Michael J. Whinihan published an analysis of Fibonacci Nim in 1963. His paper connects a take-away game with the unique decomposition of an integer into nonconsecutive Fibonacci numbers.[ref]
After the opening move, a player may remove at most twice the preceding player's removal. The smallest summand in the heap's Zeckendorf representation identifies the strategic threshold. Thus a numerical representation becomes operational information about a winning strategy: the relevant feature is not the heap's size alone but its least Fibonacci component.[ref]
Fibonacci Nim by Michael J. Whinihan. Winning-strategy construction
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