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.

Author Bio

Jingkai Ye is a student from Qingdao, China. He studied in Whitman College from Fall 2017 to Spring 2021 as an undergraduate student. He received his Bachelor of Arts degree in May 2021. During his undergraduate studies, he was majoring in Mathematics and Economics. Besides, he was also a runner in Whitman's Cross Country Team. Furthermore, he loves playing basketball and watching science fictions.

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