Rystil Arden
First Post
Awww, come now. Its not inhumane to optimise a charactertwo said:
Probability in Char. Gen.
Rystil Arden
First Post
Hahaha, so true and so insightful!two said:
Charwoman Gene
Adventurer
How about everyone sends me money, I build a cluster of Linux boxes or mac minis and We run my original 17 century verifiable method...
dvvega
Explorer
This kind of discussion appears regularly on these boards. The problem is your "view" of what you are trying to accomplish.
For example:
1. roll of 4d6 generates 12.5 as an average, since you can't have fractional abilities = 12. Point buy for 12 is 4 per stat thus 24 point buy. 25 is a little extra.
2. generate all possible valid combinations, average each stat seperately, then calculate point buy from those averages.
3. generate all possible valid combinations, and average the point buy for those combinations.
To find every possible combination of rolls is quite easy, and I'm surprised people have written programs that take "hours" to run.
You have a limited sample space that can be easily generated this way. Generating 2 characters with the same statistics averages to a single character. Following all the rules, there are only so many characters that can be generated if you had unlimited time to do so.
You do not have to go and generate 1 million characters to get a sample space, you just need to create every possible combination of characters.
D
For example:
1. roll of 4d6 generates 12.5 as an average, since you can't have fractional abilities = 12. Point buy for 12 is 4 per stat thus 24 point buy. 25 is a little extra.
2. generate all possible valid combinations, average each stat seperately, then calculate point buy from those averages.
3. generate all possible valid combinations, and average the point buy for those combinations.
To find every possible combination of rolls is quite easy, and I'm surprised people have written programs that take "hours" to run.
You have a limited sample space that can be easily generated this way. Generating 2 characters with the same statistics averages to a single character. Following all the rules, there are only so many characters that can be generated if you had unlimited time to do so.
You do not have to go and generate 1 million characters to get a sample space, you just need to create every possible combination of characters.
D
Rystil Arden
First Post
Your math is wrong on #1. The average per stat is actually 12.2446. Its a fallacious way to generate average PB though because it allows itself to ignore the increasing cost of the higher stats.dvvega said:
dvvega
Explorer
The point is that the average indicates a 12.
And it isn't incorrect to do it this way ... it doesn't matter how many times you roll the bones you will get an average of 12 for each stat.
The question of: which PB is 4d6 equivalent to is answered from one viewpoint by doing this.
In a finite sample space, the average is 12 (12.2 ...). Thus to mimic that sample space the PB of 24 would indeed give you the average.
Its a matter of point of view, however. And one thing I forgot to add is that no set of stats with a 7 or lower is acceptable in the space. Why? Because PB cannot give you stats that low. You cannot buy 7s or lower, so the VB code posted earlier is give a skewed result by posting negative PB values.
The sample space that should be looked at should only have sets of stats with 8s or more in them. That way you have a sample space that equates both with 4d6 drop lowest and Point Buy.
D
Rystil Arden
First Post
No, you are still making a slight mistake. You're trying to take a shortcut that you simply cannot take unless you have a linear PDF (like if every stat point above 8 cost exactly 1 PB). You can't find the Cumulative Probability distribution without integrating across the sample space and weighting by both probability and value. You can abstract this away and take the average only when the derivative is constant.dvvega said:
dvvega
Explorer
Well the funny thing is I've consulted a total of 5 statiticians (both professors and professionals) and each one arrived to different answers because of their view points on the matter.
The only conclusion I could come to was that it was a point of view thing. Do you look at the set of stats as a whole? Do you look at each seperate stat? etc etc.
Since the PHB stats that your set of stats as a whole affects the outcome of 4d6 (at least one > 13, sum of modifiers > 0) that is the view I would think is more logical and consitent, however 5 different "experts" had varied opinions.
D
The only conclusion I could come to was that it was a point of view thing. Do you look at the set of stats as a whole? Do you look at each seperate stat? etc etc.
Since the PHB stats that your set of stats as a whole affects the outcome of 4d6 (at least one > 13, sum of modifiers > 0) that is the view I would think is more logical and consitent, however 5 different "experts" had varied opinions.
D
Rystil Arden
First Post
Perhaps the experts you asked didn't understand the situation completely? All that I can say is that I have Introduction to Probability by Bertsekas and Tsitsiklis here on my lap, which I've found to be one of the most respected sources for simple probability theory, and it has the formulas in here that specifically indicate when you can and can't just take the average here (its a property of the iterated expected value function). There is a lot of room for interpretation on the specifics, but it is unequivocably true that you cannot just take the point buy of the average roll.dvvega said:
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