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

[Nathan]

I'm impressed. This is exactly correct! Usually, people on the boards aren't that good with probability...

Thank you

And now I have the answer to the original question:

A PC generated via the following method:

Roll 7 stats, each stat via 4d6 drop lowest.
Then drop lowest stat.


has an average total of his/her ability scores of

77.46649420...

The exact value is

475717264465598581693141/6140942214464815497216

Evaluation of my formula for that problem was done with a computer in about 5 seconds.

 

[tarchon]

Ugh.
Simply put, 348 billion total permutations sucks.

Compute the PMF of 4d6-drop-lowest and then do the order statistics on those RVs. That leaves you with only 32 million outcomes, which is quite tractable on a 500+ MHz computer.

 

[CRGreathouse]

77.46649420

Ooh, nice. This is correct, at least to the decimal places I calculated it to. (Or is it the other way around: mine is correct tot the number of decimal places I calculated it to?)

 

[Nathan]

I'm trying to find a mathematical shortcut, but have been unsuccessful thus far.

--The Sigil

Sigil, are you interested in my solution of the problem?

 

[Nathan]

Ooh, nice. This is correct, at least to the decimal places I calculated it to. (Or is it the other way around: mine is correct tot the number of decimal places I calculated it to?)

How did you do the calculation?

 

[CRGreathouse]

What are the rules for useless characters? I lent my PH out and can't look it up...

 

[CRGreathouse]

How did you do the calculation?

The easy way: I wrote a program to go through the (18-3+1)^7 total possibilities, then weighted each one by its probability of happening.

I'm now trying to do one that ignores useless characters.

 

[Nathan]

Under rerolling in Chapter One "Abilities" of the PHB it says:

at least one stat 14,
total modifiers >= 1

so that a character is non-useless.

 

[CRGreathouse]

OK, it's running. This one's much harder - it's going slowly. I'll get back in a few minutes.

 

[Nathan]

OK, it's running. This one's much harder - it's going slowly. I'll get back in a few minutes.

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