Fibonacci nim is played by two players, who alternate removing coins or other counters from a pile.
According to the normal play convention, the player who takes the last coin wins.
[1] The game was first described by Michael J. Whinihan in 1963, crediting its invention to Oregon State University mathematician Robert E. Gaskell.
[4] The game strategy also involves a number called the "quota", which may be denoted as q.
[2] Based on these definitions, the player who is about to move can win whenever q is greater than or equal to the smallest Fibonacci number in the Zeckendorf representation, and will lose (with best play from the opponent) otherwise.
In a winning position, it is always a winning move to remove all the coins (if this is allowed) or otherwise to remove a number of coins equal to the smallest Fibonacci number in the Zeckendorf representation.
When this is possible, the opposing player will necessarily be faced with a losing position, because the new quota will be smaller than the smallest Fibonacci number in the Zeckendorf representation of the remaining number of coins.