  Partizan subtraction games are combinatorial games where two players, say
Left and Right, alternately remove a number n of tokens from a heap of tokens,
with $n \in S_L$ (resp. $n \in S_R$) when it is Left's (resp. Right's) turn.
The first player unable to move loses. These games were introduced by Fraenkel
and Kotzig in 1987, where they introduced the notion of dominance, i.e. an
asymptotic behavior of the outcome sequence where Left always wins if the heap
is sufficiently large. In the current paper, we investigate the other kinds of
behaviors for the outcome sequence. In addition to dominance, three other
disjoint behaviors are defined, namely weak dominance, fairness and ultimate
impartiality. We consider the problem of computing this behavior with respect
to $S_L$ and $S_R$, which is connected to the well-known Frobenius coin
problem. General results are given, together with arithmetic and geometric
characterizations when the sets $S_L$ and $S_R$ have size at most 2.
