CPSC 370: Functional and Logic Programming (2006)
Doubling Nim Rules

This is a standard onepile Nim game, meaning that is a game between
two players involving a pile of stones. Players take turns removing
stones from the pile, and the player who takes the last stone or
stones loses.

The first player on his first move may take between 1 and 4 stones.

Thereafter a player on her turn may take between 1 and twice the
number her opponent just took (inclusive).

For play between human opponents, who plays first and the size of
the initial pile should be settled by some mutually agreeable
method.
The general idea of this game is due
to
Donald Knuth.
Those who want to know more about the general theory of twoperson games
should consult Winning Ways for Your Mathematical Plays by
Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy. I believe that
this can be found in the unbc library.