Infinitesimal combinatorial game

A game value lying strictly between $-r$ and $r$ for every positive rational number $r$, in the ordering of partizan games. Infinitesimal values can determine a sum whose numerical part is zero, while they cannot overturn a nonzero integer advantage.

The impartial game $\ast =\{0\mid 0\}$, so either player can move to zero. It is equivalent to a Nim heap of size one. It is incomparable with zero, and $\ast +\ast =0$ under the disjunctive sum of games.