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Non-local games are widely studied as a model to investigate the propertiesof quantum mechanics as opposed to classical mechanics. In this paper, weconsider a subset of non-local games: symmetric XOR games of $n$ players with0-1 valued questions. For this class of games, each player receives an inputbit and responds with an output bit without communicating to the other players.The winning condition only depends on XOR of output bits and is constant w.r.t.permutation of players.  We prove that for almost any $n$-player symmetric XOR game the entangledvalue of the game is $\Theta (\frac{\sqrt{\ln{n}}}{n^{1/4}})$ adapting an oldresult by Salem and Zygmund on the asymptotics of random trigonometricpolynomials. Consequently, we show that the classical-quantum gap is $\Theta(\sqrt{\ln{n}})$ for almost any symmetric XOR game.

Provable Advantage for Quantum Strategies in Random Symmetric XOR Games