Genus of A Game
The genus of a game is defined using the mex (minimum excludant) of the options of a game.
g+ is the grundy value or nimber of a game under the normal play convention.
g- or lambda0 is the outcome class of a game under the misère play convention.
More specifically, to find g+, *0 is defined to have g+ = 0, and all other games has g+ equal to the mex of its options.
To find g−, *0 has g− = 1, and all other games has g− equal to the mex of the g− of its options.
λ1, λ2..., is equal to the g− value of a game added to a number of *2 nim games, where the number is equal to the subscript.
Thus the genus of a game is gλ0λ1λ2....
*0 has genus value 0120. Note that the superscript continues indefinitely, but in practice, a superscript is written with a finite number of digits, because it can be proven that eventually, the last 2 digits alternate indefinitely.
Read more about this topic: Genus Theory
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