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*To*: tft@brainiac.com*Subject*: Re: (TFT) An Even More Radical Re-Imagining of TFT...*From*: dwtulloh@zianet.com*Date*: Wed, 21 Jan 2004 13:12:10 -0700*In-reply-to*: <01c001c3e03b$3398a580$8600a8c0@youroxg2elbf6o>*References*: <BAY4-DAV41Gmig3ScSv000099e5@hotmail.com> <017c01c3e02f$502088a0$8600a8c0@youroxg2elbf6o> <003101c3e037$e3e45140$e164a8c0@etclink.net> <01c001c3e03b$3398a580$8600a8c0@youroxg2elbf6o>*Reply-to*: tft@brainiac.com*Sender*: tft-owner@brainiac.com

From: "Neil Gilmore" <raito@raito.com>> 5. A defending figure adds 5 (or 3 if using 3d6) to his roll,> but never hits a foe.This definitely messes up the bell curve.Howso? If you use 3d6, the bell curve is preserved and 3 is aclose approximation of the effect of adding a 4th die. Is the4d6 bell curve really all that fabulous?

First, the 3d6 and 4d6 approximate a normal distribution, but the fit isn't all that great in either case. A 3d6 curve has a mean of 10.5 and a standard deviation of 2.95804; a 4d6 has a mean of 14.0 and a standard deviation of 3.41565. Comparing

s.d range 3d6 4d6 normal ========== ====== ====== ====== -0.5 to 0.5 0.4815 0.5216 0.3830 0.5 to 1.5 0.2130 0.1852 0.2417 1.5 to 2.5 0.0185 0.0532 0.0606

The values for the 3d6 and 4d6 curves were computed by finding

s.d value 3d6 4d6 ========== ====== ====== -0.5 9.02 => 9 12.29 => 12 0.5 11.98 => 12 15.71 => 16 1.5 14.94 => 15 19.12 => 19 2.5 17.90 => 18 22.54 => 23

So then to determine the probability that your dice roll on 3d6 falls between 0.5 and 1.5 standard deviations from the mean, you simply add up the probabilities associated with a

Second, adding a value to the total of 3d6 does NOT approximate a 4d6 curve. All you are doing is changing the mean of the curve, you aren't affecting its range or shape. The 4d6 curve has a different range and shape as compared to the 3d6 curve,

Unfortunately, the 3d6 and 4d6 curves are about as close as you are going to be able to get to the normal curve using d6. There are other methods using dice which closer approximate a normal curve, but you have to be willing to use other polyhedra or re-interpret the numbers you get from a d6 throw. ( For example, you can get a pretty good fit for standard deviations from the mean by throwing 3d6, counting the number of 6's and subtracting the number of 1's. So a roll of 6,6,1 would yield

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**References**:**(TFT) An Even More Radical Re-Imagining of TFT...***From:*"Ty Beard" <tbeard@tyler.net>

**Re: (TFT) An Even More Radical Re-Imagining of TFT...***From:*"Neil Gilmore" <raito@raito.com>

**Re: (TFT) An Even More Radical Re-Imagining of TFT...***From:*"Ty Beard" <tbeard@tyler.net>

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