Displaying similar documents to “New games related to old and new sequences.”

A morphic approach to combinatorial games : the Tribonacci case

Eric Duchêne, Michel Rigo (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We propose a variation of Wythoff’s game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

Blocking Wythoff Nim.

Larsson, Urban (2011)

The Electronic Journal of Combinatorics [electronic only]

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A two armed bandit type problem revisited

Gilles Pagès (2005)

ESAIM: Probability and Statistics

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In Benaïm and Ben Arous (2003) is solved a multi-armed bandit problem arising in the theory of learning in games. We propose a short and elementary proof of this result based on a variant of the Kronecker lemma.

Two pile move-size dynamic Nim.

Holshouser, Arthur, Reiter, Harold (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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A morphic approach to combinatorial games: the Tribonacci case

Eric Duchêne, Michel Rigo (2007)

RAIRO - Theoretical Informatics and Applications

Similarity:

We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.