On Wed, 19 Sep 2012, Joseph Heled wrote:
your test statistic is 117*-1 + 262*0 + 121*1 = 4
the standard deviation is (500 * (2/3))^0.5 = 18.25
This doesn't seem right (why 2/3 ?) and this is more than the
(1000 * 0.5 * (1 - 0.5))^0.5 = 15.8
from the dumb rollout.
On a second look I think it is :
E(x) = (close to) 0
E(x^2) = 121 + 117
for a standard deviation of 15.4 or a little less.
Duplicated dice would then be only a small improvement (at least in this
example).
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