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*To*: <tft@brainiac.com>*Subject*: Re: (TFT) scaled stats*From*: "gem6868" <gem6868@verizon.net>*Date*: Thu, 06 Oct 2011 17:55:20 -0400*In-reply-to*: <p06240818cab3cd44f184@[129.162.151.118]>*References*: <p06240818cab3cd44f184@[129.162.151.118]>*Reply-to*: tft@brainiac.com*Sender*: tft-admin@brainiac.com

Sent: Thursday, October 06, 2011 5:44 PM To: gem6868@verizon.net Cc: tft@brainiac.com Subject: 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, addedtogether, for a result is always a bell-curve, not linear. 2d6 and 3d6bothwork 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 ----------------------------------------------------------------------- Large Asteroids headed toward planets inhabited by beings that don't have technology adequate to stop them: Think of it as Evolution in Fast-Forward.

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**References**:**Re: (TFT) scaled stats***From:*Mark Tapley <mtapley@swri.edu>

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