There is no relationship. Mahjong is Chinese in origin. England and China had no direct contact until more than one hundred years after Anne Boleyn's death. Mahjong was unknown in England during the entire Tudor period.
Could it be an obscure reference by the teacher to the famous episode where Katherine of Aragon plays cards with her maid of honor Anne Boleyn? Mahjong "resembles certain card games, such as Solitaire, where uncovering hidden cards is the order of the day." Katherine of Aragon is reported to have said to her maid of honor Anne, when they were playing one day: "You have good hap to stop at a king, Lady Anne. But you are not like the others. You will have all, or none." I have seen references to mahjong that imply it can be played "winner take all."
have searched my library for a reference to this, as I have certainly read of a connection between Anne Boleyn and mahjong, so the teacher hasn't invented it. From phd's information, it sounds as if it is an urban myth, however.
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