The No-Flippancy Game

• Published in 2020
• Added on 2020-09-21

We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $n$ comprised of coin tosses. They alternate turns, choosing the outcome of a coin toss according to specific rules. As a result, the game is deterministic. The player whose string appears first wins. If neither player's string occurs, then the game must be infinite. We study several aspects of this game. We show that if, after $4n-4$ turns, the game fails to cease, it must be infinite. Furthermore, we examine how a player may select their string to force a desired outcome. Finally, we describe the result of the game for particular cases.

Links

• http://arxiv.org/abs/2006.09588v1
• http://arxiv.org/pdf/2006.09588v1

Other information

BibTeX entry

@article{TheNoFlippancyGame,
	key = {TheNoFlippancyGame},
	type = {article},
	title = {The No-Flippancy Game},
	author = {Isha Agarwal and Matvey Borodin and Aidan Duncan and Kaylee Ji and Tanya Khovanova and Shane Lee and Boyan Litchev and Anshul Rastogi and Garima Rastogi and Andrew Zhao},
	abstract = {We analyze a coin-based game with two players where, before starting the
game, each player selects a string of length {\$}n{\$} comprised of coin tosses. They
alternate turns, choosing the outcome of a coin toss according to specific
rules. As a result, the game is deterministic. The player whose string appears
first wins. If neither player's string occurs, then the game must be infinite.
  We study several aspects of this game. We show that if, after {\$}4n-4{\$} turns,
the game fails to cease, it must be infinite. Furthermore, we examine how a
player may select their string to force a desired outcome. Finally, we describe
the result of the game for particular cases.},
	comment = {},
	date_added = {2020-09-21},
	date_published = {2020-10-09},
	urls = {http://arxiv.org/abs/2006.09588v1,http://arxiv.org/pdf/2006.09588v1},
	collections = {easily-explained,games-to-play-with-friends},
	url = {http://arxiv.org/abs/2006.09588v1 http://arxiv.org/pdf/2006.09588v1},
	year = 2020,
	urldate = {2020-09-21},
	archivePrefix = {arXiv},
	eprint = {2006.09588},
	primaryClass = {math.CO}
}