Zeckendorf proved that any positive integer has a unique decomposition as a sum of non-consecutive Fibonacci numbers, here indexed by \(F_1 = 1, F_2 = 2, F_{n+1} = F_n + F_{n-1}\) . Motivated by this result, Baird et al. [3] defined the two-player Zeckendorf game, in which two players take turns acting on a multiset of Fibonacci numbers that always sums to N. The game terminates when no possible moves remain, which importantly always happens, and the final player to perform a move wins. Notably, Baird et al. [3] empirically studied the setting of random games, in the sense that the game proceeds by always choosing an available move uniformly at random, and conjecture that as the input \(N \rightarrow \infty \) , the distribution of random game lengths converges to a Gaussian. We study various combinatorial questions concerning the Zeckendorf game. We found that the sum of the number of times certain moves are performed is constant. We prove that the number of shortest games on input N is at least \(\prod _{k=1}^{n-2} \text {Cat}(F_k)\) , where n denotes the index of the largest Fibonacci number in the Zeckendorf decomposition of N and \(\text {Cat}(F_k)\) is the \(F_k\) th Catalan number. The works of Baird, Epstein, Flint, and Miller [3] and Cuzensa et al. [5] determined how to play in order to achieve the shortest and longest possible Zeckendorf game on a given input N, respectively: we improve the current understanding of achievable game lengths by establishing that for any input N, the range of possible game lengths constitutes an interval of natural numbers; in other words, for every input N, every game length between the shortest and longest game lengths can be achieved by some Zeckendorf game. Motivated towards the resolution of the Gaussianity conjecture, we also further the study of probabilistic aspects of random Zeckendorf games. In particular, we study two probability measures on the space of all Zeckendorf games on input N: the uniform measure, and the measure induced by choosing moves uniformly at random at any given configuration. We show under both measures that in the limit \(N \rightarrow \infty \) , both players win with probability 1/2 when playing under the random game setting. We also find natural partitions of the collection of all Zeckendorf games of a fixed input N, on which we observe weak convergence to a Gaussian in the limit \(N \rightarrow \infty \) . We conclude the work with many open problems.