Blocking Wythoff Nim

Details Blocking Wythoff Nim Blocking Wythoff Nim

2010-10-27

arxiv.org/abs/1010.5816v1

Mathematics

Combinatorics

14 pages, 1 Figure

Scientific paper

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 $4 \le k \le 20$.

Affiliated with

Also associated with

No associations

Rating

Blocking Wythoff Nim does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Blocking Wythoff Nim, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Blocking Wythoff Nim will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-582543