  This paper analyzes the question of where one should stand when playing
darts. If one stands at distance $d>0$ and aims at $a\in \mathbb{R}^n$, then
the dart (modelled by a random vector $X$ in $\mathbb{R}^n$) hits a random
point given by $a+dX$. Next, given a payoff function $f$, one considers $$
\sup_a Ef(a+dX) $$ and asks if this is decreasing in $d$; i.e., whether it is
better to stand closer rather than farther from the target. Perhaps
surprisingly, this is not always the case and understanding when this does or
does not occur is the purpose of this paper.
  We show that if $X$ has a so-called selfdecomposable distribution, then it is
always better to stand closer for any payoff function. This class includes all
stable distributions as well as many more.
  On the other hand, if the payoff function is $\cos(x)$, then it is always
better to stand closer if and only if the characteristic function $|\phi_X(t)|$
is decreasing on $[0,\infty)$. We will then show that if there are at least two
point masses, then it is not always better to stand closer using $\cos(x)$. If
there is a single point mass, one can find a different payoff function to
obtain this phenomenon.
  Another large class of darts $X$ for which there are bounded continuous
payoff functions for which it is not always better to stand closer are
distributions with compact support. This will be obtained by using the fact
that the Fourier transform of such distributions has a zero in the complex
plane. This argument will work whenever there is a complex zero of the Fourier
transform.
  Finally, we analyze if the property of it being better to stand closer is
closed under convolution and/or limits.
