Any Math Geeks out there that like to mess with Dice averages?

[CRGreathouse]

It's even much harder for me working out an analytical solution. If I succeed, we may compare our results...

I can't think of a good way to come up with the overlap between all scores 13 or less and total modifiers 0 or less. Ideas?

Edit: My calculation should finish around 5:15 board time (Central).

 

[Nathan]

I can't think of a good way to come up with the overlap between all scores 13 or less and total modifiers 0 or less. Ideas?

Edit: My calculation should finish around 5:15 board time (Central).

What is your current solution of that problem?

 

[CRGreathouse]

What is your current solution of that problem?

Brute force. Current estimate: 15 more minutes

 

[Nathan]

Average stat total for PHB PC's

The average stat total of a PHB PC is

74.68778863.

As always, I'll give the exact solution, which is:

21224977756742502772/284182704371643047.

I haven't checked this result so it may be erroneous but I don't think (hope) so.

 

[CRGreathouse]

Re: Average stat total for PHB PC's

The average stat total of a PHB PC is

74.68778863.

How did you come up with this?

 

[Nathan]

I can't think of a good way to come up with the overlap between all scores 13 or less and total modifiers 0 or less. Ideas?

Edit: My calculation should finish around 5:15 board time (Central).

I calculated the number of possibilities

P(n, u, m, c)

to get a total of u with a total modifier m for n stats where every stat has to be <= c.

Then the answer is

(Z18-Z13)/(N18-N13)

where

Nx = sum P(6, u, m, x) over all possible u, m>=1,

and

Zx = sum P(6, u, m, x) * u over all possible u, m>=1.

EDIT: I've changed "m >= 0" into the correct "m >= 1"

 

[Nathan]

Re: Re: Average stat total for PHB PC's

How did you come up with this?

Using the procedure described above and Maple for doing the actual evaluation.

The function P(n,u,m,c) can be calculated recursively.

I hope my answer is correct. Your program should have finished by now, shouldn't it? What is its output?

 

[CRGreathouse]

Re: Average stat total for PHB PC's

Aaugh! My program just crashed... due to an external error (i.e. not a bug).

I'll run it again, but it'll take another half-hour...

 

[Nathan]

Re: Re: Average stat total for PHB PC's

Aaugh! My program just crashed... due to an external error (i.e. not a bug).

I'll run it again, but it'll take another half-hour...

Oh, what a pity. I'll wait the 30 minutes.

By the way, what is your computer power behind the scene? Is your program a C program?

 

[CRGreathouse]

Re: Re: Re: Average stat total for PHB PC's

Using the procedure described above and Maple for doing the actual evaluation.

The functions didn't make much sense, and I don't have Maple (that's a computer algebra system, or something similar, right?).

I'm using a hand calculator, Excel, basic programming software, and what I remember of probability...