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This paper introduces a new quantum game called Quantum Tapsilou that isinspired by the classical traditional Greek coin tossing game tapsilou. The newquantum game, despite its increased complexity and scope, retains the mostimportant characteristic of the traditional game. In the classical game, bothplayers have $\frac { 1 } { 4 }$ probability to win. The quantum versionretains this characteristic feature, that is both players have the sameprobability to win, only now this probability varies considerably and dependson previous moves and choices. The two most important novelties of QuantumTapsilou can be attributed to its implementation of entanglement via the use ofrotation gates instead of Hadamard gates, which generates Bell-like states withunequal probability amplitudes, and the integral use of groups. In QuantumTapsilou both players agree on a specific cyclic rotation group of order $n$,for some sufficiently large $n$. The game is based on the chosen group, in thesense that both players will draw their moves from its elements. Morespecifically, both players will pick rotations from this group to realize theiractions using the corresponding $R_{ y }$ rotation gates. In the QuantumTapsilou game, it is equally probable for both players to win. This fact is inaccordance with a previous result in the literature showing that quantum gameswhere both players choose their actions from the same group, exhibit perfectsymmetry by providing each player with the possibility to pick the move thatcounteracts the other player's action.

Quantum Tapsilou -- a quantum game inspired from the traditional Greek coin tossing game tapsilou