2007/10/19 by Urban Larsson, Larsson, Urban
Computer Science · Social Sciences · #91A46 #Artificial Intelligence in Games #Combinatorics (math.CO) #Digital Games and Media #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.0710.3632
openalex publication_date 2007/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a variation of the combinatorial game of 2-pile Nim. Move as in 2-pile Nim but with the following constraint: Suppose the previous player has just removed say x>0 tokens from the shorter pile (either pile in case they have the same height). If the next player now removes x tokens from the larger pile, then he imitates his opponent. For a predetermined natural number p, by the rules of the game, neither player is allowed to imitate his opponent on more than p-1 consecutive moves. We prove that the strategy of this game resembles closely that of a variant of Wythoff Nim--a variant with a blocking manoeuvre on p-1 diagonal positions. In fact, we show a slightly more general result in which we have relaxed the notion of what an imitation is.