Probability in Char. Gen.

[dvvega]

Perhaps I didn't explain to them what I wanted ... I originally did for the "what PB is the same as 4d6" question.

What I stated was the following:

If i roll 4d6 and discard the lowest, then apply these rules (shows them the PHB) then I tell you that you may build your set of scores by using this table (shows them the DMG), how many points should I give you to correctly reflect 4d6 and discard the lowest??

The first guy said - "sample space is finite because of the rules application and the rolls tending to an average, therefore ..."

Another guy said - "sample space is finite, but you can take the finite, work out PB for each, average that"

and so forth.

Now perhaps I missed something in the "problem description?" If I did, point it out to me so I can go back and fix it with them.

D

 

[Rystil Arden]

Perhaps I didn't explain to them what I wanted ... I originally did for the "what PB is the same as 4d6" question.

What I stated was the following:

If i roll 4d6 and discard the lowest, then apply these rules (shows them the PHB) then I tell you that you may build your set of scores by using this table (shows them the DMG), how many points should I give you to correctly reflect 4d6 and discard the lowest??

The first guy said - "sample space is finite because of the rules application and the rolls tending to an average, therefore ..."

Another guy said - "sample space is finite, but you can take the finite, work out PB for each, average that"

and so forth.

Now perhaps I missed something in the "problem description?" If I did, point it out to me so I can go back and fix it with them.

D

My guess is that whomever told you to take the average roll first and then find the point buy of that may not have immediately realised that there was a nonlinear progression in cost for stats, causing them to immediately iterate the expectation and oversimplify the problem into something very easy. Its a bit of wishful thinking that I often do myself

 

[Asmor]

The question is really quite simple.

What is the average point buy value of a character generated using the rules in the book.

There are two ways to arrive at that answer:

The "exact" method, i.e. figuring out a statistical way of looking at it to arrive at the correct answer OR

The "make a few hundred thousand characters and figure out what the average cost of them was" method.

I'd say that no matter what you think of the first method, or the algorithms/programs/whatever we all designed to do it, absolutely every single person would have to admit that the second option would be accurate. Now, the so-called "monte carlo" method, which I tested with 1 million characters, yielded results that I think are too close to some of the "exact" outputs to attribute to coincidence.

Thus, I feel it is entirely justified to say that the average point buy value of a character rolled up per the rules is just under 30.5 and that's that, end of discussion.

 

[dvvega]

I never said that Monte Carlo was wrong, just that you didn't have to generate your own sample space.

And if you take the average of 4d6 to be 12.2 then you can argue that you will get more 12s than 13s but you'll get some 13s.

Getting 6 x 13s, then you would have a 30 PB character and thus Monte Carlo is showing that in its results.

D

 

[Rystil Arden]

I never said that Monte Carlo was wrong, just that you didn't have to generate your own sample space.

And if you take the average of 4d6 to be 12.2 then you can argue that you will get more 12s than 13s but you'll get some 13s.

Getting 6 x 13s, then you would have a 30 PB character and thus Monte Carlo is showing that in its results.

D

Getting 6 x 13s, then you would have a 30 PB character and thus Monte Carlo is showing that in its results.

Actually not at all. Once again, the reason that the Monte Carlo (and other correct algorithms) generate a higher result is because they correctly weight in the above-linear average for scores above 14, whereas "taking 12" ignores it.

Let's make a hypothetical: Dvvega, I hope you would agree that if I made every stat above 14 cost 100 points each, that the average PB would rise by a lot? But taking 12 you wouldn't see a difference at all. Hope that helps you out

 

[dvvega]

I never claimed to be a statistician, I asked experts for their advice/knowledge/solutions.

I'm also not discussing probabilities, just the bare 4d6 = x PB.

However in my thinking, the higher the PB, the more common certain abilities become. For example with 25 PB, you will see an 18 less commonly than in 32 PB.

D

 

[Rystil Arden]

I never claimed to be a statistician, I asked experts for their advice/knowledge/solutions.

I'm also not discussing probabilities, just the bare 4d6 = x PB.

However in my thinking, the higher the PB, the more common certain abilities become. For example with 25 PB, you will see an 18 less commonly than in 32 PB.

D

I'm also not discussing probabilities, just the bare 4d6 = x PB.

However in my thinking, the higher the PB, the more common certain abilities become. For example with 25 PB, you will see an 18 less commonly than in 32 PB.

You need to factor in probabilities to calculate 4d6 = x PB. To wit, the way to calculate the average point buy for one 4d6 is to sum up the probability of each stat value (from 3 to 18) multiplied by its PB value. So if you have a Probability Distribution Funciton (PDF), which we'll call P(k), and a PointBuy Function that calculates point buy, which we'll call PB(k) then you do Sigma(P(k)*PB(k),k,3,18)

 

[Thanee]

Thus, I feel it is entirely justified to say that the average point buy value of a character rolled up per the rules is just under 30.5 and that's that, end of discussion.

Which PB approximation for stats under 8 did you use?

all 0 or {7|-1, 6|-2, 5|-3, 4|-4, 3|-5} or something else?

Bye
Thanee

 

[Asmor]

Which PB approximation for stats under 8 did you use?

all 0 or {7|-1, 6|-2, 5|-3, 4|-4, 3|-5} or something else?

Bye
Thanee

The latter.

 

[Rystil Arden]

The latter.

Actually, the choice of that particular approximation has less of an effect than it would seem at first, since characters with large numbers of low stats also tend to eb hopeless