Absol197

2013-11-20, 11:15 PM

Hey there, so I'm having trouble working out how to calculate something vaguely D&D related, so I was hoping that the brilliant minds of the Playground might be able to help!

So, I've created a chart showing the probability that a certain NPC will have a certain natural score in any given ability score, as shown:

{table=head]Ability Score|Probability

18|0.882%

17|2.391%

16|4.384%

15|6.579%

14|8.833%

13|10.935%

12|11.983%

11|12.060%

10|11.367%

9|9.959%

8|8.006%

7|5.543%

6|3.606%

5|2.104%

4|1.031%

3|0.337%[/table]

Which is easy enough, when I just want to know how likely it is that a person has an 18 in any one given ability. But what I'm doing is basing the character's level off their highest mental ability score. So, what is the chance that a particular person has at least one of their three abilities that high, and none higher? For instance, the chance of having one of them be a 15 is 6.579%, but what's the chance that, out of the three, the character has at least one 15, and no ability score higher? I know there's got to be a (relatively) simple equation to figure that out, but I don't know what it is!

So: if you want to just give me the answer, that's fine, but helping me figure out the answer by sharing the equation would be awesome! I'm doing this for two different species, one with no racial bonus to a mental ability, and one with a +2 to Wisdom. If you could help me figure out both, you get triple points, and several cookies!

Thanks for all your help!

~Phoenix~

So, I've created a chart showing the probability that a certain NPC will have a certain natural score in any given ability score, as shown:

{table=head]Ability Score|Probability

18|0.882%

17|2.391%

16|4.384%

15|6.579%

14|8.833%

13|10.935%

12|11.983%

11|12.060%

10|11.367%

9|9.959%

8|8.006%

7|5.543%

6|3.606%

5|2.104%

4|1.031%

3|0.337%[/table]

Which is easy enough, when I just want to know how likely it is that a person has an 18 in any one given ability. But what I'm doing is basing the character's level off their highest mental ability score. So, what is the chance that a particular person has at least one of their three abilities that high, and none higher? For instance, the chance of having one of them be a 15 is 6.579%, but what's the chance that, out of the three, the character has at least one 15, and no ability score higher? I know there's got to be a (relatively) simple equation to figure that out, but I don't know what it is!

So: if you want to just give me the answer, that's fine, but helping me figure out the answer by sharing the equation would be awesome! I'm doing this for two different species, one with no racial bonus to a mental ability, and one with a +2 to Wisdom. If you could help me figure out both, you get triple points, and several cookies!

Thanks for all your help!

~Phoenix~