There may be some wisdom in the KISS method
(1-a)*(wd*B/D)*(sd/wd)^a
is simpler than
[(1-a)/(1-a*wd^(1-a)*(1.5D)^(a-1))]*(wd*B/D)*(min(1.5D,sd)/wd)^a.
a^2/(1-2a) is simpler than -1+((-1 + a)^2 X (-wd^(2 a) X + 2 a wd X^(2 a)))/((-1 + 2 a) (-wd^a X + a wd X^a)^2). The expression for the variance is what you need to truly bound your risks.
by putting a reasonable cap on max reward as opposed to taking a "1 in a quintillion" chance of something astronomically bad happening.
Have any of us said "the chance of X happening is so remote that we don't need to worry about it?" I have, and far too many times I've had to follow up by saying "ain't never seen that before".
You should distinguish
1. Hunches that something is unlikely, or derivation of probabilities based on strong assumptions of dubious truth value
from
2. Probability derivations for essentially pure random processes where there are virtually no relevant assumptions.
#1 are only as good as your process - in other words, usually not very good. #2 Really do mean something. Something that has a true probability of 1 in a billion to cause, say, my own death, is really nothing to worry about.