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

[Rayston]

Anyone know of a study done on dice averages, specifically dealing with common rolls done in RPG's?

I know its kinda silly info to care about but I was wondering what the average of the ability score generation system

4d6 drop the lowest. rolled 7 times, drop the lowest roll. would be?

i.e

you roll 4d6 drop the lowest,do that 7 times to obtain 7 #'s, and then drop the lowest of those #'s

what is the average # you will arrive at? I did it 10 times and came out with an average of 13.13, and was wondering if that was accurate to the laws of averages.

Also was wondering the average occurence of 18's, 17's 16's and on down the line. and any other cool info that would go with that ( the average lowest score in one characters stats, the average highest so on, and so on. )

A program that made this easy info to extrapolate would be cool as theres a few other systems I would like to find out this kinda info on.


Thanx

Del

 

[Storminator]

If you can work with any kind of programming language (or even Excel I think), it isn't to hard to just brute force thru all the possibilities and count them up.

I don't have time to go thru them now, but with 4d6 drop low, roll 7 keep 6 you have nearly an 11% chance of [at least] one 18.

That's all I have time for.

PS

Edit in brackets

 

[DanMcS]

Eh. Those are some complicated stats.

Average of 3d6 is 10.5. Average of 4d6 drop the lowest is probably higher; the average of 4d6 is 14, and you're dropping the low roll (a 1,2, or 3 on average, statistically a 2), so that puts you at about 12.

What would the effects be of 4d6 x 7, drop the low rolls, drop the low sum? I bet around a point, point and a half, so your 13.xx is right about on. Your way is probably faster than calculating it, and doing it a thousand times with a program would give us the exact answer If you did it 10 times, that's 280 rolls (wow, take a break), so you're approaching the average worth of the dice with that many reps.

Probably somebody else here can rattle off the stats by heart, so I'll stop speculating.

 

[tarchon]

This page has 6 4d6 drop lowest, reroll hopeless characters (standard 3e), but I know there was an error at one time, which may or may not have been corrected.
http://www.darkshire.org/~jhkim/rpg/dnd/index.html

These are the probabilities. You probably really care more about the modal (most common) than the mean stats, but the means aren't hard to compute either.

> highest 2nd 3rd 4th 5th 6th
>
> 3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0026
> 4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0128
> 5 0.0000 0.0000 0.0000 0.0000 0.0003 0.0318
> 6 0.0000 0.0000 0.0000 0.0000 0.0032 0.0753
> 7 0.0000 0.0000 0.0000 0.0001 0.0141 0.1277
> 8 0.0000 0.0000 0.0000 0.0038 0.0614 0.1911
> 9 0.0000 0.0000 0.0004 0.0230 0.1426 0.2103
> 10 0.0000 0.0003 0.0145 0.1091 0.2359 0.1772
> 11 0.0000 0.0051 0.0719 0.2174 0.2484 0.1086
> 12 0.0000 0.0503 0.2019 0.2807 0.1816 0.0471
> 13 0.0000 0.1652 0.2960 0.2251 0.0851 0.0131
> 14 0.1295 0.2997 0.2536 0.1079 0.0236 0.0021
> 15 0.2362 0.2754 0.1243 0.0288 0.0035 0.0002
> 16 0.2964 0.1549 0.0335 0.0038 0.0002 0.0000
> 17 0.2320 0.0448 0.0038 0.0002 0.0000 0.0000
> 18 0.1059 0.0043 0.0001 0.0000 0.0000 0.0000

The modal stats are 16,14,13,12,11,9 (+6 mods) then. Definitely a little beefier than the base point-buy system in the DMG, but not by a whole lot (standard 15,14,13,12,10,8, +5 mods). It's interesting that the DMG's standard stat array is so close to the modal abilities. It seems pretty likely that they worked this out to derive the point buy system. 29 points would probably tend to be closer to the random rolls than the 25 point allowance though.

Sorry the table sucks - this board doesn't seem to render pre tags very well and I just pasted it from an old USENET post of mine.

The code for this is very easy to write, but sometimes people run into problems with underflows and making unwarranted approximations.

 

[Storminator]

I don't hink that page takes into account rolling 7 stats and taking 6 of them.

Pretty good basic stats tho

PS

 

[Rayston]

Geekiness!!

At this point, I am more curious for the sake of figuring it out more than they are actually usefull for anything.

i.e

I kinda like to screw with numbers, but have forgotten almost all of the formulary type stuff for figuring out averages.

;-)

Especially when it comes to how to extrapolate not only the average stat, but stuff like the percentage occurence of a given stat and such.

;-)

Thanx for the comments though.

Rayston

 

[tarchon]

I can give you the C code for 6 4d6s if you want to adapt it. With 7 4d6, it should execute in a minute or less on a contemporary system.

 

[Chacal]

Come on, we're talking about math geeks, not programmers

Is there a cool general formula for the average of:
roll N S-sided dice, then keep K and add ?


Chacal

 

[Nathan]

Please wait a moment... I'm working on the formula. Soon it'll be posted.

 

[Dr Lucky]

I actually asked an engineering professor of mine to work out the average for 4d6, drop the lowest. He worked the probability out for me, but unfortunately I don't have the formula any more. It worked out to 11 and some change. I don't know how adding in 7 total roles and dropping the lowest would work.