Re: (TFT) scaled stats

[Mark Tapley <mtapley@swri.edu>]

gem6868,

At 16:06 -0400 9/30/11, gem6868 wrote:
>I think that what's being noted is that the use of multiple dice, added
>together, for a result is always a bell-curve, not linear.  2d6 and 3d6 both
>work that way.  While I can rattle off the 2d6 from memory, the average is
>'7' (most number of combinations) and with 3d6 it's 10-11 (most
>combinations, averaging to 10.5 I believe).  I'm not a math person, so
>someone else will have to provide details.

	attached, a plot showing how the bell curve steepens for more 
dice. This is the same data as presented in the reference Jay gave,

http://alumnus.caltech.edu/~leif/FRP/probability.html

(at least I hope so! I calculated it independently and have not 
checked) but the "bell curve" for each different number of dice is 
scaled so that they superpose. For n die, the horizontal axis is the 
die roll divided by n, and the vertical axis is the probability of 
that exact roll.

yellow - 1 die
green - 2 dice
light blue - 3 dice
dark blue - 4 dice
purple - 5 dice
orange - 6 dice

	So you can see that for 1 die, each result from 1 to 6 has a 
probability of 0.1666 of coming up on a given roll. For 2 dice, the 
possibilities run from 2 to 12 (so on the plot it looks like (2 to 
12) / 2 -> (1 to 6). The most likely result, 7, comes up 0.1666 of 
the time, but others are less likely, down to 2 and 12 at 0.02777 of 
the time. (Total area under the curve looks less, but there are more 
possibilities - the horizontal scaling compresses the area for each 
possibility, but the total still adds up to 1.0000 for all of the 
possibilities.)

	As you go to more and more dice, the "bell curve" gets 
steeper and steeper, so crossing over the "halfway mark" gets more 
and more important if you want to hit.

	Scaling the curves up by n (number of dice) makes this even 
more apparent (but harder to interpret correctly mathematically); 
that's the second plot (DieDistrosVertScale) also attached.


Mailing list readers,
	Pretty sure the attachment won't make it on the list; email 
me or post here if you want a copy of the plots or if you have a good 
place to post them.
-- 
						- Mark     210-379-4635
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[demime 1.01d removed an attachment of type application/octet-stream which had a name of DieDistros.pdf]

[demime 1.01d removed an attachment of type application/octet-stream which had a name of DieDistrosVertScale.pdf]
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