The game of Fibonacci Nim is an easy game in which players take turns removing chips from a central pot. You may start with any number of chips. Each player must take at least one chip out of the pile...

The game of Fibonacci Nim is an easy game in which players take turns removing chips from a central pot. You may start with any number of chips. Each player must take at least one chip out of the pile but not more than twice the number just removed by his opponent. (The first player may not remove all the chips on the first move.) The player who takes the last chip(s) wins. Start with 20 chips and play Nim five times. What do you notice about the number of chips remaining just before the game was won?