Fibonacci Nim and a full characterization of winning moves
Cody W. Allen, Vadim Ponomarenko · Involve a Journal of Mathematics · 2014
In this paper we will fully characterize all types of winning moves in the "takeaway" game of Fibonacci Nim.We prove the known winning algorithm as a corollary of the general winning algorithm and then show that no other winning algorithms exist.As a by-product of our investigation of the game, we will develop useful properties of Fibonacci numbers.We conclude with an exploration of the probability that unskilled player may beat a skilled player and show that as the number of tokens increase, this probability goes to zero exponentially.