Nim games with arbitrary periodic moving orders
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).
scientific article; zbMATH DE number 4068655