Abstract
In this paper we will fully characterize all types of winning moves in the “take-away” 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.
Citation
Cody Allen. Vadim Ponomarenko. "Fibonacci Nim and a full characterization of winning moves." Involve 7 (6) 807 - 822, 2014. https://doi.org/10.2140/involve.2014.7.807
Information