One pile misère bounded Nim with two alliances
Xiao Zhao, Wen An Liu · Discrete Applied Mathematics · 2016
The game of n -person one-pile bounded Nim with two alliances is investigated: Given an integer m ≥ 1 and a pile of counters, each player is allowed to remove ℓ counters from the pile, where ℓ ∈ { 1 , 2 , … , m } . Suppose that n ≥ 2 players form two alliances and that each player is in exactly one alliance. Also assume that each player will support his alliance’s interests. Under misère play convention, all unsafe positions of two alliances are determined for some structures of two alliances. We also point out that some conclusions given by A.R. Kelly are not correct. Moreover, we present a possible explanation for Kelly’s inaccurate conclusions.