This　paper　reviews　the　coin　flipping　problem　of　＇PQ＇　in　a　classical　two-player　game,　and　shows　that　when　one　player　adopts　quantum　strategy,　he　can　beat　his　classical　opponent　and　gain　higher　returns.　By　using　quantitative　means,　the　whole　＇PQ＇　problem　is　put　under　a　more　general　and　fair　condition,　and　it　is　generalized　and　studied　again　from　many　aspects　and　angles.　Finally,　we　obtain　some　more　essential　and　important　conclusions,　and　explain　the　conclusions　and　its　practical　significance　through　some　practical　examples.　At　the　same　time,　this　paper　gives　the　definition　of　imperfect　fair　game　and　the　definition　of　perfect　fair　game,　revises　the　quantum　coin　flipping　game　to　make　the　game　fair,　and　studies　a　multi-round　version　of　quantum　coin　flipping.　Some　basic　conclusions　of　fair　quantum　game　are　obtained,　and　the　meaning　of　perfectly　fair　game　is　explained　in　practice.　©　2024　Institute　of　Physics,　Chinese　Academy　of　Sciences.　All　rights　reserved.