5D6 drop the lowest two (math ?)

[JiffyPopTart]

Ok folks, and more specifially statistics guys and gals, heres the scoop.

I am running a Forgotten Realms campaign in which I want the PC's to be extra heroic with their stat rolls. So, with that idea in mind, I decided to throw them an extra bonus in character creation and roll 5D6 instead of 4, and drop the lowest two dice to determine their stats. I have run this through a giant number mill and determined the average score is 13.4.

I am also offering the option to instead take a base score of 8 in each stat, and add 33 points, which also would give you an average score of a 13.4.

My question to you, the reader, is this...

I know how to find the average stat by brute force, but I have become interested in finding out how to determine the average by an actual formula or proper math, not just repetition. Does anyone know how to figure this out, or else where I could find some information on the web helping me out?

Thanks ahead of time
DS

 

[theoremtank]

This is a very good question and one I have pursued also. I too am able to calculate the average by numerical methods but I have yet to solve the problem using any symbolic mathematical methods or equations.

I believe this is a combinatorics problem where we need to figure out the pattern for how many ways we can roll up each possible ability score. As soon as you introduce dropping the lowest dice you introduce a decision in the process which I believe is what complicates things.

If anyone has figured this out yet I would love to hear your solution.

Heres a link to an excel spreadsheet a friend of mine whipped up for the 4d6 drop the lowest average.
http://www.members.cox.net/theoremtank1/maps/4d6 drop lowest average.xls

 

[Ycore Rixle]

I would also like to see the math on this one.

 

[HellHound]

Ask Charles Greathouse about the math.

He posted an analysis of all our standard character creation methods on another forum a few days ago...

From the various point-buys, to 4d6 drop lowest, 5d6 drop 2, 3d6+1d8 drop lowest, etc.

---

Hound Post #1968 - The year of 2001: A Space Odyssey. 'I'm sorry, Dave. I'm afraid I can't do that.'

 

[Winternight]

Can some nice person please link this threat?

Thanx in advance

 

[Drawmack]

I've had this discussion a couple of times. One of the threads on this board yielded a formula for finding the % chance of rolling any given number when roll any combination of any dice.

This could easily be extrpolated upon to get the average roll.

Could some nice comunity support use their search abilities to find this thread for this nice gentleman please?

 

[Tabarnak Smokeblower]

The general way to calculate an average is thus:

You take the sum of ((sum of dice) * (chance of getting that sum))

Of course you have to calculate the probability of getting every possible combination (3 to 18), which can get a little complicated with drop-die methods. The spreadsheet posted by theoremtank can easily be adapted for 5d6, I think.

I'll try to whip up something at lunch, if the answers haven't been posted yet.

TS, who's trying desperately to remember stuff from his stats degree...

 

[Tabarnak Smokeblower]

Ok it's not lunch yet but I'm bored out of my mind at work.

Here's the lowdown on 5d6 drop 2 lowest.

It's not elegant, and I haven't found an easy mathematical formula to calculate these things in the future.

See the attached excel file for results... (the excel file is too big dang it! Had to zip it)

TS

 

[theoremtank]

Ok it's not lunch yet but I'm bored out of my mind at work.

Here's the lowdown on 5d6 drop 2 lowest.

It's not elegant, and I haven't found an easy mathematical formula to calculate these things in the future.

See the attached excel file for results... (the excel file is too big dang it! Had to zip it)

TS

Thanks for the work Tabarnak. Do you have any insight on a method for counting (combinatorally) the different ways each ability score can come up. This is the tricky part as you already noted. I imagine if we solved a simpler problem first such as 2d6, 3d6 or 4d6 (drop the lowest) we might be able to generalize the formula.

 

[Tabarnak Smokeblower]

Thanks for the work Tabarnak. Do you have any insight on a method for counting (combinatorally) the different ways each ability score can come up. This is the tricky part as you already noted. I imagine if we solved a simpler problem first such as 2d6, 3d6 or 4d6 (drop the lowest) we might be able to generalize the formula.

I'll try to do some research during the week-end But i'm pretty sure there's no "simple" way of finding the answer... the "drop lowest" is what makes it a little more complicated.

Have a good one!

TS