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**Harvard**

Larsson, U. (2010) *Blocking Wythoff Nim*.

** BibTeX **

@unpublished{

Larsson2010,

author={Larsson, Urban},

title={Blocking Wythoff Nim},

abstract={The 2-player impartial game of Wythoff Nim is played on two piles of tokens. A move consists in removing any number of tokens from precisely one of the piles or the same number of tokens from both piles. The winner is the player who removes the last token. We study this game with a blocking maneuver, that is, for each move, before the next player moves the previous player may declare at most a predetermined number, $k - 1 \ge 0$, of the options as forbidden. When the next player has moved, any blocking maneuver is forgotten and does not have any further impact on the game. We resolve the winning strategy of this game for $k = 2$ and $k = 3$ and, supported by computer simulations, state conjectures of the asymptotic behavior of the $P$-positions for the respective games when $4 \le k \le 20$.},

year={2010},

note={14},

}

** RefWorks **

RT Unpublished Material

SR Electronic

ID 134968

A1 Larsson, Urban

T1 Blocking Wythoff Nim

YR 2010

AB The 2-player impartial game of Wythoff Nim is played on two piles of tokens. A move consists in removing any number of tokens from precisely one of the piles or the same number of tokens from both piles. The winner is the player who removes the last token. We study this game with a blocking maneuver, that is, for each move, before the next player moves the previous player may declare at most a predetermined number, $k - 1 \ge 0$, of the options as forbidden. When the next player has moved, any blocking maneuver is forgotten and does not have any further impact on the game. We resolve the winning strategy of this game for $k = 2$ and $k = 3$ and, supported by computer simulations, state conjectures of the asymptotic behavior of the $P$-positions for the respective games when $4 \le k \le 20$.

LA eng

LK http://urbanlarsson.mine.nu/homepage/preprints/BW_27okt.pdf

OL 30