Quantum pseudo-telepathy (QPT) is a new type of game where the quantum team can win with certainty while the classical one cannot. It means the advantages of quantum participants over classical ones in game. However, there has been no systematic and formal analysis on the QPT game before. Here we present the formal description of the QPT game and the definition of the most simplified QPT. Based on the above definitions, we simplify a famous QPT game, i.e. the Cabllo game. Then, according to some instances, we analyze the minimum best success probability by classical strategies of the two-player QPT, which reflects the advantage of the quantum strategies. Finally, we prove the best success probability by classical strategies for the most simplified QPT is totally related to the number of all possible question combinations.
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