Star, as defined by John Conway in Winning Ways for your Mathematical Plays, is a value, but not a number in the traditional sense.
Star is not zero, but neither positive nor negative, and is therefore said to be fuzzy and confused with (a fourth alternative that means neither "less than", "equal to", nor "greater than") 0.
Likewise, a combinatorial game is won (assuming optimal play) by the second player if and only if its value is 0.
Star does have the property that the sum ∗ + ∗, has value 0, because the first-player's only move is to the game ∗, which the second-player will win.
The numbers ∗z for integers z form an infinite field of characteristic 2, when addition is defined in the context of combinatorial games and multiplication is given a more complex definition.