  We introduce a class of normal play partizan games, called Complementary
Subtraction. Let $A$ denote your favorite set of positive integers. This is
Left's subtraction set, whereas Right subtracts numbers not in $A$. The Golden
Nugget Subtraction Game has the $A$ and $B$ sequences, from Wythoff's game, as
the two complementary subtraction sets. As a function of the heap size, the
maximum size of the canonical forms grows quickly. However, the value of the
heap is either a number or, in reduced canonical form, a switch. We find the
switches by using properties of the Fibonacci word and standard Fibonacci
representations of integers. Moreover, these switches are invariant under
shifts by certain Fibonacci numbers. The values that are numbers, however, are
distinct, and we find a polynomial time bit characterization for them, via the
ternary Fibonacci representation.

Combinatorics;Number Theory