  Zeckendorf proved that every natural number $n$ can be expressed uniquely as
a sum of non-consecutive Fibonacci numbers, called its Zeckendorf
decomposition. Baird-Smith, Epstein, Flint, and Miller created the Zeckendorf
game, a two-player game played on partitions of $n$ into Fibonacci numbers
which always terminates at a Zeckendorf decomposition, and proved that Player 2
has a winning strategy for $n\geq 3$. Since their proof was non-constructive,
other authors have studied the game to find a constructive winning strategy,
and lacking success there turned to related problems. For example, Cheigh,
Moura, Jeong, Duke, Milgrim, Miller, and Ngamlamai studied minimum and maximum
game lengths and randomly played games. We explore a new direction and
introduce the reversed Zeckendorf game, which starts at the ending state of the
Zeckendorf game and flips all the moves, so the reversed game ends with all
pieces in the first bin. We show that Player 1 has a winning strategy for $n =
F_{i+1} + F_{i-2}$ and solve various modified games.
