* (pronounced "star"), is a technical term in
combinatoric game theory for a type of two-player, perfect-information
game in which the first player wins (assuming correct play). In a game of value *, the only move for either player is to a zero game, that is, a game where the player whose turn it is loses.
For example, in the game domineering, the following corner-shaped grid is of value *:
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Whichever player goes first will play a domino in two of the three squares on the grid. The unfortunate second player will not have a move, and will thus lose.
* is interesting re: smallest number greater than 0. It has value less than any positive game (a positive game is one where the Left player wins) and greater than any negative game, but is not greater than, less than, or equal to zero itself. Technically, * is not even a number.
For those interested, the partial order assumed in the last paragraph is defined as follows:
A > B iff A + (-B) > 0, where -B is the inverse of the game B.
A > 0 iff the Left player can win regardless of who goes first.
A point of interest is that * + * = 0.
The mathematicians among us should recognize this as just the adjoining of an element to the additive group of real numbers that is its own inverse.
Combinatoric game theory is full of non-numerical elements (switches are another fine example), but * is the simplest and most common of them all.