The Geometric Sequence with common ratio 2 is one of the most well-known geometric sequences. Every term is a nonnegative power of 2. Using this popular sequence, we can create a Geometric Game which contains combining moves (combining two copies of the same terms into the one copy of next term) and splitting moves (splitting three copies of the same term into two copies of previous terms and one copy of the next term). For this Geometric Game, we are able to prove that the game is finite and the final game state is unique. Furthermore, we are able to calculate the upper bound and lower bound of the length of Geometric Game. We are also able to prove some interesting results in terms of the winning strategy of 2-player games, and some special cases of multiplayer games and multialliance games.
"Winning Strategy For Multiplayer And Multialliance Geometric Game,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 22:
2, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss2/7