# Re: (TFT) scaled stats

```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.

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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