,6+6 = 15

2d6+6
2,3+6 = 11

2d6+6
3,2+6 = 11

2d6+6
3,1+6 = 10

2d6+6
3,4+6 = 13

2d6+6
3,6+6 = 15

2d6+6
6,5+6 = 17

2d6+6
6,5+6 = 17


And, finally, 2d8+2 averaged at 12.25

2d8+2
4,6+2 = 12

2d8+2
6,1+2 = 9

2d8+2
5,6+2 = 13

2d8+2
2,5+2 = 9

2d8+2
4,6+2 = 12

2d8+2
8,7+2 = 17

2d8+2
6,5+2 = 13

2d8+2
3,2+2 = 7

2d8+2
6,7+2 = 15

2d8+2
2,8+2 = 12

2d8+2
4,7+2 = 13

2d8+2
4,7+2 = 13

2d8+2
3,7+2 = 12

2d8+2
1,5+2 = 8

2d8+2
8,5+2 = 15

2d8+2
6,6+2 = 14

2d8+2
7,5+2 = 14

2d8+2
4,7+2 = 13

2d8+2
5,4+2 = 11

2d8+2
5,6+2 = 13

Why not just calculate and save all the hard work?

3d6+3 = average 13.5 (and can go as high as 21, so I'm not sure why you would want this)
4d4+4 = average 14 (and can go as high as 20)
2d6+6 = average 13
2d8+2 = average 11


Well, a 'standard' 28 Point Buy is 16, 14, 14, 10, 10, 10. Now, if we set it to an average ability score, we'd get 12.33

So, we need something that averages around that.

4d6-best-3 averages to 12.26, so there you go.

[ericgrau]

Average is not very good as higher numbers are more of an advantage than lower numbers are a drawback. As it happens I have a spreadsheet for just this thing. It rolls the dice 100,000 times and finds the average point buy:

5d6b3: 35 pb
4d6b3: 27 pb

Assumptions: Odd numbers are not worth more than even ones, except for 17.


I think 4d6b3 won't be that much of a drawback. Even a minor boost like the ability to reroll one of your many 1's adds +2.5 on average which usually makes it worth more than 28 pb. I thought I'd try out some of the other suggestions here:

3d6+3: 38.5 pb (you can roll a 21, which I pegged at 29 points)
3d6+2: 30 pb
2d6+6: 31 pb
2d6+5: 24 pb
2d8+2: 24.5 pb
2d8+3: 29 pb (but higher variation => more super low stats)
4d4+4: 39 pb
4d4+3: 30 pb (and less variation => less low stats)


I'd shoot for 29-30 pb since rolling is less flexible on moving numbers around, especially for SAD classes. The high stats from higher variation is already represented in the point buy amount, so more variation for a given point buy is typically only a drawback. Lower dump stats don't make a huge difference though.

[Zombimode]

Thats a great help! Thanks, ericgrau :smallsmile:

I think I will provide 2d8+3 as an alternative to 28 pp.
Those who want save can use point buy. Those who want to gamble can try their hands at the dice, whith good chances to get high stats but also good chances to get low ones. A good balance I think.