Friday, August 22, 2008

We MAY not be nerds...

But we are completely and thoroughly unrecognizable from them at this point. In fact, I created a new gmail account so my old one wouldn't even be linked to our adventure. I view the divorce from reality as a two-way street.

Anyway here are some interesting numbers I was thinking about... the odds of rolling a certain sum when you roll three dice:

3: 0.5% (actually 0.46, or 1 in 216, but rounded off for this table)
4: 1.4%
5: 2.8%
6: 4.6%
7: 6.9%
8: 9.7%
9: 11.6%
10: 12.5%
11: 12.5%
12: 11.6%
13: 9.7%
14: 6.9%
15: 4.6%
16: 2.8%
17: 1.4%
18: 0.5% (as 3’s note above)

The 3d6 method (as it's known, I assume, in the community of other non-nerds) produces an almost perfect bell curve, but of course our odds of rolling a higher sum were slightly higher since we were allowed to ditch the lowest number out of four die. (leaving aside for the moment that we had the option, judiciously exercised, of throwing out our first roll if we wanted.)

I've been thinking about this in my free time, and I have absolutely NO idea how to calculate our particular character creation odds. How do you account for the odds of particular sums of three out of four dice? Has anyone else thought about this?


Taran said...

Actually, I have. I ran a bunch of random dice rolls in excel. I ran roughly 130,000 groups (actually 2 65k groups) of 4 random rolls, summed them and subtracted the lowest number. I got an average of 12.251. Seems like that's statistically significant enough to call 12.25 the average. But the distribution said differently. Here was the distribution on the second group of 65k:

3 - 0.06%
4 - 0.28
5 - 0.71
6 - 1.63
7 - 3.03
8 - 4.85
9 - 6.98
10 - 9.29
11 - 11.43
12 - 12.77
13 - 13.53
14 - 12.33
15 - 10.16
16 - 7.17
17 - 4.10
18 - 1.66

You actually have a better chance to get a 13 than a 12. The bell curve is shifted to the right and is much steeper on the right side as well. I haven't crunched any of the stats on this (like, what were the chances of Angela rolling as low as she did), but I have the data.

Taran said...

John, if you're interested on how to do this in excel:

Do 4 columns of rand() functions down to the bottom of the sheet. Copy and paste special values once all the functions are there.

Then do 4 columns to the right using the function =roundup(A1*6,0), where A1 is the first random value entry. Copy that all the way down. Lets assume you used columns E:H for this.

Then to the right of that use the function =small(E1:H1,1) which returns the smallest value in your group of four rolls.

Then to the right of that do a sum of the four rolls less the smallest value, and you've got yourself a gigantic list of 4d6 rolls where you keep the top 3.

Taran said...

Update: Angela's chance of rolling a 67 (total of all 6 die rolls) or less: 19.45%.

Bethany's chance of rolling an 81 or higher: 15.59%. The rest of us were between those.

This was obviously much less statistically significant, since I only had 11,000 mutually exclusive random groups of 6 rolls to work with, but the most common total was 75 at 5.81%.

Lord Bolt said...

i don't totally understand how distribution relates to probability... isn't the distribution likely to be somewhat different on every 65k group?

Taran said...

Yeah, somewhat...I didn't feel like doing the stat analysis so I just gave you the raw data. I figure I used a large enough sample that the real curve won't be far off from that.

Ieuan said...

You are NERDS.