The　Quantum　Penny　Flip　is　a　classic　thought　experiment　in　quantum　mechanics　that　demonstrates　the　weird　and　counterintuitive　nature　of　the　quantum　world.　To　solve　the　＇PQ＇　problem,　we　proposed　a　quantum　strategy　selection　and　optimization　algorithm,　and　designed　a　quantum　algorithm　for　this　problem.　In　terms　of　practical　applications　and　Case　study,　this　paper　reviews　the　classic　two　player　game　-　＇PQ　coin　flipping＇　problem,　and　shows　that　when　one　of　the　participants　adopts　quantum　strategies,　he　can　defeat　his　classic　opponent　and　obtain　higher　returns.　By　using　quantitative　methods,　the　entire　＇PQ＇　problem　is　placed　under　a　more　general　and　fair　condition,　and　it　is　promoted　and　studied　again　from　multiple　aspects　and　perspectives.　At　the　same　time,　this　article　provides　the　definitions　of　＇incomplete　fair　game＇　and　＇complete　fair　game＇,　modifies　the　quantum　coin　flipping　game　[Meyer,　Phys.　Rev.　lett.　82　(1999)　1052]　to　make　the　game　fair,　and　studies　the　multi　round　versions　of　quantum　coin　flipping.　We　have　drawn　some　basic　conclusions　about　fair　quantum　games　and　explained　the　meaning　of　completely　fair　games　in　practice.　We　discussed　the　limitations　and　scalability　of　the　＇PQ＇　problem　and　looked　forward　to　the　future　development　direction　of　quantum　game　research.　©　2023　The　Authors.