ABSTRACT
In the game of Nimstring, the amount by which a move changes the nimstring value is called its “nimstring incentive”. A very common incentive is *1, which is often abbreviated more succinctly as *. Any nonzero nimber can be an incentive. For example, suppose a Nimstring game is played on the sum of three disconnected components, X, Y, and Z, whose respective nimstring values are 0, *, and *3. The total position is
G = X + Y + Z = 0 + * + *3 = *2
Any winning move from G must change the value from *2 to 0, so it must have incentive *2. One such move would change the value of Z from *3 to *. Another such move might change the value of Y from * to *3. Since the nimber value of Y is 1, we know that the nimber values of its followers, Y´, satisfy
1 = mex (Y´)
so Y´ necessarily includes 0 and excludes 1. Y´ might or might not include the nimber 3.
