Nim games with arbitrary periodic moving orders
type: Item
instance of: scholarly article
title: Nim games with arbitrary periodic moving orders
zbMATH Open document ID: 0654.90101
DOI: 10.1007/BF01242859
published in: International Journal of Game Theory
publication date: 1988-01-01T00:00:00Z
review text: A set T of t players is partitioned into parties A and B. Initially there is a pile of \(m>0\) chips. Players move in succession in the order t, t- 1,...,2,1, t, t-1,..., each subtracting \(n_ 1\) or \(n_ 2\) or... or \(n_ k\) \((0\leq n_ 1<n_ 2<...<n_ k\); \(k\geq 2)\) chips from the pile. A party wins if one of its players makes the pile size nonpositive. The author proves for \(m>tn_ k(tn_ k+1)\) and \(| A| >| B|\), that party A has a winning strategy which uses only \(n_ 1\) and \(n_ k\). The result is generalized to multiple heaps and to a pile which is any positive number and moves in a bounded interval (including adding to the pile).
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 4068655
zbMATH Keywords: deterministic games
zbMATH Keywords: Nim
zbMATH Keywords: winning strategy
author: Ingo Althöfer
MaRDI profile type: Publication
cites work: Q5668821
cites work: Q3944542
cites work: \(N\)-person Nim and \(N\)-person Moore's games
cites work: Q5545175
full work available at URL: https://doi.org/10.1007/bf01242859
OpenAlex ID: W1484094422
description: scientific article; zbMATH DE number 4068655